Morgane Rolland

Samuel Alizon

Katie Hampson

Lulla

Laurent Dacheux

Philippe Lemey

Kirstyn Brunker

Laurence Ma

Cécile Troupin

Philippe Dussart

Véronique Chevalier

James Wood

Sowath Ly

Veasna Duong

Miki Tal Gonen

Lilac Goldenfeld

Mayan Meltzer

Gili Gilboa

Regev-Yochay

Nicola Nicola Müller

De Maio

Ine Nena Kanika

Barney Sam

Eve, Salam, Guillem David

Emile Andrew

Wilfried, Sophie Lucia Simon

Camille Alexandre

Claire

Keywords: Scientific conferences infectious diseases, molecular epidemiology, rabies, household studies, modeling, SARS-CoV-2. xi . . . . . . . . . . . . . . pathogen transmission. . . . . .

I had diverged, digressed, wandered, and become wild. I didn't embrace the word as my new name because it defined negative aspects of my circumstances or life, but because even in my darkest days -those very days in which I was naming myself -I saw the power of the darkness.

Résumé

Parmi les méthodes pour l'étude quantitative de la transmission des maladies infectieuses dans les populations, les épidémiologistes ont récemment focalisé leur attention sur l'épidémiologie moléculaire qui vise à reconstruire la phylogénie des pathogènes en utilisant leurs séquences génétiques, et la modélisation mathématique des maladies infectieuses qui ajuste des modèles mécanistes de transmission des maladies à des données épidémiologiques telles que le nombre de cas. Ces deux approches se basent sur des données très différentes dont la disponibilité varie selon le contexte. Les concepts et les modèles qu'elles utilisent permettent d'explorer des facettes différentes de la transmission des maladies. L'objectif principal de cette thèse est de mieux comprendre comment les maladies virales comme la rage et la covid-19 circulent dans les populations hôtes en utilisant pour la première des séquences génétiques virales datées et géolocalisées, et pour la deuxième, des données épidémiologiques à l'échelle individuelle. La première partie de cette thèse s'intéresse à la rage, une zoonose tropicale négligée, responsable d'environ 59,000 morts chaque année principalement dans les populations pauvres et rurales d'Afrique et d'Asie.

Son agent étiologique, le virus de la rage (RABV), circule principalement dans les populations canines domestiques dont les modes de transmission restent peu étudiés et mal compris malgré l'existence de vaccins efficaces chez l'homme et l'animal. Nous avons tout d'abord synthétisé dans une revue de la littérature l'apport relatif des modèles mathématiques et de l'épidémiologie moléculaire dans la compréhension des dynamiques de la rage chez le chien. Puis, nous avons décrit la circulation endémique de la rage au Cambodge, un des pays les plus affectés, à partir de génomes de la rage isolés chez le chien et analysés avec des méthodes de phylogéographie Bayésienne continue. Nous avons montré que les introductions depuis d'autres pays ne sont pas nécessaires au maintien de la circulation. Toutefois, ces résultats sont conditionnés par l'échantillonnage des génomes. Pour mieux comprendre leurs impacts sur les méthodes de phylogéographie Bayésienne, nous avons entrepris une étude de simulation dans laquelle nous avons comparé les performances de trois algorithmes de phylogéographie discrète face à un échantillonnage plus ou moins biaisé. Nous avons testé des stratégies d'échantillonnage alternatives et intégré des données épidémiologiques afin d'atténuer l'effet potentiel des biais d'échantillonnage sur la performance des trois algorithmes. La deuxième partie de la thèse se concentre sur la transmission du SARS-CoV-2 dans une des plus petites populations, les ménages. Cette configuration est particulièrement adaptée au suivi détaillé de l'ensemble des membres du foyer après l'introduction d'un cas et permet ainsi d'évaluer comment la susceptibilité et l'infectivité varient au niveau individuel. Dans un premier temps, nous avons estimé l'effectivité vaccinale contre l'infection et la transmission si infecté pendant la vague de variant Alpha en Israël grâce à un modèle de transmission dans des ménages partiellement vaccinés. Nous avons ensuite exploré comment l'hétérogénéité de contact dans les ménages, notamment entre les adultes et les enfants, impacte les estimations de l'infectivité et de la susceptibilité relatives des enfants par rapport aux adultes. En conclusion, cette thèse explore les contributions de l'épidémiologie moléculaire et de la modélisation pour la compréhension de la transmission des maladies infectieuses à différentes échelles de population et souligne la nécessité d'intégrer les données génétiques et épidémiologiques.

Mots-clés: maladies infectieuses, épidémiologie moléculaire, rage, études de ménages, modélisation, SARS-CoV-2.

Table of Contents

List of Figures xxi

List of Tables xxiii

List of Abbreviations xxv

General introduction

General introduction

1. Epidemics of infectious diseases are complex processes that must be described with models 1.1. What is an epidemic?

1.1.1. Definition

The Centers for Disease Control and Prevention (CDC) defines an epidemic as "an increase, often sudden, in the number of cases of a disease above what is normally expected in that population in that area"

(Disease [START_REF] Control | Principles of Epidemiology in Public Health Practice, Third Edition: An Introduction[END_REF]. Infectious diseases that are caused by the transmission of harmful organisms called pathogens from infected individuals to uninfected ones can lead to epidemics when the number of new cases exceeds the baseline number of cases. While the desired baseline level is zero case, the baseline level corresponds to the observed endemic level in the area under study. Here, endemic defines any disease that is commonly present within a geographic area (Disease [START_REF] Control | Principles of Epidemiology in Public Health Practice, Third Edition: An Introduction[END_REF]. In a stricter acceptation, endemicity characterizes diseases that circulate within a geographic area without the need for external introductions. In infectious disease epidemiology, epidemic and endemic circulations are not exclusive types of transmission and should be rather considered as different levels of transmission.

The transmission process can affect a more or less large population and it can be studied at different levels of resolution. Four levels of transmission are commonly distinguished depending on the size of the affected population or the resolution of observation: clusters that are confined to a small community like a school or a church, outbreaks that affect a larger population in a limited geographic area, epidemics that are similar to outbreaks but affect larger geographic areas, and pandemics that have spread over several countries or continents (Disease [START_REF] Control | Principles of Epidemiology in Public Health Practice, Third Edition: An Introduction[END_REF].

Many common diseases are infectious diseases. We can cite strep throat, measles, flu, toxoplasmosis, eradicated diseases such as smallpox, or the very recent coronavirus disease 2019 . They are caused by pathogens of different taxonomic origin, more specifically viruses, bacteria, protozoa, arthropods, helminths, and fungi. In this thesis, we primarily focus on viral diseases and examples of infectious diseases caused by other taxonomic groups are described for strict illustrative purposes.

Description of the transmission process

Despite the wide taxonomic diversity of pathogens, they all share the same basic transmission cycle.

First, the pathogen infects its host, then it multiplies within the host, and it eventually propagates to other hosts (Fig. 1A). This basic transmission cycle applies to diseases with direct transmission such as airborne, respiratory (droplet), or sexually-transmitted diseases. Other routes of transmission generally lead to more complex transmission cycles. In the case of zoonoses (diseases that naturally transmit from animal populations to humans) and a variety of vector-borne diseases, multiple host species are involved and human is not always an essential link in the transmission cycle. For example, West Nile virus (WNV) disease is a vector-borne zoonosis that circulates in birds through mosquito bites but it can also infect mammal hosts among which humans and horses that are dead-ends of transmission (Fig. 1B).

Rabies is another example of viral zoonosis whose causative agent, rabies virus (RABV), circulates in bat populations, and domestic and wild non-flying carnivores through bites. It can spill over to many other mammal species including cattle and humans with no further transmission (Fig. 1C). Sometimes, human is not necessary to pathogen persistence but, once introduced, the pathogen causes large epidemics. This is the case of Ebola virus that persists in animal reservoirs and leads to self-sustaining chains of transmission in human. Food and water transmission routes are other types of indirect transmission that can involve complex food supply systems or multiple host species, respectively.

Determinants of the transmission process

The transmission process is multifactorial. Pathogen, host, and environmental factors influence the success of transmission by controlling the transmissibility of the pathogen, the contagiousness of the infector, the susceptibility of exposed individuals, and the environmental stress on the pathogen (Fig. 2).

Pathogen determinants

Pathogen characteristics determine its routes of transmission, its ability to spread and to cross species barriers, and its evolutionary speed [START_REF] Leung | Transmissibility and transmission of respiratory viruses[END_REF].

Pathogen molecular composition governs the sites of infection within the organism and the host range that can be infected. Viruses, for example, are compulsory intracellular parasites and first interact with host cells through their surface proteins before hijacking the inner cellular machinery to multiply. The success of this interaction depends on the physicochemical and tridimensional properties of viral surface proteins. Influenza viruses are a typical example of the impact of molecular composition on host range as their ecology is primarily driven by the shape and composition of the hemagglutinin antigen [START_REF] Long | Host and viral determinants of influenza A virus species specificity[END_REF]. Pathogen immune escape strategies determine reinfection patterns. Indeed, pathogens are recognized and fought by the immune system of the host upon infection, ultimately leading to pathogen clearance and the constitution of an effective immune memory that will prevent reinfection. Most of the vaccinepreventable childhood diseases (e.g., measles, rubella) induce sterilizing immunity conveying life-long protection against reinfection. However, many pathogens have developed an arsenal of strategies to escape the immune system and leave no-or short-lived immunity. This way, they can reinfect the same host leading to very different disease dynamics at the population level compared to pathogens that leave sterilizing immunity. Rapid evolution, pathogen diversity, and gene expression variability are common immune escape strategies [START_REF] Bjørnstad | Epidemics: Models and Data using R[END_REF]. RNA viruses are fast-evolving pathogens that can adapt to the rapid build-up of population immunity during an epidemic, of which influenza viruses constitute a paradigmatic example. Influenza viruses evade pre-existing immunity in the host population by antigenic drift (gradual accumulation of mutations in antigens) causing seasonal influenza epidemics and imposing continuous update of flu vaccines. They are also of pandemic potential because sharpest changes of their antigens can arise from genome reassortment between different strains (antigenic shifts) inducing crossspecies transmission [START_REF] Kim | Influenza Virus: Dealing with a Drifting and Shifting Pathogen[END_REF]. Another consequence of the fast evolution of RNA viruses is their presence under diverse genomic variants (quasispecies) within the same host which also contributes to their fast adaptation [START_REF] Vignuzzi | Quasispecies diversity determines pathogenesis through cooperative interactions in a viral population[END_REF]. Numerous strains of Plasmodium falciparum (causative agent of malaria) co-circulate while having non-overlapping antigenic repertoires. Such pathogen diversity allows repeated infections of the same individual (Gupta et al., 1998). Finally, variable gene expression of surface proteins enables pathogen to escape the immune system and prevents the host to build an effective immune memory as exemplified by Nesseria gonorrhoeae [START_REF] Stern | Opacity determinants of Neisseria gonorrhoeae: Gene expression and chromosomal linkage to the gonococcal pilus gene[END_REF][START_REF] Tettelin | Complete Genome Sequence of Neisseria meningitidis Serogroup B Strain MC58[END_REF]. It is important to note that the host tissue range of some pathogens drastically limits the host immune response. This is the case of RABV that hides from the host immune system by infecting the central nervous system. In such cases, the immune escape strategies based on rapid evolution, pathogen diversity, and gene expression variability have little impact on transmission dynamics in host populations.

Host determinants

Host characteristics modulate host infectivity and susceptibility at the individual level, as well as pathogen transmission at the population level [START_REF] Leung | Transmissibility and transmission of respiratory viruses[END_REF].

The host immune response plays a critical role in transmission at both the individual and population levels. At the individual level, the host immune system controls infections and modulates disease severity.

Its controlling capacities varies with multiple factors: sex, age (young children and elderly individuals are typically more susceptible to infections; Brodin and Davis 2017), and underlying disease conditions (individuals with heart disease or diabetes are more susceptible to severe forms of COVID-19;[START_REF] Sanyaolu | Comorbidity and its Impact on Patients with COVID-19[END_REF]). The immune system also shapes the individual response to vaccines that varies with age.

Pre-existing immunity from past infections or vaccination can also modulate pathogen shedding in infector individuals, and consequently host contagiousness [START_REF] Leung | Transmissibility and transmission of respiratory viruses[END_REF]. More generally, host genetics govern susceptibility. For example, glycosylation patterns of host cell receptors determine which hosts can be infected by SARS-CoV and Middle East respiratory syndrome coronavirus (MERS-CoV; [START_REF] Jones | Viral and host heterogeneity and their effects on the viral life cycle[END_REF]. At the population level, pre-existing immunity induced by past epidemics or vaccination campaigns conveys indirect protection against transmission to susceptible individuals. This phenomenon is called herd immunity and determines the magnitude of spread and the shape of the epidemic curve [START_REF] Anderson | Vaccination and herd immunity to infectious diseases[END_REF].

Host behavior and social structures are additional factors shaping transmission at the population level [START_REF] Buckee | Thinking clearly about social aspects of infectious disease transmission[END_REF]. They encompass social contact and age-related mixing patterns, mass gatherings that may lead to superspreading events, and interactions with wildlife that modulate the risk of zoonotic emergence. 1.1.3.3

. Environmental determinants

Environmental factors influence the survival and persistence of pathogens after their release in the environment. For example, respiratory pathogens are transmitted through fomites, droplets, or aerosols whose stability is impacted by temperature, humidity, ventilation, airflow etc. This mechanism explains why most respiratory tract infections spread when temperature and humidity are low [START_REF] Mäkinen | Cold temperature and low humidity are associated with increased occurrence of respiratory tract infections[END_REF]. Environmental factors can also act indirectly on the geographic occurrence of diseases by delimiting the geographic range of the animal reservoirs or vector populations [START_REF] Rocklöv | Climate change: an enduring challenge for vector-borne disease prevention and control[END_REF].

Seasonal changes of environmental variables may lead to seasonal patterns of disease occurrence. For instance, seasonal rainfalls are associated with cholera outbreaks in sub-Saharan Africa and Southeast Asia [START_REF] Emch | Seasonality of cholera from 1974 to 2005: a review of global patterns[END_REF][START_REF] Perez-Saez | The seasonality of cholera in sub-Saharan Africa: a statistical modelling study[END_REF], or more indirectly, they multiply the breeding sites of insect vectors in turn intensifying the circulation of vector-borne diseases [START_REF] Rocklöv | Climate change: an enduring challenge for vector-borne disease prevention and control[END_REF].

Epidemics are complex processes

Overall, the transmission process is complex because it is multifactorial but also stochastic, meaning due to random chance. Indeed, the introduction of a new pathogen in the population does not always lead to sustained transmission, epidemics can die out by chance. Besides, epidemics of infectious diseases can be explosive contrary to non-communicable diseases, especially when the pathogen is highly transmissible and the host population is dense with little pre-existing immunity.

Infectious diseases burden and threats 1.2.1. Burden of infectious diseases

The burden of infectious diseases has greatly changed over the ages. In the pre-modern world, life expectancy did not exceed 30 years in all regions of the world [START_REF] Riley | Estimates of Regional and Global Life Expectancy, 1800-2001[END_REF] as half of the children died from infectious disease before reaching adulthood [START_REF] Volk | Infant and child death in the human environment of evolutionary adaptation[END_REF]. In parallel, humankind has been afflicted over the ages by pandemics like the Black Death that killed one third of the European population and tremendously impacted European geopolitics and history [START_REF] Herlihy | The Black Death and the Transformation of the West[END_REF]. During the Enlightenment, most western countries experienced a slight but non-negligible increase of life expectancy thanks to income growth. A sharper increase occurred at the end of the 19th century thanks to the development of hygiene and sanitation that reduced infectious disease mortality. In the 20th century, life expectancy continued to increase thanks to the advent of vaccination, antibiotics, nutrition, medical practices, and health systems that all helped combat infectious diseases [START_REF] Omran | The Epidemiologic Transition: A Theory of the Epidemiology of Population Change[END_REF]. Today, most countries have undergone the health transition: their populations are aging and more at risk of noncommunicable diseases than infectious diseases [START_REF] Vos | Global burden of 369 diseases and injuries in 204 countries and territories, 1990-2019: a systematic analysis for the Global Burden of Disease Study 2019[END_REF]. However, global disparities remain, as some low-and middle-income countries such as Kenya are still majorly affected by infectious diseases [START_REF] Vos | Global burden of 369 diseases and injuries in 204 countries and territories, 1990-2019: a systematic analysis for the Global Burden of Disease Study 2019[END_REF]. Besides, health systems have to fight not only old pathogens like measles but also new infectious diseases risks: (i) emerging zoonoses that are a new array of infectious diseases of high epidemic potential that can spill over from vertebrate reservoirs to human, (ii) multi-resistant "superbugs" that are responsible of antimicrobial resistance (AMR), and (iii) the geographic expansion of endemic diseases such as dengue, malaria, or tuberculosis [START_REF] Bloom | Infectious Disease Threats in the Twenty-First Century: Strengthening the Global Response[END_REF]. Consequently, infectious diseases are still a major health problem in the world. For instance, lower respiratory tract infections, diarrheal infections, HIV/AIDS, tuberculosis, and malaria still ranked among the 15 leading causes of global disability adjusted life years (DALYs) in 2019 (Fig. 3A; [START_REF] Vos | Global burden of 369 diseases and injuries in 204 countries and territories, 1990-2019: a systematic analysis for the Global Burden of Disease Study 2019[END_REF] and AMR was a leading cause of death, notably in low-resource settings [START_REF] Murray | Global burden of bacterial antimicrobial resistance in 2019: a systematic analysis[END_REF].

A B

Figure 3: Global burden of infectious diseases and global changes increasing their risk (A) Leading 25 causes of disability-adjusted life years (DALYs) at all ages in the world in 2019 and percentage of total DALYs with its 95% confidence interval. Communicable, maternal, neonatal, and nutritional diseases are colored in red. Noncommunicable diseases are colored in blue, and injuries in green (adapted from [START_REF] Vos | Global burden of 369 diseases and injuries in 204 countries and territories, 1990-2019: a systematic analysis for the Global Burden of Disease Study 2019[END_REF]). (B) Effects of global changes on disease emergence, dynamics, and spread (from [START_REF] Baker | Infectious disease in an era of global change[END_REF]. Age-related hearing loss=age-related and other hearing loss.

Infectious diseases threats

Beyond their direct health consequences, infectious diseases pose social and economic risks. New pathogens of epidemic potential can overwhelm health systems which limit their capacity to deal with routine health issues as experienced during the COVID-19 pandemic when many non-infected patients were left on the side of the road [START_REF] Rosenbaum | The Untold Toll -The Pandemic's Effects on Patients without Covid-19[END_REF]. They can also delay biomedical research on other diseases by concentrating all the investigation efforts and resources as experienced during the COVID-19 pandemic [START_REF] Rosenbaum | The Untold Toll -The Pandemic's Effects on Patients without Covid-19[END_REF]. The fear of novel pathogens may refrain global travel and tourism which has huge economic implications as experienced by Brazil and Southeast Asian countries during dengue peaks [START_REF] Bärnighausen | Valuing the broader benefits of dengue vaccination, with a preliminary application to Brazil[END_REF][START_REF] Constenla | Assessing the Economics of Dengue: Results from a Systematic Review of the Literature and Expert Survey[END_REF]. The protracted circulation of endemic infectious diseases also disrupt productivity and may considerably impact the gross domestic product (GDP).

For example, a 10% reduction in malaria incidence is associated with a 0.3% higher growth of GDP in (sub)tropical countries [START_REF] Gallup | The economic burden of malaria[END_REF]. The impacts of infectious diseases may go further and even increase the vulnerability of weak health systems.

The three major infectious risks -emerging zoonoses, AMR, and endemic diseases expansion -will very likely gain ground due to ongoing demographic, climatic, and technological changes (Fig. 3; [START_REF] Baker | Infectious disease in an era of global change[END_REF]. Demographic and urbanization growth, especially in countries with weak health systems, favor contagious transmission. Ageing is another critical challenge for infectious disease spread as immunosenescence (age-related alterations of the immune system) makes the elderly more susceptible to infectious diseases [START_REF] Aw | Immunosenescence: emerging challenges for an ageing population[END_REF]. On top of that, climate change contributes to the geographical expansion of vector-borne diseases by widening the habitats of disease-carrying vectors, as already occuring for dengue in western Europe [START_REF] Lazzarini | First autochthonous dengue outbreak in Italy, August 2020[END_REF]. Climate change, changes in land use, and intensive livestock farming that aims to satisfy the increasing demand for animal protein modify the human-animal interactions and increase the risk of zoonotic emergence. Finally, globalization through human transportation and global trade amplifies the pandemic risk of emerging zoonotic pathogens as well as antimicrobial resistant pathogens (Fig. 3B; [START_REF] Petersen | Emerging infections-an increasingly important topic: review by the Emerging Infections Task Force[END_REF][START_REF] Bloom | Infectious Disease Threats in the Twenty-First Century: Strengthening the Global Response[END_REF][START_REF] Baker | Infectious disease in an era of global change[END_REF].

In this rapidly evolving context, health systems need to adapt and reinforce epidemic preparedness, disease transmission surveillance, and response to infectious emergencies. Rapid access and analysis of epidemiological data is crucial to ensure a timely response. In parallel, research and development efforts are required to better understand disease spread, develop new therapeutics, and design control strategies to mitigate the impact of epidemics.

1.3. Quantitative approaches to study epidemics of infectious diseases 1.3.1. A modeling approach to integrate the complexity of the transmission process

Epidemics of infectious diseases constitute a growing threat but their dynamics and determinants are not directly accessible because they are complex processes. Mathematical models, that are simplified but informative representations of complex systems or processes formalized by equations, can help describe and anticipate epidemic processes by accounting for multiple determinants of disease spread and integrating multiple sources of information in a single framework [START_REF] Keeling | Modeling Infectious Diseases in Humans and Animals[END_REF].

Epidemiological modeling for the description of between-host transmission dynamics

Epidemiological models were the first mechanistic models of disease transmission, that is to say that they explicitly describe the transmission process under a set of assumptions. They first aimed at modeling disease transmission between individuals of the same host population, although they are more and more used to model within-host transmission. In this section, we will briefly present their history, conceptual framework, and underlying hypothesis, focusing on between-host transmission models.

Compartmental models, a milestone in epidemiological modeling

In their seminal work, [START_REF] Kermack | A contribution to the mathematical theory of epidemics[END_REF] introduced the basics of the Susceptible-Infectious-Recovered (SIR) model that was later formalized by [START_REF] Dietz | Epidemics and Rumours: A Survey[END_REF]. In this model, the host population is divided into In mathematical terms, the model consists in a system of ordinary differential equations (ODEs):

dS dt = - β N S(t)I(t) dI dt = β N S(t)I(t) -γI(t) dR dt = γI(t) (1)
Where β is the transmission rate, γ the rate of recovery from infection, S(t), I(t), and R(t) are the state variables representing the number of individuals as a function of time t in the susceptible, infectious, and recovered compartments, respectively, and N = S(t) + I(t) + R(t) is the total population size. Several assumptions underlie this model:

• The infectious period 1 γ is exponentially distributed,

• β and γ do not change over the course of the infection,

• Recovered individuals are immune from reinfection over their lifetime,

• Individuals from the same compartment contact each other at random which is known as homogeneous mixing, and

• The transmission rate β is invariant with respect to the population size N which is generally referred to as frequency-dependent transmission.

Some of these assumptions can be relaxed by adding compartments to account for transient immunity [START_REF] He | Phylogeography Reveals Association between Swine Trade and the Spread of Porcine Epidemic Diarrhea Virus in China and across the World[END_REF][START_REF] Hawkes | Seasonality of Respiratory Viruses at Northern Latitudes[END_REF], age-related or spatially heterogeneous contact patterns [START_REF] Viboud | Synchrony, waves, and spatial hierarchies in the spread of influenza[END_REF], transmission from animal reservoirs [START_REF] Allen | Mathematical Modeling of Viral Zoonoses in Wildlife[END_REF][START_REF] Hussaini | Mathematical analysis of a model for zoonotic visceral leishmaniasis[END_REF], vectorborne transmission [START_REF] Smith | Ross, Macdonald, and a Theory for the Dynamics and Control of Mosquito-Transmitted Pathogens[END_REF] etc. This modularity provides an ideal flexibility that allows to adapt the model to very diverse disease natural histories and account for multiple host-related determinants of spread. Most compartmental models make the assumption of frequency-dependent transmission.

Alternatively, one can assume a density-dependent transmission where the transmission rate scales linearly with population density.

The analysis of compartmental models provides insights on the transmission process in the system under study. For simple compartmental models such as the SIR model presented in Fig. 4, analytical solutions that describe the steady states of the system can be easily derived. Otherwise, numerical integration is possible. By analyzing the dynamics of the SIR model, [START_REF] Kermack | A contribution to the mathematical theory of epidemics[END_REF] showed that a pathogen can invade the host population only if the initial fraction of susceptible individuals S(0) is less than γ β . This threshold effect led to the definition of one of the most important metrics in infectious disease epidemiology, the reproduction number (R). The basic reproduction number R 0 is the average number of secondary cases arising from the primary case in an entirely susceptible population. In the SIR model, it is equal to β γ , the inverse of the critical threshold [START_REF] Keeling | Modeling Infectious Diseases in Humans and Animals[END_REF]. Thus, the pathogen spreads in a fully susceptible host population only if R 0 > 1. When part of the host population is protected against infection, we would rather use the effective reproduction ratio R t that is the product of the basic reproduction ratio and the fraction of susceptible individuals at time s(t). In the SIR model, this would be β γ s(t).

From deterministic to stochastic models

The compartmental model presented above is deterministic, hence it overlooks the stochastic nature of the transmission process. It can be translated, as well as any other compartmental model, in its stochastic equivalent using discrete Markov chains, continuous-time Markov chains (CTMCs), or stochastic differential equations [START_REF] Allen | A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis[END_REF]. Numerical simulations of disease dynamics under these models can be produced using the Gillespie algorithm or the Euler-Maruyama method [START_REF] Allen | A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis[END_REF].

Stochastic models are useful to capture the variability of the epidemic profile notably when disease incidence is low, the population is small, or environmental variables or demographics strongly impact disease dynamics. In such cases, deterministic models are not a good approximation of disease dynamics because stochastic fluctuations may lead to disease extinction or introduce variance and covariance that influence disease transmission [START_REF] Keeling | Modeling Infectious Diseases in Humans and Animals[END_REF][START_REF] Allen | A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis[END_REF]. Stochastic modeling is thus more appropriate when studying disease eradication as incidence is low, disease transmission in households that are very small populations, or zoonoses, vector-borne and waterborne diseases for which environmental variability is important [START_REF] Keeling | Modeling Infectious Diseases in Humans and Animals[END_REF][START_REF] Allen | A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis[END_REF].

Individual-based models to integrate heterogeneity at the individual model

Host heterogeneity can be integrated in compartmental models by specifying additional compartments, that is additional ODEs. However, when multiple layers of heterogeneities are to be accounted for, model formulation becomes rapidly cumbersome, or may even be limited. Alternatively, individualbased models (also called agent-based models) describe disease transmission by explicitly modeling the interactions between a finite number of fully characterized and autonomous individuals. Any attribute, constant or time-varying, related to social behavior, spatial location, and/or physiological traits governing susceptibility and contagiousness can be associated to the individuals. Hence, the history of every individual can be tracked, and at the same time, the impact of individual-level heterogeneity on disease transmission in a restricted population can be investigated [START_REF] Willem | Lessons from a decade of individualbased models for infectious disease transmission: a systematic review (2006-2015)[END_REF]. This category of models is very diverse and particularly adapted to the combined study of between-and within-host interactions and the analysis of targeted interventions such as targeted screening and vaccination in nosocomial infections [START_REF] Smith | Optimizing COVID-19 surveillance in long-term care facilities: a modelling study[END_REF]. Over the past decade, individual-based models have been more widely used but important pitfalls subsist concerning calibration methods and goodness-of-fit measures which limits study reproducibility and affects the quality of inference [START_REF] Hazelbag | Calibration of individual-based models to epidemiological data: A systematic review[END_REF]. 1.3.3. Phylodynamics, or epidemiology from the perspective of the pathogen

Definition of phylodynamics

Epidemiological models can easily integrate host and environmental determinants which is less the case for pathogen determinants because these models do not explicitly describe the evolutionary processes that pathogens undergo during transmission. Indeed, in the specific case of fast-evolving pathogens such as RNA viruses, evolutionary forces (mutation, migration, selection, and drift) not only shape pathogen genetic evolution and diversity, but they occur at the same time scale as the transmission process and can be influenced by it. For example, the genetic bottleneck at transmission shapes the viral diversity transmitted to other hosts and can be influenced by the seasonal or spatially heterogeneous dynamics of the host population. In such cases, evolution is measurable and genetic diversity that is informative about the transmission process [START_REF] Drummond | Measurably evolving populations[END_REF] can be exploited to investigate the relationship between pathogen evolution and epidemic and immunological processes. Phylodynamics studies this interplay between evolutionary, epidemiological, immunological, and sometimes even ecological processes in epidemics by combining quantitative methods from phylogenetics and population genetics [START_REF] Grenfell | Unifying the Epidemiological and Evolutionary Dynamics of Pathogens[END_REF]. It is a recent discipline that emerged in the 2000s and has expanded rapidly. It completes the arsenal of quantitative tools already available for the study of infectious diseases spread and can be considered, in this sense, as a specific approach of epidemiological modeling. For better clarity, we refer to the models presented in Section 1.3.2 as epidemiological models as opposed to phylodynamics, and we use the term epidemiology in its widest acceptance by including epidemiological modeling and phylodynamics.

In the following paragraphs, we outline the basic modeling components of phylodynamics.

Substitution models link phylogenies and molecular sequences of pathogens

A phylogeny corresponds to the evolutionary relationships between sampled organisms. It is depicted as a phylogenetic tree whose external nodes correspond to sampled organisms (here pathogens isolated from cases), internal nodes correspond to their common ancestors, branches correspond to ancestral lineages, and branch length corresponds to the level of genetic divergence. Phylogenies are at the basis of phylodynamic analyses because their shape is an indicator of the underlying epidemic process (Fig. 5A; [START_REF] Grenfell | Unifying the Epidemiological and Evolutionary Dynamics of Pathogens[END_REF]Volz et al. 2013).

Nucleotide sequences (DNA and RNA) are a good source of information of phylogenies because they gradually accumulate substitutions over time due to replication errors during pathogen multiplication (Lemey et al., 2009b). This means that any two sequences coming from the same ancestor but evolv- ing independently eventually diverge by accumulating different substitutions. Stochastic approaches like CTMCs allow to model substitutions as random events and account for multiple substitutions per site (i.e., location in the genetic sequence). In CTMC models, the substitution process is entirely specified by the Q matrix that contains the instantaneous relative rates of change of each nucleotide along the sequence. These instantaneous rates depend on the mean instantaneous substitution rate, relative rate parameters, and nucleotide frequencies (Fig. 6). Depending on the assumptions made on these parameters, one can specify a wide range of models from the simple Jukes-Cantor 69 model where all instantaneous substitution rates are equal to the mean instantaneous substitution rate in the Q matrix, to the complex general-time reversible model (GTR) where all instantaneous substitution rates are different. Importantly, whatever the parameterization of the Q matrix, all CTMC models share the same underlying assumptions (Lemey et al., 2009b):

1. Markov property: at any given site in a sequence, the rate of change from base i to base j is

General introduction

independent from the base that occupied that site prior base i.

2. Homogeneity: substitution rates are constant over time.

3. Stationarity: the relative frequencies of A, C, G, and T (π A , π C , π G , π T ) are at equilibrium.

Q = -𝜇 𝑎𝜋 ! + 𝑏𝜋 " + 𝑐𝜋 # 𝑎𝜇𝜋 ! 𝑏𝜇𝜋 " 𝑐𝜇𝜋 # 𝑔𝜇𝜋 $ -𝜇 𝑔𝜋 $ + 𝑑𝜋 " + 𝑒𝜋 # 𝑑𝜇𝜋 " 𝑒𝜇𝜋 # ℎ𝜇𝜋 $ 𝑖𝜇𝜋 % -𝜇 ℎ𝜋 $ + 𝑗𝜋 ! + 𝑓𝜋 # 𝑓𝜇𝜋 # 𝑗𝜇𝜋 $ 𝑘𝜇𝜋 % 𝑙𝜇𝜋 " -𝜇 𝑖𝜋 $ + 𝑘𝜋 ! + 𝑙𝜋 " 𝐴 𝐶 𝐺 𝑇
Figure 6: Instantaneous rate matrix Q from the continuous-time Markov chain (CTMC) model applied to nucleotide substitution. Q is a square matrix whose entries represent the instantaneous substitution rates from one nucleotide to another. The instantaneous substitution rates are a function of the mean instantaneous substitution rate µ, the twelve relative substitution rates a, b, c, d, e, f , g, h, i, j, k, and l, and the four nucleotide frequencies π A , π C , π G , and π T . Diagonal elements are chosen so that the sum of each row is equal to zero. Rows and columns follow the order A, C, G, and T (from Lemey et al. 2009b).

Dating pathogen phylogenies using molecular clock models

Molecular clock models link genetic divergence with time which allows to scale the branch lengths of a phylogenetic tree on calendar time (Fig. 5B). The strict molecular clock model, introduced by Zuckerkandl and Pauling in the 1960s, assumes that nucleotide substitutions accumulate at a roughly constant rate (evolutionary rate) in the genetic sequences of pathogens [START_REF] Zuckerkandl | Molecular disease, evolution and genetic heterogeneity[END_REF][START_REF] Zuckerkandl | Evolutionary Divergence and Convergence in Proteins[END_REF]. With this model, one can date the origin of an epidemic or the start of an infection, but it is restricted to cases where the evolutionary rate is the same among all lineages in the considered phylogeny although multiple factors are known to modulate it such as the underlying mutation rate, metabolic rates in a species, generation times, population sizes, or selective pressures [START_REF] Bromham | The modern molecular clock[END_REF]. Relaxed molecular clock models overcome this limitation by allowing evolutionary rates to vary through time or among lineages. In the local clock model, the number of rate changes along the phylogeny is prespecified. In the autocorrelated relaxed clock model, the evolutionary rate along one branch depends on the evolutionary rate of its ancestral branch. In the uncorrelated relaxed clock model, the evolutionary rates associated with each branch are independent and identically distributed, generally following a lognormal or gamma distribution [START_REF] Ho | Molecular-clock methods for estimating evolutionary rates and timescales[END_REF].

Once informed by substitution and molecular clock models, pathogen phylogenies are approximatively a subtree of the whole transmission chain that connects the sampled individuals located at the tips of the phylogeny. Due to within-host evolution, transmission events in the transmission chain are more recent than ancestral nodes in the associated time-stamped phylogenetic tree [START_REF] Plessis | Getting to the root of epidemic spread with phylodynamic analysis of genomic data[END_REF]. 1.3.3.4

. Pathogen demographic models

In population genetics, the coalescent theory provides a conceptual framework that links population dynamics of sampled individuals to the topology of their phylogenetic tree (Fig. 5C). The most simple model is the Kingman coalescent in which the expected time at which two individuals coalesce into their common ancestor in a discrete and non-overlapping population of size N (the Wright Fisher population)

is N generations going backwards in time [START_REF] Kingman | On the Genealogy of Large Populations[END_REF]. Branch lengths in the phylogenetic tree thereby reflect pathogen population size: the longer the branches, the larger the population. In the Kingman coalescent, population size is constant over time, but extensions allow to account for timevarying dynamics. These refinements are either deterministic [START_REF] Griffiths | Sampling theory for neutral alleles in a varying environment[END_REF] like the exponential and logistic growth models, or non-parametric models [START_REF] Pybus | An integrated framework for the inference of viral population history from reconstructed genealogies[END_REF][START_REF] Strimmer | Exploring the Demographic History of DNA Sequences Using the Generalized Skyline Plot[END_REF][START_REF] Drummond | Measurably evolving populations[END_REF][START_REF] Opgen-Rhein | Inference of demographic history from genealogical trees using reversible jump Markov chain Monte Carlo[END_REF][START_REF] Minin | Smooth Skyride through a Rough Skyline: Bayesian Coalescent-Based Inference of Population Dynamics[END_REF]. In all these extensions, the overall pathogen population is supposed to be large compared to the number of sampled individuals (tree tips)

and to evolve under neutral evolution. Although these assumptions are generally violated, an effective population size (Ne) that leads to the coalescent rate of an idealized population of size N can be derived.

Interestingly, [START_REF] Volz | Phylodynamics of infectious disease epidemics[END_REF] showed that the exponential coalescent model, i.e., a coalescent model where Ne follows an exponential growth, can be linked to the SIR model by expressing Ne as a function of the transmission rate and the prevalence. This formulation allows to calculate the reproduction number.

Coalescent models are deterministic and require sampled individuals to represent a small fraction of the total population. Thus, they are not adapted to model early epidemic dynamics or infection clusters because pathogen populations are small hence their dynamics are impacted by stochasticity, and sampling proportions are large [START_REF] Pybus | Evolutionary analysis of the dynamics of viral infectious disease[END_REF]. Birth-death approaches on the contrary are stochastic and describe a forward-in-time process particularly adapted to model the start of epidemics [START_REF] Plessis | Getting to the root of epidemic spread with phylodynamic analysis of genomic data[END_REF]. In these models, extant lineages either generate new lineages at birth rate λ , die at extinction rate µ, or are sampled at sampling rate ψ [START_REF] Featherstone | Epidemiological inference from pathogen genomes: A review of phylodynamic models and applications[END_REF]. 1.3.3.5. Describing spatial dynamics using phylogeography

The demographic models presented above assume that transmission occurs in a homogenous mixing host population, although host population is often structured due to age-structured contact patterns or spatial clustering. Phylogeographic approaches aim at filling this gap by modeling spatial diffusion along a phylogenetic tree between discrete populations (Fig. 5D) or in a continuous space (Fig. 5E).

Discrete phylogeography

There are three major approaches to modeling spatial dynamics between discrete populations: (i) the structured coalescent model, (ii) the multitype birth-death process, and (iii) the CTMC model. The structured coalescent model corresponds to an extension of the coalescent model. It explicitly models how lineages coalesce within and migrate between subpopulations from present to past. Likewise, the multitype birth-death process is an extension of the birth-death process where extant lineages generate a new lineage in their population, generate a new lineage in another population, migrate to another population, are sampled, or die [START_REF] Kühnert | Phylodynamics with Migration: A Computational Framework to Quantify Population Structure from Genomic Data[END_REF]. Finally, the CTMC treats the geographic location of pathogens as a neutral trait that evolves just like nucleotides along the phylogenetic tree without explicitly modeling population demographics (Lemey et al., 2009a).

The applications of discrete phylogeography exceed spatial spread modeling as the discrete populations can represent different host species [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF][START_REF] Dudas | MERS-CoV spillover at the camelhuman interface[END_REF], host social groups [START_REF] Stadler | Uncovering epidemiological dynamics in heterogeneous host populations using phylogenetic methods[END_REF], or host body compartments [START_REF] Chaillon | HIV Migration Between Blood and Cerebrospinal Fluid or Semen Over Time[END_REF].

Continuous phylogeography

Continuous phylogeography provides a more realistic representation of the spatial diffusion process because it does not rely on the pre-specification of the number of discrete locations. In continuous phylogeography, pathogens' geographic coordinates (i.e., latitude and longitude) are continuous traits that evolve according to a Brownian diffusion process. To overcome the limiting assumption of constant diffusion rate along the phylogenetic tree, the relaxed random walk model uses the same approach as the uncorrelated molecular clock model by assuming that the diffusion rates associated with each tree branch are independent and identically distributed according to a discretized rate distribution [START_REF] Lemey | Phylogeography takes a relaxed random walk in continuous space and time[END_REF].

Challenges in estimating key parameters of the transmission process

Although the development of theoretical models is crucial to the advancement of epidemiology, calibrating and validating such models with empirical data is necessary to explore the submerged part of the transmission process and unravel the determinants of spread, estimate key epidemiological parameters, and thereby inform public health programs. Statistical methods that make the connection between models and data come in very different flavors. In epidemiology, statistical inference faces a major challenge related to the imperfect observation of the transmission process. We discuss here how imperfect epidemic data are, then we outline the different types of data that can be collected for outbreak evaluation, and finally, we present the statistical methods developed to overcome these challenges.

The transmission process is imperfectly observed

Unlike experimental sciences, epidemiology analyzes real-world data that result from complex processes occurring in uncontrolled conditions. This leads to two major challenges: (i) observed data are generally very limited which requires methodological development, and (ii) data collection and interpretation may be subject to bias.

By essence, the transmission process is never fully observed. The exact time of infection and all the factors that influence the transmission event are rarely directly observed or measured. Detailed transmission chains obtained by comprehensive contact tracing are an invaluable source of information from which key epidemiological parameters such as R 0 can be derived directly, but they are very difficult to obtain for most pathogens [START_REF] Cauchemez | How Modelling Can Enhance the Analysis of Imperfect Epidemic Data[END_REF]. In some cases, like zoonotic pathogens, detailed transmission chains are not sufficient to characterize the transmission potential of the pathogen in human.

Indeed, zoonotic pathogens stutter to extinction after spillover from the animal reservoir because they are not yet adapted to human [START_REF] Lloyd-Smith | Epidemic Dynamics at the Human-Animal Interface[END_REF]. They do not cause enough cycles of transmission in human to allow the calculation of inter-human R 0 . Nevertheless, [START_REF] Ferguson | Public Health Risk from the Avian H5N1 Influenza Epidemic[END_REF] demonstrated that there is a relation between inter-human R 0 and the distribution of the size of case clusters. This way, the authors could estimate the transmission potential of avian H5N1 influenza in human using very coarse data.

In addition, multiple sources of bias may impact data collection and interpretation [START_REF] Cauchemez | How Modelling Can Enhance the Analysis of Imperfect Epidemic Data[END_REF] generally resulting in under-reporting. During cluster investigation, some cases may be missed because investigated cases do not remember all their contacts, some of their contacts may not adhere to the investigation or may test false-negative due to imperfect diagnostic tests. Under-reporting is also an issue at larger scales like national routine surveillance systems that are rarely exhaustive because they rely on simple systems that collect a limited amount of information on each case. For example, influenza surveillance in France relies on a network of primary health-care providers that report weekly numbers of patients with flu-like illness [START_REF] Debin | Evaluating the Feasibility and Participants' Representativeness of an Online Nationwide Surveillance System for Influenza in France[END_REF]. This syndromic surveillance system does not include all health-care providers and all affected patients do not necessarily seek care, thus only a fraction of the cases is reported. Models are thus necessary to estimate disease incidence. The extent of under-reporting also depends on the capacities of the surveillance systems that can vary in space and time [START_REF] Moon | Will Ebola change the game? Ten essential reforms before the next pandemic. The report of the Harvard-LSHTM Independent Panel on the Global Response to Ebola[END_REF][START_REF] Mastin | A method of determining where to target surveillance efforts in heterogeneous epidemiological systems[END_REF]. In parallel, severe cases are more likely to be detected compared to mild, pauci-symptomatic, and asymptomatic cases leading to a selection bias. The detection of milder cases is crucial because they generally contribute to disease spread and their under-detection may lead to biased forecasts. In the pyramid of severity, hospitalization and death data are generally more robust to underdetection, although attributing the cause of death is challenging in certain contexts like RABV infections when molecular testing is not available. Besides, hospitalization and death data do not necessarily reflect transmission patterns in the general population.

Data granularity gradient

Various data can be used to inform the transmission process. They range from detailed data at the individual level in contexts where epidemiological links between cases are more or less known to coarse data at the population level like aggregated number of cases for which epidemiological links between cases are generally unknown. Pathogen genetic sequences can be placed at either ends of the data granularity gradient depending on the way they are collected. When collected in an individual at different time points of infection, pathogen genetic data correspond to individual-level data. But, when they are collected in unrelated individuals at large spatial scales, they correspond to population-level data. In general, epidemiological and genetic data are accompanied with the background characteristics of cases related to their biology, behavior, and environment [START_REF] Cori | Key data for outbreak evaluation: building on the Ebola experience[END_REF][START_REF] Polonsky | Outbreak analytics: A developing data science for informing the response to emerging pathogens[END_REF]. In the following paragraphs, we present three types of data, individual-level epidemiological data, populationlevel epidemiological data, and pathogen genetic data at the population level, as well as the potential biases occurring at the collection, generation, and interpretation steps.

Individual-level data

Individual-level data consist in detailed data on cases related to their disease, demographics, behavior, and environment. In linelist data, each row corresponds to a case, and each column to an individual characteristic such as age, gender, location, symptom onset, detection date, clinical outcome, diagnostic test results, recent travel history, recent contacts with animals, dietary habits etc. [START_REF] Polonsky | Outbreak analytics: A developing data science for informing the response to emerging pathogens[END_REF].

Useful statistics can be derived from linelists, including the case fatality rate (proportion of identified cases dying from the infection), demographics of the affected population (e.g., age, occupation), and case delays (e.g., times to hospitalization, recovery, and death). The collection of detailed individuallevel information is feasible when the number of cases is limited like at the start of an epidemic or in cluster investigation. In other settings, data on uninfected individuals are collected to complete case data which allows the investigation of infection risk factors. Households are a good example of such setting in addition to being a great laboratory of disease transmission because the number of contacts is small and well-defined, and participant adherence is generally high ensuring data completeness [START_REF] Cauchemez | How Modelling Can Enhance the Analysis of Imperfect Epidemic Data[END_REF]. When collected longitudinally, individual-level data on cases can inform case delays, viral load dynamics that are generally used as a proxy of infectiousness, and antibody response dynamics that point to long-term protection against reinfection. Overall, individual-level data are highly valuable to tackle disease transmission dynamics and determinants.

Nevertheless, individual-level data do not directly capture the underlying transmission process, as infection times, sources, and dynamics are not perfectly known. For example, the high level of physical proximity between household members may hide the exact transmission chain, or another example, the temporal dynamics of viral load is informed by only few data points per individual. More generally, the number of participants and data completeness are limiting factors to achieve robust statistical inference and multiplying biological testings or questionnaires may exhaust participants. Consequently, study designs should find the right balance between data exhaustivity and participant adherence. In parallel, individual-level data often rely on molecular tests that are inherently imperfect, meaning that their sensitivity (true negative rate) and specificity (true positive rate) are lower than 100%. Serological tests are often subject to cross-reactivity issues, meaning that they not only detect past infections from the pathogen of interest but also from closely related pathogens. This is the case of many arboviruses (Hozé et al., 2021a). Finally, observational studies that aim to collect individual-level data are expensive and require interdisciplinary teams that define the ethical framework of the study, recruit and follow-up participants, perform biological tests, and analyze the generated data. That is why, individual-level data are generally more difficult to collect compared to population-level data.

Population-level data

Population-level data encompass any epidemiological data aggregated at the population level such as case and death counts, hospital and ICU admissions, seroprevalence, the number of vaccinated individuals etc. Aggregated data, except seroprevalence data, are generally collected through surveillance systems at national or regional levels and reflect past and present disease transmission dynamics. Their sole analysis already provides valuable information on the effective reproduction ratio or the impact of interventions. Additional data on climate, population mobility, and population behavior can help forecast (near) future transmission or make predictions under various intervention scenarios. The characteristics of the surveillance system determine the representativeness and the specificity of the collected data (Disease [START_REF] Control | Principles of Epidemiology in Public Health Practice, Third Edition: An Introduction[END_REF]. For instance, a case definition based on a diagnostic test is more specific than a case definition based on a set of symptoms, but it poses practical issues and representativeness is not guaranteed due to testing strategies that can over-represent specific populations and to testing behavior that varies with social class [START_REF] Buckee | Thinking clearly about social aspects of infectious disease transmission[END_REF]. Furthermore, the representativeness of surveillance system data is generally subject to selection bias as severe cases seek more care than mild cases.

Serosurveys aim to estimate seroprevalence, a measure of herd immunity [START_REF] Hozé | Monitoring the proportion of the population infected by SARS-CoV-2 using age-stratified hospitalisation and serological data: a modelling study[END_REF]. When stratified by age, seroprevalence can indicate the long-term history of pathogen circulation [START_REF] Hens | Seventy-five years of estimating the force of infection from current status data[END_REF]. This is particularly insightful in resource-limited countries with weak surveillance systems.

However, there is a risk of misdiagnosis for some diseases due to cross-reactivity (Hozé et al., 2021a).

Recent studies have tried to bridge the gap between individual-level and population-level data by collecting detailed data on a very large number of individuals. For example, digital epidemiology has capitalized on the rapid growth of digital data, the widespread penetration of mobile phones and internet and social media usage to collect data on mobility for example, or on symptomatic search queries for syndromic tracking of influenza-like illnesses [START_REF] Bansal | Big Data for Infectious Disease Surveillance and Modeling[END_REF]Salathé, 2018;[START_REF] Tarkoma | Fighting pandemics with digital epidemiology[END_REF].

Digital epidemiology has strongly benefited from the developments of machine learning to efficiently analyze big data. Similar advancements were made by national surveillance systems that also try to link individual-level and population-level data. Countries with cutting edge health information systems (e.g.

the UK, Israel) have matched national health registries with demographic databases during the SARS-CoV-2 pandemic and thereby could analyze transmission in tens of thousands households [START_REF] Harris | Effect of vaccination on household transmission of SARS-CoV-2 in England[END_REF]Shah et al., 2021), unattainable numbers in traditional observational household studies. However, data granularity in big data remains limited especially when it comes to behavior.

Pathogen genetic sequences

Thanks to the decreasing costs of high-throughput next-generation sequencing, pathogen genetic sequences isolated from infected hosts now constitute an abundant source of information on disease spread.

Pathogen genetic sequences are now so affordable that genomic surveillance is more insightful than traditional surveillance systems in resource-limited countries with weak surveillance capacities [START_REF] Wilkinson | A year of genomic surveillance reveals how the SARS-CoV-2 pandemic unfolded in Africa[END_REF]. In addition, the time scale of data generation and analysis has greatly improved thanks to the development of genomic surveillance and the increased affordability of portable sequencers (Grubaugh et al., 2019a) allowing real-time analyses. The SARS-CoV-2 pandemic has led to a paradigm shift in terms of sampling: the number of sampled sequences increased from a few dozens to a few millions [START_REF] Hill | Progress and challenges in virus genomic epidemiology[END_REF], the spatial coverage extended from a few regions or countries to the entire world, and the sampling strategy shifted from opportunistic to targeted (Hodcroft et al., 2021a). However, these changes mostly concern viral diseases of pandemic potential as other pathogens like bacteria and protozoa have much larger genomes which requires more intense sequencing efforts and prevents the democratization of ge-nomic surveillance. Besides, during the SARS-CoV-2 pandemic, the global sequencing effort was highly heterogeneous which was a major issue for the study of cross-country transmission. Sequencing errors are another potential source of bias [START_REF] Ma | Analysis of error profiles in deep next-generation sequencing data[END_REF][START_REF] Stoler | Sequencing error profiles of Illumina sequencing instruments[END_REF]. They are a central consideration at the beginning of an outbreak or when there is an intense sampling over a short time window because the pathogen did not have time to accumulate mutations. Finally, multiple sequence alignment tools can be a source of bias when they do not align correctly homologous sites [START_REF] Bromham | Bayesian molecular dating: opening up the black box[END_REF].

Ethical and scientific considerations related to epidemiological and genetic data

Epidemiological data should not only be relevant and reliable to appropriately inform models, they should also follow broader requirements related to ethics and data sharing [START_REF] Cori | Key data for outbreak evaluation: building on the Ebola experience[END_REF]. In terms of ethics, anonymity must be protected while ensuring a sufficient level of details, notably when it comes to individual-level data. In terms of data sharing, rapid data collection and sharing to the scientific community allow independent analyses, each with its own limitations, which fosters results comparison, scien- Contrary to genetic data that are directly curated by researchers, epidemiological data in the Our World

In Data global database are compiled from official sources including health ministries, government reports, and official social media accounts. All these data sharing tools, although impactful, pose practical challenges related to data quality and completeness. For genetic sequences, impaired processing may lead to incorrect mutations (Hodcroft et al., 2021a), while for epidemiological data official sources may not communicate frequently enough or extensively enough about vaccination rollouts or case numbers [START_REF] Ritchie | Coronavirus Pandemic (COVID-19)[END_REF]. what we see to update our knowledge. This approach is consistent with the way we think and learn facilitating result interpretation [START_REF] Hoekstra | Robust misinterpretation of confidence intervals[END_REF]. The denominator θ ′ p(x|θ ′ )p(θ ′ )dθ ′ in equation 2 corresponds to the total evidence, that is to say the likelihood marginalized over all parameter values. Its calculation is generally not necessary to evaluate the posterior [START_REF] Gilks | Markov Chain Monte Carlo in Practice[END_REF].

Bayes
p(θ |x) = p(x|θ )p(θ ) θ ′ p(x|θ ′ )p(θ ′ )dθ ′ (2)
The quantity of data used to inform the model determines the relative importance of the likelihood and the prior at informing the posterior. While the prior is less influential with more data, its choice remains important and may even be a pitfall in Bayesian analysis. Whenever possible, prior choice should reflect real prior information. If such information is not available, one can opt for a prior that does not exert much influence on the posterior [START_REF] Kruschke | Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan[END_REF].

Markov chain Monte Carlo

In epidemic modeling, models are often too complex to derive the analytical form of the total evidence preventing the calculation of the posterior distribution. Alternatively, numerical approximation of the posterior distribution is achievable using Markov chain Monte Carlo (MCMC) methods. These methods sample from the posterior distribution while exploring as efficiently as possible the parameter space.

The Metropolis-Hastings algorithm [START_REF] Hastings | Monte Carlo Sampling Methods Using Markov Chains and Their Applications[END_REF] is the most simple and commonly used MCMC algorithm (Algorithm 1). In a nutshell, the algorithm explores the parameter space using a random walk, at each iteration a new value of the parameter is proposed x cand based on the previous value x (i-1) using a proposal distribution q, and the relative change in the posterior density is evaluated to determine whether

x cand is accepted. x cand is always accepted when it leads to a higher posterior density, and it is accepted with probability α otherwise. This algorithm is stochastic to avoid getting stuck in local maxima, but it requires some time (burn-in) before converging to the highest density regions. Exploration efficiency relies on the variance of the proposal distribution which might necessitate some tuning.

Algorithm 1 Metropolis-Hastings algorithm

Initialize x (0) ∼ q(x)

for iteration i = 1, 2, ... do Propose: x cand ∼ q(x (i) |x (i-1) )
Acceptance Probability: α(x cand |x (i-1) ) = min 1, q(x (i-1) |x cand )π(x cand ) q(x cand |x (i-1) )π(x (i-1) )

u ∼ Uniform(u; 0, 1) if u < α then Accept the proposal:

x (i) ← x cand else
Reject the proposal:

x (i) ← x (i-1) end if end for
Convergence can be assessed visually (chains of parameter values as a function of iteration should look like white noise), or dedicated metrics such as the effective sample size (ESS) can help assessing convergence. In phylodynamics, convergence is presumed when ESS is higher than 200.

Data augmentation

Models describing the epidemic process sometimes rely on latent variables, variables that are not directly observable but meaningful such as the infection time. In such cases, the likelihood is convenient to write with the latent variables but the augmented data posterior p(θ |x, y) can be calculated only if latent data y are imputed (Tanner and Wong 1987). The Metropolis-Hastings algorithm can be adapted to sample from the posterior while marginalizing over the augmented data by iterating the two following steps [START_REF] Neal | Exact Bayesian inference via data augmentation[END_REF]:

1. Update θ given x and y by sampling from p(θ |x, y) 2. Update y given x and θ by sampling from p(y|x, θ )

The reconstruction of transmission chains in household studies from symptom onsets or molecular tests is a case study of data augmentation. Indeed, viral respiratory diseases are characterized by short or even negative serial intervals which makes the reconstruction of transmission chains hazardous. By augmenting the observed symptom onsets with the unobserved infection dates, one can integrate over all possible transmission chains and account for observation uncertainty (Cauchemez et al., 2004). Data augmentation is also applicable in the case of missing or incomplete data.

BEAST: a milestone for phylodynamics

In phylodynamics, the Bayesian framework allows the estimation of past demographics and, if desired, of past spatial spread from sequence alignments while accounting for phylogenetic uncertainty. The likelihood of Bayes' theorem (equation 2) corresponds to the probability of observing the sequence data given a phylogenetic history that is characterized by the substitution process, tree topology, branch lengths, and node geographic locations. Depending on the molecular clock, demographic, and spatial models, the likelihood can take on multiple forms. Let us consider the simplest configuration where the likelihood decomposes into the substitution model and the tree model [START_REF] Bromham | Bayesian molecular dating: opening up the black box[END_REF]. The substitution model is fully specified by the nucleotide substitution parameters, whereas the tree model is characterized by the tree prior (i.e., the demographic model) and the molecular clock model that are in turn specified by hyperparameters. This complex multi-layer model structure is known as a hierarchical model. This is the key mathematical structure that allows the joint inference of epidemiological and evolutionary processes. Such as any other Bayesian approach, prior choice in terms of prior parameter distribution, tree prior, and molecular clock model is crucial to achieve unbiased inference [START_REF] Bromham | Bayesian molecular dating: opening up the black box[END_REF]. Concerning model choice, model selection procedures are available but not for all models and their implementation can be very tedious [START_REF] Baele | Emerging Concepts of Data Integration in Pathogen Phylodynamics[END_REF]. During the MCMC procedure, locationand time-stamped phylogenetic trees are sampled from the tree posterior distribution, and after sampling, the sampled trees are generally summarized using the maximum clade credibility (mcc) tree. This tree corresponds to the sampled tree that maximizes the product of the posterior clade probabilities.

Bayesian evolutionary analysis sampling trees (BEAST) is a software package that achieves such Bayesian phylodynamics inference. It comes in two different flavors, BEAST 1 (Suchard et al., 2018) and BEAST 2 (Bouckaert et al., 2019), that share the same Metropolis-Hastings MCMC core algorithm [START_REF] Drummond | BEAST : Bayesian evolutionary analysis by sampling trees[END_REF], but BEAST 2 is more modular as it allows the integration of third parties extensions. BEAST has gained a lot of popularity since its early development because it can be used as an all-in-one evolutionary toolbox. It is now an essential tool in outbreak investigation and response [START_REF] Plessis | Getting to the root of epidemic spread with phylodynamic analysis of genomic data[END_REF][START_REF] Gardy | Towards a genomics-informed, real-time, global pathogen surveillance system[END_REF][START_REF] Hill | Progress and challenges in virus genomic epidemiology[END_REF].

Applications and challenges of epidemiological and phylodynamic modeling

Modelling is a means of estimating key epidemiological parameters such as disease transmissibility, severity, or transmission heterogeneity which cast light on the underlying epidemiological processes.

Beyond allowing the better understanding of transmission dynamics, modeling is also a flexible tool for scenario comparison, notably when it comes to the evaluation of control strategies, which is a great source of scientific evidence for public health authorities (Fig. 7; [START_REF] Cauchemez | How Modelling Can Enhance the Analysis of Imperfect Epidemic Data[END_REF].

Epidemiological and phylodynamic modeling can be used restrospectively to untangle the relative contributions of different drivers of the epidemic process, evaluate the efficacy of past control measures, and test alternative control and prevention measures. Such retrospective studies are generally held between outbreak periods which is more suitable to model development and validation. In a prospective way, modeling assists in the analysis of surveillance data and is a valuable tool for disease emergence and public health planification through forecasts and comparison of control strategies in hypothetical scenarios (Fig. 7A).

Here, we describe the prospective and retrospective applications of epidemiological and phylodynamic modeling to better understand transmission dynamics and guide public decision-making (Fig. 7B). Finally, we highlight their complementarity and specific challenges.

Understanding transmission dynamics

Quantifying transmission risk factors at the individual-level

Individual-level data are essential to characterize case heterogeneity and identify factors underlying it.

Pathogen genetic sequences can also be valuable. We present here key epidemiological quantities that can be estimated at the individual level as well as the design of the studies allowing their estimation.

Case delays related to the natural history of the disease are easily estimated by fitting parametric probability density functions such as the gamma, Weibull, and lognormal distributions, to interval-censored data on the timings of symptom onset and exposure. The incubation period (time from infection to symptom onset) is typically estimated by fitting these density functions to individual data on the timing of exposure and symptom onset. The shape of the distribution gives an insight on individual heterogeneity. For example, the incubation period of rabies in dogs is highly variable with a mean of 22 days, but a non-negligible fraction of cases develop symptoms more than three months after infection [START_REF] Hampson | Transmission Dynamics and Prospects for the Elimination of Canine Rabies[END_REF]. The estimation of the incubation period can also guide the isolation and case management policies such as during the Monkeypox pandemic in 2022 [START_REF] Miura | Estimated incubation period for monkeypox cases confirmed in the Netherlands, May 2022[END_REF]. Two other delays are of particular interest: the serial interval (time between onsets of a case and their infector) derived from symptom onset data in transmission pairs, and the generation time (time between the dates of infection of a case and their infector) that generally requires pre-existing estimates of the incubation period and relies on household data [START_REF] Hart | Inference of the SARS-CoV-2 generation time using UK household data[END_REF] or transmission pairs [START_REF] Ferretti | The timing of COVID-19 transmission[END_REF]. These two delays are key to estimate time-varying reproduction numbers from incidence data [START_REF] Ganyani | Estimating the generation interval for coronavirus disease (COVID-19) based on symptom onset data[END_REF]. Although the serial interval may lead to biased estimates compared to the generation time, it is easier to estimate [START_REF] Thompson | Improved inference of time-varying reproduction numbers during infectious disease outbreaks[END_REF].

Individual heterogeneity may not only concern the timing of the transmission process but also the magnitude of transmission. Superspreading events are an extreme case of transmission heterogeneity as they result from the unusual infection of many individuals by a single case. Detailed epidemiological data on clusters of cases allow to identify potential superspreading events but pathogen genetic sequences are much more informative to discriminate multiple independent introductions from within-cluster transmission, and homogeneous transmission from superspreading. [START_REF] Lemieux | Phylogenetic analysis of SARS-CoV-2 in Boston highlights the impact of superspreading events[END_REF] analyzed the SARS-CoV-2 genomes of all confirmed early cases in Massachusetts between March and May 2020 along with cases from putative superspreading events. They reveal that one of the first lineages introduced in Massachusetts is associated with the largest superpreading event at an international business conference and led to sustained community transmission, circulation in homeless and higher-risk communities, and was exported internationally. This study exemplifies the role of superspreading events in explosive transmission that generally require targeted control policies [START_REF] Lloyd-Smith | Superspreading and the effect of individual variation on disease emergence[END_REF]. The low genetic diversity that characterizes cluster transmission and that is exploited to unravel superspreading events can also arise from over-sampling. In this case, it does not reflect epidemiological processes and can play as a confounding effect of superspreading events (Dearlove et al., 2017).

Finally, the study of age-related heterogeneity of respiratory disease transmission like influenza has greatly benefited from household transmission modeling. Children are shown to be more susceptible than adults to influenza infection but they are as infectious as adults (Cauchemez et al., 2004;[START_REF] Cauchemez | Household transmission of 2009 pandemic influenza A (H1N1) virus in the United States[END_REF][START_REF] Cauchemez | Determinants of Influenza Transmission in South East Asia: Insights from a Household Cohort Study in Vietnam[END_REF]. Even when children have high pre-season haemagglutinationinhibition antibody titers indicating partial protection from past infections, they are more susceptible than adults [START_REF] Cauchemez | Determinants of Influenza Transmission in South East Asia: Insights from a Household Cohort Study in Vietnam[END_REF]. These results have been replicated for multiple types of influenza viruses (seasonal influenza and 2009 pandemic influenza A) as well as in different settings (European and Asian households) highlighting that children are the entry door of influenza infections in households [START_REF] Endo | Fine-scale family structure shapes influenza transmission risk in households: Insights from primary schools in Matsumoto city, 2014/15[END_REF]. This supports targeted influenza vaccination campaigns in school-aged individuals. in the Americas when air passenger flows increased from endemic countries that were experiencing Zika outbreaks at the time [START_REF] Faria | Zika virus in the Americas: Early epidemiological and genetic findings[END_REF]. Phylogeographic techniques have also unraveled the modes of persistence of Ebola in the three most affected countries, Guinea, Liberia, and Sierra Leone, during the 2014 West African epidemic [START_REF] Dudas | Virus genomes reveal factors that spread and sustained the Ebola epidemic[END_REF]. Transmission in Sierra Leone resulted from sustained local transmission after a single introduction, while the Guinean epidemic was fed by infrequent introductions from Libera and Sierra Leone. Interestingly, [START_REF] Dudas | Virus genomes reveal factors that spread and sustained the Ebola epidemic[END_REF] also showed that younger populations were drivers of importations. Highlighting differential epidemic dynamics and drivers of spread is necessary to carry out appropriate control measures.

Metapopulation models explicitly incorporate the spatial structure of the host population which generally leads to the better understanding of disease spread. For example, the comparison of alternative metapopulation models of rabies transmission in dogs in Tanzania shows that the distance between villages is a strong predictor of disease spread whereas village size has little impact (Beyer et al., 2011).

This supports gradual spatial diffusion in Tanzania rather than long-distance introductions suggested by landscape phylogeography approaches in North Africa (Dellicour et al., 2017). Similarly, age-structured SIR models parameterized with setting-specific contact patterns such as national contact heterogeneities are more realistic and better describe disease spread at large spatial scales as shown for influenza [START_REF] Mistry | Inferring high-resolution human mixing patterns for disease modeling[END_REF].

Understanding the transmission dynamics between different host reservoirs in the context of zoonoses is necessary to assess the epidemic risk and the most adapted control measure. Depending on their evolutionary stage, zoonoses lead to either stuttering or sustained transmission in human [START_REF] Lloyd-Smith | Epidemic Dynamics at the Human-Animal Interface[END_REF] and discriminating these two categories of transmission is crucial in the context of emergence.

Phylodynamic approaches supported the hypothesis of sustained inter-human transmission following a single introduction from the animal reservoir during the 2014 West African Ebola epidemic [START_REF] Gire | Genomic surveillance elucidates Ebola virus origin and transmission during the 2014 outbreak[END_REF], whereas they clearly demonstrated stuttering chains originating from recurrent introductions from camel populations for MERS-CoV in Saudi Arabia [START_REF] Dudas | MERS-CoV spillover at the camelhuman interface[END_REF]. Due to limited data in animal populations, it is particularly challenging to identify the most important animal reservoirs in disease maintenance. Beyer et al. (2011) nevertheless argued using a metapopulation model that dog rabies does not originate from wildlife but from sustained and low-grade transmission in highly spatially-structured dog populations. In Iran, the picture is quite different as demonstrated by Dellicour et al. (2019). Using phylogeography, they showed that multiple viral lineages circulate independently in both domestic dogs and wildlife reservoirs.

Dynamics related to the pathogen

The analysis of pathogen genetic sequences provides valuable information on the role of pathogens'

genetic diversity on their transmission potential, and thereby their epidemic growth. The relative transmissibility and virulence of new variants should be rapidly assessed when the first cases arise, such as during the COVID-19 pandemic, but it is not an easy task. Indeed, the evolutionary theory predicts that pathogens' fitness is maximal at intermediate levels of transmissibility and virulence. However, there is scarce empirical evidence of a trade-off between transmissibility and virulence, besides the drivers of this trade-off are unknown [START_REF] Acevedo | Virulence-driven trade-offs in disease transmission: A meta-analysis[END_REF].

Practically speaking, new variants of SARS-CoV-2 are identified using phylogenetic approaches [START_REF] Rambaut | A dynamic nomenclature proposal for SARS-CoV-2 lineages to assist genomic epidemiology[END_REF] and their transmissibility is quantified by estimating variant-specific growth rate or effective reproduction numbers from variant frequency data [START_REF] Volz | Assessing transmissibility of SARS-CoV-2 lineage B.1.1.7 in England[END_REF][START_REF] Davies | Estimated transmissibility and impact of SARS-CoV-2 lineage B.1.1.7 in England[END_REF].

These methodologies allowed to identify the repeated emergence of new variants during the pandemic and monitor their relative transmissibility. Most of them were shown to be more transmissible [START_REF] Campbell | Increased transmissibility and global spread of SARS-CoV-2 variants of concern as at June 2021[END_REF], but virulence was significantly greater only for the Delta variant.

Other diseases are subject to the emergence of new strains with higher transmissibility. For example, [START_REF] Wymant | A highly virulent variant of HIV-1 circulating in the Netherlands[END_REF] have recently shown that a new subtype-B HIV strain is currently circulating in the Netherlands. Patients infected with this subtype exhibit higher viral loads and a faster decline of CD4 cells indicative of a greater virulence. Phylodynamic analyses suggest that the new subtype emerged at the end of the 20th century and is more transmissible compared to other transmission clusters. Similar to the Delta variant of SARS-CoV-2, the new subtype-B HIV strain is more transmissible and more virulent.

Dynamics related to the environment

The incorporation of environmental factors in epidemiological or phylodynamic modeling allows to identify and sometimes quantify the role of ecological processes on the dynamics of infectious diseases. For example, cholera is a waterborne bacterial infection generally causing outbreaks after floods or monsoons in tropical areas. [START_REF] Koelle | Refractory periods and climate forcing in cholera dynamics[END_REF] have confirmed this climatic forcing by comparing environmental changes to time-varying transmission rates estimated from a four-decade time-series of cholera cases in Bangladesh with a model that accounts for the number of susceptible individuals, immunity decay, and seasonal transmission. Landscape phylogeography can also unravel key landscape features in infectious disease circulation. For example, mean annual temperature is strongly and positively associated with WNV lineage dispersal velocity and variations in viral genetic diversity in the USA [START_REF] Dellicour | Epidemiological hypothesis testing using a phylogeographic and phylodynamic framework[END_REF]. Counter-intuitively, migratory bird flyways are not identified as correlates of viral spread which suggests that local mosquito and bird populations play a major role in disease circulation.

Modelling for public decision-making

Early-warning signals and surveillance

In addition to better understanding the transmission process, modeling can exploit surveillance data to estimate basic and effective reproduction numbers to inform public health authorities on the current and near future epidemiological situation.

At the start of an epidemic, R 0 R 0 R 0 informs on the transmission potential of the disease, in other words, whether large and explosive outbreaks should be expected, which is highly valuable in a context of high uncertainty such as disease emergence. During the 2014 West African Ebola outbreak, [START_REF] Althaus | Estimating the Reproduction Number of Ebola Virus (EBOV) During the 2014 Outbreak in West Africa[END_REF] estimated R 0 for Sierra Leone, Guinea, and Liberia, by fitting a simple SEIR model to incidence data. The maximum likelihood estimate for Sierra Leone was almost twice as high as for the two other countries.

However, the estimation procedure required fixing the average duration of the incubation and infectious periods to previous estimates from an outbreak in Congo in 1995. Alternatively, birth-death approaches that rely on pathogen genetic sequences can jointly estimate R 0 , the incubation period, and the infectious period. This way, [START_REF] Stadler | Insights into the Early Epidemic Spread of Ebola in Sierra Leone Provided by Viral Sequence Data[END_REF] have estimated a similar R 0 , however the median estimate of the infectious period was not in agreement with other estimates [START_REF] Team | Ebola Virus Disease in West Africa -The First 9 Months of the Epidemic and Forward Projections[END_REF], and sample size was too small to estimate the incubation period with high certainty. Overall, both approaches showed that transmission was more intense in Sierra Leone compared to Guinea and Liberia.

Rapidly after disease introduction, the depletion of susceptible individuals due to past infection or control measures should be accounted for in the calculation of the reproduction number that becomes the effective reproduction number R e R e R e . Monitoring R e over an epidemic provides evidence of changes in transmission over time due to changes in pathogen transmissibility, host mobility, or the implementation of control measures. Bourhy et al. (2016) have quantified the instantaneous R e of dog rabies in an endemic African city, Bangui, over more than one decade. R e rarely exceeded the critical value of 1, even during epidemic waves, indicating no self-sustained transmission and suggesting that control measures were effective. This analysis was done retrospectively but R e can be estimated in real-time which can help planning outbreak response. Indeed, outbreaks usually increase pressure on health systems, especially on hospitals. Public health authorities can use predictions on the maximal number of beds for outbreak management to organize patient care in advance without overwhelming the rest of the health system.

Predictions for response planning are particularly useful during pandemic times or in settings with little care capacities. For example, [START_REF] Andronico | Real-Time Assessment of Health-Care Requirements During the Zika Virus Epidemic in Martinique[END_REF] have assessed a few weeks ahead using a compartmental model that the Zika outbreak in Martinique would require at most eight intensive care beds and seven ventilators for individuals with Guillain-Barré syndrome. R e can also be estimated using phylodynamic modeling. A structured birth-death model fitted to the first Omicron genomes sequenced in South Africa has allowed the estimation of R e that was up to 3.6 indicating intense community-transmission and the need for rapid response. This was further supported by continuous phylogeography suggesting rapid spatial spread [START_REF] Viana | Rapid epidemic expansion of the SARS-CoV-2 Omicron variant in southern Africa[END_REF].

The COVID-19 pandemic has facilitated and accelerated the development of two new types of surveillance systems: genomic surveillance and wastewater-based surveillance. Genomic surveillance is either deployed at the national level [START_REF] Wilkinson | A year of genomic surveillance reveals how the SARS-CoV-2 pandemic unfolded in Africa[END_REF] or targets higher-risk groups like heathcare workers (HCWs) and patients at hospitals [START_REF] Meredith | Rapid implementation of SARS-CoV-2 sequencing to investigate cases of health-care associated COVID-19: a prospective genomic surveillance study[END_REF]. National-level genomic surveillance allows to follow the emergence of new variants, and targeted genomic surveillance informs clinical, infection control, and hospital management teams to improve infection-control interventions in hospital settings [START_REF] Meredith | Rapid implementation of SARS-CoV-2 sequencing to investigate cases of health-care associated COVID-19: a prospective genomic surveillance study[END_REF]. However, genomic surveillance like surveillance systems based on case numbering remains costly. An alternative strategy relies on the monitoring of pathogen genetic material in wastewater resulting from fecal shedding and reflecting community-level transmission. The COVID-19 pandemic has really stimulated wastewater-based surveillance as well as the development of methodologies based on compartmental models [START_REF] Mcmahan | COVID-19 wastewater epidemiology: a model to estimate infected populations[END_REF][START_REF] Nourbakhsh | A wastewater-based epidemic model for SARS-CoV-2 with application to three Canadian cities[END_REF] or deconvolution (Huisman et al., 2022a) to robustly estimate R e from wastewater pathogen load.

Evaluating (non)pharmaceutical interventions

When the main drivers of disease spread are known and a transmission model that accurately captures the epidemic process is available, modeling and more specifically epidemiological modeling can be used to design and evaluate in silico the potential impact of vaccination and nonpharmaceutical interventions.

Nonpharmaceutical interventions are also known as community mitigation strategies and encompass social distancing measures (e.g., quarantine, curfews, lockdowns, closure of places where people gather), travel bans, and combined testing and quarantine measures. Intervention evaluation can be done retro-spectively to validate their implementation, or prospectively to guide decision-making.

Predicting the impact of vaccination and designing the best campaign to avoid spread provide incentives to governments or health authorities to take action, continue their control efforts, or strengthen them, particularly in the context of neglected tropical diseases. [START_REF] Mancy | Rabies shows how scale of transmission can enable acute infections to persist at low prevalence[END_REF] reconstructed transmission chains from contact tracing data in dog populations in Serengeti district, Tanzania, and showed that with negligible vaccination coverage rabies would very probably circulate 10 to 30 weeks in dog populations after a single introduction. This argument strongly supports current vaccination efforts. The effect of vaccination can also be evaluated at the individual level. For example, [START_REF] Tsang | Indirect protection from vaccinating children against influenza in households[END_REF] evaluated direct and indirect vaccine effectiveness against influenza infection in households and showed that even when other household members are vaccinated the individual benefit of vaccination still stands.

Community-level social distancing interventions have been evaluated worldwide during the COVID-19 pandemic. Compartmental models are an essential tool to do so. They allowed among others to quantify the effect of curfew [START_REF] Andronico | Evaluating the impact of curfews and other measures on SARS-CoV-2 transmission in French Guiana[END_REF], school closures [START_REF] Flaxman | Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe[END_REF], or agestratified lockdowns [START_REF] Roche | The impact of lockdown strategies targeting age groups on the burden of COVID-19 in France[END_REF]. More simple approaches that rely on the estimation of the instantaneous R e allowed to dissect the most effective control strategies at a time when governments adapted control interventions on a monthly basis [START_REF] Davies | Effects of non-pharmaceutical interventions on COVID-19 cases, deaths, and demand for hospital services in the UK: a modelling study[END_REF][START_REF] Huisman | Estimation and worldwide monitoring of the effective reproductive number of SARS-CoV-2[END_REF]. Testing strategies were also in the radar but studied with more complex tools like agent-based models. For example, [START_REF] Pullano | Underdetection of cases of COVID-19 in France threatens epidemic control[END_REF] showed that most cases were not detected during the first wave of the pandemic in France, and that detection rates were considerably heterogeneous across regions. West Africa Ebola outbreak. However, these results do not translate easily into real world intervention measures.

Complementarity of epidemiological and phylodynamic modeling

In addition to relying on data of different nature, epidemiological and phylodynamic modeling provide complementary approaches for the study of infectious diseases spread. Phylodynamics opens the door to the analysis of pathogen-related drivers of the epidemic process and brings an evolutionary standpoint to epidemiology. One can estimate viral fitness, study adaptive evolution to the host, and discriminate local transmission from imports. It also reliably infers transmission routes in cluster investigation, and thereby, cross-validates transmission chains or even identifies new epidemiological links. However, epidemiological modeling remains the tool of choice to perform real-time analyses, forecast epidemics, and test hypothetical intervention scenarios. Consequently, the evaluation of (non)pharmaceutical interventions to guide decision-making remains more amenable and detailed with epidemiological modeling.

Importantly, the COVID-19 pandemic has illustrated the need for interdisciplinary studies that combine genetic and epidemiological data analyzed with classical statistical analyses, epidemiological, and phylodynamic modeling to gain broad insights on the drivers and characteristics of the epidemic process [START_REF] Viana | Rapid epidemic expansion of the SARS-CoV-2 Omicron variant in southern Africa[END_REF][START_REF] Müller | Viral genomes reveal patterns of the SARS-CoV-2 outbreak in Washington State[END_REF].

Assessing inference bias, a key challenge in epidemiological and phylodynamic modeling

As in any statistical analysis, epidemiological and phylodynamic modeling can be affected by statistical biases that lead to a difference between the true parameter value and the expected value obtained with the estimator. Epidemiologists tend to use this term to indicate any phenomenon that leads to a systematic difference between the true parameter value and the one estimated from the data. These phenomena can arise at data collection when sampled data do not reflect the underlying epidemic process. This particular phenomenon is called sampling bias. Statistical biases can also arise at the model specification level when models do not account for a process that drives epidemic dynamics or are overparameterized, meaning that they try to estimate many correlated parameters. In this section, we focus on the inference challenges related to statistical biases in phylogeography and household transmission models.

Potential impact of sampling bias in phylogeography

The availability of pathogen genetic sequences was a limiting factor in phylodynamic analyses for a long time. Sample collection was mostly opportunistic, relying on existing surveillance systems and not planned as part of a grounded road map. Opportunistic sampling certainly allows rapid and low cost data collection and generation, but it also implies a high risk of sampling bias with sequences that are not reflective of outbreak dynamics [START_REF] Hill | Progress and challenges in virus genomic epidemiology[END_REF]. For example, some areas may be over-or under-sampled, and in extreme cases, they may even be left unsampled while they experience intense circulation. In other situations, many samples are available but all of them cannot be sampled due to limited financial resources as it is still the case for neglected diseases, or there is a known sampling bias as this was the case during the COVID-19 pandemic (Hodcroft et al., 2021a). Samples to analyze should be selected according to a rationale. So far, subsampling strategies used external data such as incidence [START_REF] Candido | Evolution and epidemic spread of SARS-CoV-2 in Brazil[END_REF][START_REF] Lemey | Accommodating individual travel history and unsampled diversity in Bayesian phylogeographic inference of SARS-CoV-2[END_REF] or hospitalization (Dellicour et al., 2021b) data to guide sample composition. Importantly, subsampling allows to save computational resources as Bayesian phylogeographic analyses are computationally-demanding and very large data sets do not necessarily provide more accurate results [START_REF] Magee | The effects of random taxa sampling schemes in Bayesian virus phylogeography[END_REF].

Some studies have investigated the impact of spatial sampling bias on phylogeographic analyses. In discrete phylogeography, CTMC has been argued to be sensitive to spatial sampling bias whereas the structured coalescent model is robust to bias and its performances are maximized when the sample composition is even [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF]. However, there is no comprehensive understanding of how sampling bias acts on discrete phylogeography inference, neither the ways this impact could be mitigated. In continuous phylogeography, the picture seems more clear. Indeed, Brownian Motion phylogeography is strongly affected by the lack of sampling in certain areas, but this can be mitigated by adding sequencefree cases to inform the model [START_REF] Kalkauskas | Sampling bias and model choice in continuous phylogeography: Getting lost on a random walk[END_REF]. On the other hand, the Λ-Fleming-Viot process, another model of continuous phylogeography that is more rarely used, is robust to spatial sampling bias but is more adapted to endemic long-term transmission [START_REF] Kalkauskas | Sampling bias and model choice in continuous phylogeography: Getting lost on a random walk[END_REF].

So far, three strategies have been used to assess or mitigate the impact of sampling bias. First, multiple models are tested on the same data set and results are compared. This has been particularly implemented for discrete phylogeographic analyses in which researchers compared CTMC to the structured coalescent model [START_REF] Faria | Establishment and cryptic transmission of Zika virus in Brazil and the Americas[END_REF][START_REF] Brynildsrud | Global expansion of Mycobacterium tuberculosis lineage 4 shaped by colonial migration and local adaptation[END_REF][START_REF] Yang | Bayesian phylodynamics of avian influenza A virus H9N2 in Asia with time-dependent predictors of migration[END_REF][START_REF] Mavian | Toxigenic Vibrio cholerae evolution and establishment of reservoirs in aquatic ecosystems[END_REF]Dudas et al., 2018). The best case scenario is when results across methods are in good agreement [START_REF] Faria | Establishment and cryptic transmission of Zika virus in Brazil and the Americas[END_REF][START_REF] Brynildsrud | Global expansion of Mycobacterium tuberculosis lineage 4 shaped by colonial migration and local adaptation[END_REF][START_REF] Yang | Bayesian phylodynamics of avian influenza A virus H9N2 in Asia with time-dependent predictors of migration[END_REF][START_REF] Mavian | Toxigenic Vibrio cholerae evolution and establishment of reservoirs in aquatic ecosystems[END_REF]. When this is not the case, the experimenter expectations may strongly orient model choice. Second, at least one model is tested on multiple subsamples. However, this approach is feasible only when enough samples are available, and there is currently no evidence to prefer one subsampling strategy over the others. Third, statistical methodologies are adapted to account for potential unrepresentative sampling. For example, [START_REF] Chaillon | HIV persists throughout deep tissues with repopulation from multiple anatomical sources[END_REF] corrected the metric of statistical support of migration rates between discrete locations in CTMC to accomodate for spatial sampling frequency and identify migration rates that participate the most to the epidemic process and are not just supported due to more intense sampling. In a recent study, [START_REF] Guindon | Accounting for spatial sampling patterns in Bayesian phylogeography[END_REF] explicitely modelled the sampling strategy and showed that the assumptions on the sampling strategy may radically impact the reconstruction of past spatial dynamics.

In brief, spatial sampling bias is a key challenge in phylogeographic analyses. There is still a need to better characterize its impact. New methodologies should be developed in parallel to account for the potential impact of bias.

3.4.2. Model misspecification and overparameterization

In discrete phylogeography

The number of parameters to estimate in a discrete phylogeographic analysis exceeds the amount of information contained in the spatial location of the analyzed sequences that is condensed in a single observation. In CTMC, n(n -1) parameters from the asymmetric rate matrix are to be estimated, with n the number of discrete locations included in the analysis. In the structured coalescent model, n deme sizes are to be estimated in addition to the n(n -1) migration rates. There is very low chance that all migration events occurred in a given sample (Lemey et al., 2009a;[START_REF] Bloomquist | Three roads diverged? Routes to phylogeographic inference[END_REF]. Bayesian stochastic search variable selection (BSSVS) circumvents this overparameterization issue by associating an indicator variable that has a Dirac delta distribution (i.e., equals to 0 or 1) to each migration parameter and by exploring in the MCMC all combinations of parameters that explain the most the diffusion process. However, this inference workaround does not necessarily imply correct inference as [START_REF] Gascuel | A Darwinian Uncertainty Principle[END_REF] have recently shown that it is not possible to estimate both migration rate parameters and node locations with the CTMC model.

The structured coalescent model faces another model misspecification challenge, the ghost deme issue [START_REF] Ewing | Estimating Population Parameters using the Structured Serial Coalescent with Bayesian MCMC Inference when some Demes are Hidden[END_REF][START_REF] Beerli | Effect of unsampled populations on the estimation of population sizes and migration rates between sampled populations[END_REF]. Ghost demes are discrete locations that are not specified in the structured coalescent model despite intervening in the diffusion process. Accounting for ghost demes when they actually don't exist and not accounting for them when they actually exist lead to biased estimations of migration rates. To model spatial diffusion with a structured coalescent model, one should first make sure that the epidemic occurs in a closed environment and that all discrete locations affected by the epidemic were sampled. The impact of ghost demes in CTMC has not been tested yet, but would very certainly lead to biased inference.

In the end, the inference abilities of discrete phylogeographic models are little known and the impact of model misspecification remains poorly characterized.

In models of household transmission

Household transmission models generally hypothesize homogeneous mixing between household contacts [START_REF] Longini | Stastical inference for infectious diseases and risk-specific household and community transmission parameters[END_REF]Cauchemez et al., 2004;Prunas et al., 2022;[START_REF] Dattner | The role of children in the spread of COVID-19: Using household data from Bnei Brak, Israel, to estimate the relative susceptibility and infectivity of children[END_REF] although [START_REF] Goeyvaerts | Household members do not contact each other at random: Implications for infectious disease modelling[END_REF] showed that household members do not necessarily contact each other at random. So far, there has been no study on the potential impact of misspecification of within household contact patterns in the estimation of transmission parameters. Furthermore, contact patterns are expected to vary across settings and contact heterogeneities cannot be easily deduced.

Thesis objectives

This thesis aims at better understanding viral disease spread using either highly detailed individual-level data or coarse pathogen genetic sequences data at large spatial scale that correspond to the two ends of the data granularity gradient presented in Section 2.2 of the introduction. The objective is not only to gain insights from empirical data by using adapted quantitative approaches, but also to compare the evidence that can be drawn from individual-level data and pathogen genetic sequences. Another aim of this thesis is to investigate in a more theoretical framework the limitations of the quantitative methodolo- First, I review the epidemiological and phylodynamic modeling approaches applied to dog rabies using the rigorous methodology of a scoping review (Chapter 1). Indeed, the scoping review approach extends the scientific methodology of systematic reviews for article search, selection, and analysis to a heterogeneous scientific production. In this review, I explore the uses of modeling approaches and synthesize their contributions to the understanding of RABV circulation and control. I highlight their complementarity in a context of limited resources and potentially very biased sampling, without omitting their limitations, and I propose future directions to broaden their inputs. Third, I investigate the limitations of phylodynamic (Chapter 4) and epidemiological (Chapter 5) modeling using simulations when the determinants of the epidemic process are unknown. In Chapter 4, I assess the impact of spatial sampling bias on discrete phylogeographic reconstruction when viral spatial dynamics are unknown. To do so, I simulate RABV epidemics in dog populations in Morocco and proceed to biased or unbiased sampling. Then, I reconstruct spatial dynamics using different discrete phylogeographic algorithms before assessing their relative inference performance. I also showcase how discrete phylogeographic algorithms lead to contrasting results on empirical data sets. In Chapter 5, I investigate how a major assumption in models of disease transmission in households impacts the inference of transmission heterogeneity at the individual-level. Indeed, household transmission models generally assume homogeneous mixing between household contacts which is not necessarily true. In this study, I use simulated epidemics under a heterogeneous mixing scenario to quantify the inference bias of age-dependent transmission.

Chapter 1

Epidemiological and phylodynamic modeling of dog rabies

Rabies is a fatal yet vaccine-preventable disease. In the last two decades, domestic dog populations have been shown to constitute the predominant reservoir of rabies in developing countries, causing 99% of human rabies cases. Despite substantial control efforts, dog rabies is still widely endemic and is spreading across previously rabies-free areas. Developing a detailed understanding of dog rabies dynamics and the impact of vaccination is essential to optimize existing control strategies and develop new ones. In this scoping review, we aimed at disentangling the respective contributions of epidemiological models and phylodynamic approaches to advancing the understanding of rabies dynamics and control in domestic dog populations. We also addressed the methodological limitations of both approaches and the remaining issues related to studying rabies spread and how this could be applied to rabies control.

Through a detailed search of the PubMed, Web of Science, and Scopus databases, we identified a total of n = 59 relevant studies using epidemiological models (n = 30, referred to mathematical models hereafter), phylodynamic inference (n = 22) and interdisciplinary approaches (n = 7). We found that despite often relying on scarce rabies epidemiological data, mathematical models investigated multiple aspects of rabies dynamics and control. These models confirmed the overwhelming efficacy of massive dog vaccination campaigns in all settings and unraveled the role of dog population structure and frequent introductions in dog rabies maintenance. Phylodynamic approaches successfully disentangled the evolutionary and environmental determinants of rabies dispersal and consistently reported support for the role of reintroduction events and human-mediated transportation over long distances in the maintenance of rabies in endemic areas. Potential biases in data collection still need to be properly accounted for in most of these analyses. Finally, interdisciplinary studies were determined to provide the most comprehensive assessments through hypothesis generation and testing. They also represent new avenues, especially concerning the reconstruction of local transmission chains or clusters through data integration. Despite advances in rabies knowledge, substantial uncertainty remains regarding the mechanisms of local spread, the role of wildlife in dog rabies maintenance, and the impact of community behavior on the efficacy of control strategies including vaccination of dogs. Future integrative approaches that use phylodynamic analyses and mechanistic models within a single framework could take full advantage of not only viral sequences but also additional epidemiological information as well as dog ecology data to refine our understanding of rabies spread and control. This would represent a significant improvement on past studies and a promising opportunity for canine rabies research in the frame of the One Health concept that aims to achieve better public health outcomes through cross-sector collaboration.

1. Introduction

Background

Rabies is a viral zoonosis affecting the central nervous system of mammals that is almost always fatal to humans. Domestic dogs represent the main reservoir of rabies virus (RABV) worldwide. After infection, that occurs through the bite of an infected animal, RABV travels through the nerves to the spinal cord and brain. This incubation period lasts on average 3 weeks in dogs [START_REF] Hampson | Transmission Dynamics and Prospects for the Elimination of Canine Rabies[END_REF]. Symptoms appear when RABV reaches the brain and can last up to ten days [START_REF] Hampson | Transmission Dynamics and Prospects for the Elimination of Canine Rabies[END_REF]. There are two classical forms of rabies, furious or paralytic (World Health Organization (WHO), 2018). While dogs affected by the furious form become aggressive and attack with no trigger, dogs affected by the paralytic form develop paralysis and have difficulty swallowing leading to hypersalivation.

Dogs are responsible for 99% of human rabies cases (World Health Organization (WHO), 2018). Indepth understanding of dog ecology and host-pathogen interactions is necessary to characterize rabies dynamics and design appropriate control measures. Rabies is a vaccine-preventable disease in both human and canine populations, and dog vaccination is the most cost-effective control measure (Anothaisintawee et al., 2019). Strong evidence is available for the efficacy of dog rabies elimination programs in endemic areas (Cleaveland and Hampson, 2017;Lembo et al., 2010;[START_REF] Arechiga Ceballos | Control of canine rabies in developing countries: key features and animal welfare implications[END_REF]Cleaveland et al., 2014;Cleaveland et al., 2018), notably in South America where massive dog vaccination campaigns in the 1980s alleviated the burden of canine rabies. Regardless, there has been only little improvement of the global burden since the successes in South America. Dog rabies is still endemic in Africa, Asia, and the Middle East [START_REF] Hampson | Estimating the Global Burden of Endemic Canine Rabies[END_REF][START_REF] Mbilo | Dog rabies control in West and Central Africa: A review[END_REF].

In 2015, the World Health Organization (WHO), the Global Alliance for Rabies Control (GARC), the World Organization for Animal Health (OIE) and the Food and Agriculture Organization of the United Nations (FAO) launched a comprehensive framework targeting the global elimination of dog-mediated human rabies by 2030 (World Health Organization (WHO) et al., 2018). Effective One Health interventions such as the improvement of the current prophylaxis in both humans (Hampson et al., 2019b;Hampson et al., 2019b) and dogs should enable reaching this goal. Despite valuable efforts in several endemic countries [START_REF] Mbilo | Dog rabies control in West and Central Africa: A review[END_REF]World Health Organization (WHO) et al., 2019;[START_REF] Broban | Bolstering human rabies surveillance in Africa is crucial to eliminating canine-mediated rabies[END_REF], control strategies have not stopped rabies from circulating due to inadequate political, economic, and social responses. Weak interest from veterinary services, lack of sustainable resources and political neglect (Welburn et al., 2017) prevent most endemic countries to reach the 70% vaccination coverage recommended by the WHO [START_REF] Mbilo | Dog rabies control in West and Central Africa: A review[END_REF]. Moreover, rabies infections continue to spread, notably in previously rabies-free areas in countries such as Indonesia [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF]Dibia et al., 2015;Mahardika et al., 2014) and the Philippines (Tohma et al., 2014;[START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF]. In this resource-limited context, in-depth knowledge of the mechanisms underlying rabies dynamics (environmental drivers of spread, impact of dog density, impact of dog behavior, etc.) would be a key asset to limiting the spread of this vaccine-preventable disease, notably by aiding to design more effective vaccination campaigns that are robust to resurgence in the long-term. The development of novel methodologies to better understand rabies epidemiology and transmission dynamics therefore constitutes a promising avenue of research.

Objectives

In this scoping review, we focused on the insights of two quantitative approaches applied to the study of rabies: mathematical modeling of infectious diseases and phylodynamics. The former is a field of research that exploits epidemiological data to unravel the spread of diseases in populations, assess the impact of interventions, support policy making, and optimize control strategies. The latter studies the interactions between epidemiological, immunological, and evolutionary processes from the analysis of viral genetic sequence data (Volz et al., 2013). Within phylodynamics, phylogeographic inference specifically aims at reconstructing the dispersal history and dynamics of viral lineages in space and time. Here, we assessed the uses and respective contributions of both approaches, as well as their limitations and the remaining knowledge gaps concerning rabies dispersal and control in domestic dog populations.

Methods

Search strategy

This review follows the guidelines of the PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analyses Extension for Scoping Reviews) statement for scoping reviews [START_REF] Tricco | PRISMA extension for scoping reviews (PRISMA-ScR): Checklist and explanation[END_REF]. In this review, we screened PubMed, Web of Science and Scopus databases on the 2nd of June, 2020 using the following combination of terms ["rabies" AND ("dog" OR "canine") AND ("modelling" OR "modeling" OR "phylogeography" OR "phylodynamics") AND "dynamics"] along with the "all fields" option and without restriction on publication year. The "all fields" option enabled to apply the search terms for their appearance in the title, abstract and keywords. Only English-written papers published in scientific journals were considered. All data were searched and screened by the same researcher (ML). The search strategy identified 65, 94 and 768 publications in PubMed, Web of Science and Scopus databases respectively, which corresponded to 797 unique records. In addition, references of selected publications were screened manually, leading to the identification and inclusion of two additional studies (Coleman and Dye, 1996;Kitala et al., 2002) that were not identified during the searching step. Finally, the paper of Colombi et al. (Colombi et al., 2020), which was not identified in the databases nor in the references, was also included (Fig. 8).

Selection of studies

In total, 797 records were included and processed manually in a multi-stage procedure. At each selection step, a conservative approach was taken to ensure the best sensitivity level. Firstly, studies were selected based on their title using the following inclusion criteria: mathematical models of dog and human rabies assessing the impact of control strategies, the risk of rabies importation, the drivers of rabies spread or models estimating epidemiological parameters, cost-effectiveness studies, phylodynamic studies including RABV isolated from dogs, and broad studies on new phylodynamic or mathematical models. Indeed, rabies has often been used as a model disease in phylodynamics and mathematical modeling, and a reference to rabies might not appear directly in the title or the abstract. The following exclusion criteria were used: reviews, studies strictly on wildlife rabies, dog ecology and population dynamics, conservation biology, and evolutionary analyses for diagnostic purposes. Secondly, studies were selected based on their abstract with a refined set of exclusion criteria to exclude statistical analyses of epidemiological data, cost-effectiveness studies with no focus on rabies dynamics, experimental rabies cross-species transmission which did not incorporate a modeling aspect and studies on the evolutionary processes of RABV.

Finally, studies went through a full-text reading step to verify that their content matched our selection criteria. At this step, theoretical models which were not grounded in a specific epidemiological context were excluded (Fig. 8).

Data extraction and analysis

Selected studies were classified into three categories based on their methodology: mathematical models, phylodynamic and interdisciplinary studies. Most phylodynamic studies identified in this review correspond to phylogeographic analyses, where the main focus is on inferring the spread of a pathogen over time using location data associated with the available sequence data. The interdisciplinary category covers studies either integrating epidemiological and genetic data in a unified modeling framework or mixing modeling approaches with phylodynamics. Data were systematically charted in an Excel spreadsheet designed to retrieve: i) the main modeling strategy with its assumptions; ii) the data source; iii) remarks about potential bias of the data in relation to the underlying evolutionary and epidemiological processes; iv) the qualitative and quantitative results concerning the dynamics of dog rabies; and v) if performed, the sensitivity analysis determining the robustness of the methodology to parameter values or potential biases.

Results

General characteristics of selected studies

Our selection procedure identified 59 studies that meet our selection criteria with 30 mathematical models [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF]Kitala et al., 2002;Coleman and Dye, 1996;Colombi et al., 2020;Zhang et al., 2012;Fitzpatrick et al., 2012;[START_REF] Beyer | The implications of metapopulation dynamics on the design of vaccination campaigns[END_REF]Townsend et al., 2013a;[START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]2011;Yu et al., 2012;Mollentze et al., 2013;Guo et al., 2013;Carnieli et al., 2013;Horton et al., 2015;Brunker et al., 2015;Yao et al., 2015;Troupin et al., 2016;Zhang et al., 2017;[START_REF] Ma | Re-emerging of rabies in Shaanxi province, China, from 2009 to 2015[END_REF]Dellicour et al., 2017;Brunker et al., 2018b;Wang et al., 2019;Dellicour et al., 2019), and 7 interdisciplinary studies [START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF]Talbi et al., 2010;Mollentze et al., 2014;Bourhy et al., 2016;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]Cori et al., 2018;[START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF], all published between 1996 and 2020 (Fig. 8 and Fig. 9A-B). Mathematical models were first published followed by phylodynamic and interdisciplinary studies (Fig. 9B). This timeline can be explained by the recent developments of Bayesian phylodynamic, and in particular phylogeographic, models in BEAST [START_REF] Baele | Emerging Concepts of Data Integration in Pathogen Phylodynamics[END_REF]Suchard et al., 2018;[START_REF] Bouckaert | BEAST 2.5: An advanced software platform for Bayesian evolutionary analysis[END_REF]. Africa and Asia are the most studied continents in the three methodological categories, while

China accounts for most of the Asian studies (Fig. 9C). Oceania is not represented in the interdisciplinary and phylodynamic categories since it is a rabies-free area (Fig. 9A).

Topics addressed by the studies

Phylodynamic studies are homogeneous in terms of methodologies (essentially phylogeographic studies) and research goals. They predominantly focus on unraveling the dispersal dynamics of rabies at the regional and country levels (n = 16;Dibia et al. 2015;Tohma et al. 2014;Bourhy et al. 2008;Lemey et al. 2009a;Talbi et al. 2009;Meng et al. 2011;Hayman et al. 2011;Carnieli et al. 2011;Yu et al. 2012;Carnieli et al. 2013;Brunker et al. 2015;Yao et al. 2015;[START_REF] Ma | Re-emerging of rabies in Shaanxi province, China, from 2009 to 2015[END_REF]Dellicour et al. 2017;Wang et al. 2019;Dellicour et al. 2019). In four of them, the authors deciphered the role of lineage introduction in rabies maintenance or emergence (Mollentze et al., 2013;Guo et al., 2013;Horton et al., 2015;Zhang et al., 2017). In recent years, researchers have been trying to identify external factors impacting the spatial dynamics of RABV spread (n = 5;Brunker et al. 2015;Yao et al. 2015;Dellicour et al. 2017;Brunker et al. 2018b;Dellicour et al. 2019;Fig. 9D and Table A1). Contrary to phylodynamic studies, the modeling category gathers a diverse panel of models with aims that cover the implementation of new mathematical methodologies (n = 2; Hudson et al. 2019b;Ortega et al. 2000), the characterization of rabies dynamics (n = 11;Zhang et al. 2012;Fitzpatrick et al. 2012;Ferguson et al. 2015;Chen et al. 2015;[START_REF] Abdul Taib | Model Simulation for the Spread of Rabies in Sarawak, Malaysia[END_REF]Huang et al. 2019;Brookes et al. 2019;Hampson et al. 2007;Zinsstag et al. 2009;Zhang et al. 2011;[START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF], the identification of factors driving the resurgence or maintenance of rabies (n = 9;[START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF]Kitala et al. 2002;Colombi et al. 2020;Sparkes et al. 2016;Leung and Davis 2017;Laager et al. 2018;Laager et al. 2019;[START_REF] Wilson-Aggarwal | High-resolution contact networks of free-ranging domestic dogs Canis familiaris and implications for transmission of infection[END_REF]Hudson et al. 2019a), the assessment of control strategies efficacy (n = 18;[START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF]Kitala et al. 2002;Coleman and Dye 1996;Fitzpatrick et al. 2012;[START_REF] Beyer | The implications of metapopulation dynamics on the design of vaccination campaigns[END_REF]Townsend et al. 2013a; For phylodynamic studies, countries were not considered if their genetic data were included only in regular phylogenetic tree reconstructions. Similarly, two studies which described rabies dynamics at the global scale (Bourhy et al., 2008;Troupin et al., 2016) were not considered in this figure. In our collected records, China accounts for most Asian studies. Spain appears on the map because Ceuta and Melilla, which are Spanish enclaves in North Africa, are represented in two data sets of RABV genetic sequences (Dellicour et al., 2017;Talbi et al., 2010). (D) Number of studies per topic and methodological category. The World Bank, https://datacatalog.worldbank.org/dataset/world-bank-official-boundaries,CC-BY4.0. Tohma et al. 2014;Talbi et al. 2010;Mollentze et al. 2014;Bourhy et al. 2016;Cori et al. 2018;[START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF], and the identification of environmental factors influencing rabies spread and maintenance such as recurrent reintroductions (n = 3;Talbi et al. 2010;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF]. Two of these used genetic and epidemiological data of dog rabies in a unified modeling approach (Mollentze et al., 2014;Cori et al., 2018), whereas the others analyzed sequences through regular phylogenetic approaches and completed their analysis with a mathematical model (Talbi et al. 2010;Bourhy et al. 2016;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF][START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF]Fig. 9D and Table A1).

Potential sources of bias in the data

Data source (active/passive surveillance), resolution (number and length of RABV sequences, incidence per country/region, etc.) and representativeness influence the level of evidence of the studies on the underlying epidemiological and evolutionary processes. In particular, recorded cases collected through passive surveillance systems are expected to underestimate the disease burden and to be potentially spatiotemporally biased [START_REF] Hampson | Estimating the Global Burden of Endemic Canine Rabies[END_REF][START_REF] De La Puente-León | Spatial Inequality Hides the Burden of Dog Bites and the Risk of Dog-Mediated Human Rabies[END_REF]. Similarly, genetic sequences collected from publicly available databases such as GenBank often lack precise metadata (e.g., sampling time and location) and/or are of short length.

In our text corpus of phylodynamic and interdisciplinary studies, passive surveillance systems and Gen-Bank represent the main sources of RABV genetic sequence data (Tables A2 to A4). By combining these two data sources, researchers have generally managed to increase the spatiotemporal coverage of their data set. This however does not guarantee a good representativeness of the epidemic process. Active surveillance was mostly used to collect dog specimens from animal markets in China (n = 2; Yu et al. 2012;Guo et al. 2013) and thorough contact tracing after biting events in China and Tanzania (n = 2; Brunker et al. 2015;Zhang et al. 2017). On average, the data sets analyzed in these studies contained 183 sequences spanning from approximatively 3% to 100% of the RABV genome length. Short sequences containing the N gene constitute the most common type of data. They are less informative than whole genomes which were only generated and analyzed in recent years across four studies (Brunker et al. 2015;Troupin et al. 2016;Brunker et al. 2018b;Dellicour et al. 2019; Table A2).

In studies from the modeling and interdisciplinary categories, authors generally simulated rabies epidemics (n = 24; [START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF]Kitala et al. 2002;Colombi et al. 2020;[START_REF] Beyer | The implications of metapopulation dynamics on the design of vaccination campaigns[END_REF]Townsend et al. 2013a;[START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Ferguson et al. 2015;Chen et al. 2015;Sparkes et al. 2016;Leung and Davis 2017;Laager et al. 2018;Kadowaki et al. 2018;[START_REF] Wilson-Aggarwal | High-resolution contact networks of free-ranging domestic dogs Canis familiaris and implications for transmission of infection[END_REF][START_REF] Abdul Taib | Model Simulation for the Spread of Rabies in Sarawak, Malaysia[END_REF]Hudson et al. 2019b;Hudson et al. 2019a;Brookes et al. 2019;Carroll et al. 2010;Ortega et al. 2000;Hampson et al. 2007;Zhang et al. 2011;Beyer et al. 2011;[START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF]Talbi et al. 2010), and thus predominantly relied on publicly available estimates of the natural history of rabies, dog demographics and dog ecology (Tables C3 andC4). When models were fitted to incidence data (n = 13; Mollentze et al. 2014;Bourhy et al. 2016;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]Cori et al. 2018;[START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF][START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF]Coleman and Dye 1996;Zhang et al. 2012;Fitzpatrick et al. 2012;Laager et al. 2019;Beyene et al. 2019;Huang et al. 2019;Zinsstag et al. 2009), human and/or dog case data from passive surveillance systems were used, or bite incidence data from thorough active surveillance. In general, there was a lack of data on dog rabies cases (available in 10 studies; [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF]Coleman and Dye 1996;Zhang et al. 2012;Fitzpatrick et al. 2012;Laager et al. 2019;Zinsstag et al. 2009;Mollentze et al. 2014;Bourhy et al. 2016;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]Cori et al. 2018;[START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF] and estimates on dog demographics and ecology integrating the local specificities of host ecology were available in only seven studies (Fitzpatrick et al., 2012;Laager et al., 2019;Beyene et al., 2019;Huang et al., 2019;Zinsstag et al., 2009;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF]. Access to local data is crucial since differences in rabies spread (Fitzpatrick et al., 2012) and dog carrying capacities (Beyene et al., 2019) were estimated between areas of the same country. We would expect these differences to be more pronounced across different countries. To overcome the lack of epidemiological data on dog rabies, one study used serological data (from vaccination campaigns) to model the dynamics of rabies (Ortega et al., 2000), and another study (Kadowaki et al., 2018) based its analyses on historical records in Japan from the 1950s. Similarly, most Australian studies [START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Hudson et al., 2019b;Hudson et al., 2019a;Brookes et al., 2019) took the perspective of dog ecology data since Australia is free of rabies.

This way, the authors explored the impact of dog population structure and dog roaming behavior on rabies dynamics.

Description of the models

In studies using phylodynamic approaches, the geographical dispersal of rabies was studied using either parsimony (n = 4; Bourhy et al. 2008;Talbi et al. 2009;Meng et al. 2011;Yu et al. 2012), Bayesian discrete phylogeography (n = 18;Dibia et al. 2015;Tohma et al. 2014;[START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF]Lemey et al. 2009a;Hayman et al. 2011;Carnieli et al. 2011;Mollentze et al. 2013;Guo et al. 2013;Horton et al. 2015;Brunker et al. 2015;Yao et al. 2015;Zhang et al. 2017;[START_REF] Ma | Re-emerging of rabies in Shaanxi province, China, from 2009 to 2015[END_REF]Wang et al. 2019;Dellicour et al. 2019;Talbi et al. 2010;[START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF]Brunker et al. 2015), or Bayesian continuous phylogeography (n = 6;Carnieli et al. 2013;Dellicour et al. 2017;Brunker et al. 2018b;Dellicour et al. 2019;Bourhy et al. 2016;[START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF]; Tables A2 to A4). All Bayesian phylogeographic studies were carried out in BEAST 1 (Suchard et al., 2018) with discrete trait analysis (DTA) to perform a phylogeographic reconstruction based on discrete/discretized sampling locations (e.g. provinces or countries) or with continuous trait analysis to perform a phylogeographic reconstruction based on spatially-explicit sampling location data (latitude and longitude coordinates). Several methodologies take advantage of such phylogeographic inferences to investigate the impact of external factors on the dispersal of viruses: a generalized linear model (GLM) extension of DTA developed by (Lemey et al., 2014) to test predictors of dispersal transition frequencies among discrete locations which was implemented by Brunker et al. (2018b); and post hoc statistical approaches developed by Dellicour et al. (Dellicour et al., 2019;Dellicour et al., 2016b;Dellicour et al., 2018a) to investigate the impact of environmental factors on the dispersal velocity, direction, or frequency of viral lineages in continuous phylogeographic frameworks which were applied in four rabies studies (Dellicour et al., 2017;Brunker et al., 2018b;Dellicour et al., 2019;[START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF]. Finally, [START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF] were the only authors to implement a birth-death model in BEAST 2 [START_REF] Bouckaert | BEAST 2.5: An Advanced Software Platform for Bayesian Evolutionary Analysis[END_REF] to reconstruct R e along vaccination campaigns and compare it to estimates obtained with a modeling approach (Table A4).

Compared to phylodynamics, mathematical models display a large diversity of specifications and parameterizations. Compartmental models (n = 18;[START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF]Kitala et al. 2002;Coleman and Dye 1996;Zhang et al. 2012;Fitzpatrick et al. 2012;Sparkes et al. 2016;Leung and Davis 2017;Beyene et al. 2019;[START_REF] Abdul Taib | Model Simulation for the Spread of Rabies in Sarawak, Malaysia[END_REF]Huang et al. 2019;Carroll et al. 2010;Ortega et al. 2000;Hampson et al. 2007;Zinsstag et al. 2009;Zhang et al. 2011;[START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF]) are the most represented models, followed by agent-based (n = 8; [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF][START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Ferguson et al. 2015;Laager et al. 2018;Kadowaki et al. 2018;Hudson et al. 2019b;Hudson et al. 2019a;Brookes et al. 2019) and metapopulation (n = 5) models (Colombi et al., 2020;[START_REF] Beyer | The implications of metapopulation dynamics on the design of vaccination campaigns[END_REF]Chen et al., 2015;Laager et al., 2019;Beyer et al., 2011). Other model types such as network models or branching processes are also represented (Townsend et al. 2013a;[START_REF] Wilson-Aggarwal | High-resolution contact networks of free-ranging domestic dogs Canis familiaris and implications for transmission of infection[END_REF]Mollentze et al. 2014;Bourhy et al. 2016;Cori et al. 2018; Tables A3 andA4). The development of new dog rabies models builds upon the literature since 15 models out of the 37 identified were adapted from previously published dog rabies or wildlife rabies models (Tables A3 andA4). This is the case notably for compartmental models which correspond to the simplest models of rabies dynamics.

Metapopulation, agent-based, and other model types are more complex, in that these approaches often integrate spatial dynamics of dog rabies (Colombi et al., 2020;[START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Chen et al., 2015;Laager et al., 2018;Kadowaki et al., 2018;Laager et al., 2019;[START_REF] Wilson-Aggarwal | High-resolution contact networks of free-ranging domestic dogs Canis familiaris and implications for transmission of infection[END_REF]Hudson et al., 2019b;Hudson et al., 2019a;Talbi et al., 2010;Mollentze et al., 2014;Cori et al., 2018).

Population structure can be integrated in any modeling framework under the form of contact heterogeneity, age-structured populations, roaming behavior, or individual heterogeneity. In compartmental models, population structure is integrated either as a set of strata (stray dogs, owned free-roaming dogs, owned confined dogs) interacting together (Sparkes et al., 2016), or by specifying a structured next-generation matrix from which R 0 is generally derived (Leung and Davis, 2017). Such models are also referred to as multi-host models and may integrate other hosts: humans (Chen et al., 2015;Beyene et al., 2019;[START_REF] Abdul Taib | Model Simulation for the Spread of Rabies in Sarawak, Malaysia[END_REF]Zinsstag et al., 2009;Zhang et al., 2011;[START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF][START_REF] Zhang | Spatial spread of rabies in China[END_REF], cattle (Beyene et al., 2019), wildlife (Fitzpatrick et al., 2012;Huang et al., 2019). In agent-based and network models, population structure is defined at the individual level using spatial kernels [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF]Colombi et al., 2020;[START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Ferguson et al., 2015;Kadowaki et al., 2018;Hudson et al., 2019b), individual contact rates [START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Laager et al., 2018;Brookes et al., 2019), vaccination status [START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Kadowaki et al., 2018), life span, infectious period [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF]Ferguson et al., 2015;Brookes et al., 2019), etc.

Sensitivity analyses

Sensitivity analyses are commonly used to assess the robustness of inference to both data representativeness and model specifications, and to identify the most influential parameters on specific model outputs.

In our text corpus, no sensitivity analyses were found to be carried out in phylodynamic studies which can be attributed to the relatively small number of sequences analyzed in those studies. In contrast, sensitivity analyses were commonly performed in mathematical models, either to unravel the key parameters influencing rabies dynamics or to verify the robustness of the results to model assumptions. Dog ecology parameters such as birth rate and carrying capacities are often reported as key parameters on rabies dynamics predictions although they are not estimated using local data. Transmission rates are also determinant in model predictions (Table A3). In spatially explicit studies, mobility parameters also have a strong impact on model inferences. Finally, the impact of under-reporting was tested only in interdisciplinary studies, two of which reported a strong impact of the reporting rate on model inference [START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF]Cori et al., 2018) whereas the other two were robust to a change in this parameter (Bourhy et al. 2016;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]; Table A4).

Insights into dog rabies dynamics and its drivers from phylodynamic and modeling studies

Phylogeographic analyses have aimed to unravel the spatial dynamics of dog rabies at the global and regional scales and showed that dog RABV lineages cluster spatially at the global scale, except for one lineage, referred to as the cosmopolitan lineage, which is largely distributed across the world (Bourhy et al., 2008). At the regional and country scales, there is co-circulation of dog-related lineages, notably in China (Meng et al., 2011;Yu et al., 2012;Yao et al., 2015;Zhang et al., 2017;Wang et al., 2019), in the Middle East (Dellicour et al., 2019;Horton et al., 2015), as well as in Western and Central Africa (Talbi et al., 2009). However, each lineage exhibits a strong geographical structure. In the case of country-specific lineages, various studies have suggested that transboundary movements are not a major force of rabies dispersal (Tohma et al., 2014;Lemey et al., 2009a;Talbi et al., 2009;Mollentze et al., 2013;Guo et al., 2013;Dellicour et al., 2017). All study categories unraveled the role of human-mediated movements in rabies spread. Overall, phylogeographic analyses provided evidence for the effect of anthropogenic factors: major roads are associated with rabies dispersal in North Africa (Talbi et al., 2010), and RABV lineages tended to preferentially circulate within populated areas in North Africa (Dellicour et al., 2017) and the Middle East (Dellicour et al., 2019). Other factors are associated with rabies spread in Yunnan (China, Tables 1 andA6). These results may reflect the intimate link between rabies dynamics, host ecology and dog-human interactions. Mathematical models highlighted the short length of canine rabies transmission chains (Mollentze et al., 2014;Cori et al., 2018;Ferguson et al., 2015) and unraveled the importance of long-range human movements in disease spread (Colombi et al., 2020;Chen et al., 2015).

Finally, interdisciplinary approaches highlighted the crucial role of long-distance transmission events likely due to humans in rabies dynamics in North Africa (Talbi et al., 2010) and also showed that main roads act as barriers to dog rabies dispersal in an urban setting in Africa (Laager et al., 2018). The sampling window and the spatial scale of the studies are highly variable. Thus, it is not possible to directly compare the velocity and diffusion coefficients amongst the different study settings.

a Depending on the study, estimates of RABV lineage velocity or diffusivity were obtained by estimating different dispersal statistics. Talbi et al. (2010) reconstructed for each branch of the phylogenetic tree the expected number of migrations between two locations using a discrete phylogeographic model. The authors multiplied these estimates by the great-circle distance between the two locations, and thus, obtained the expected distance travelled within the time elapsed on each branch. Carnieli et al. (2013), Bourhy et al. (2016), Brunker et al. (2018b), [START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF]Dellicour et al. (2019) estimated the mean branch velocity using continuous phylogeographic reconstructions. Finally, Dellicour et al. (2017) estimated the temporal evolution of the wavefront velocity that corresponds to the distance between the reconstructed epidemic origin and the maximal epidemic wavefront. While the mean branch velocity (v)

and diffusion coefficient (D) are estimates of the dispersal velocity and of the diffusion coefficient averaged over all tree branches, respectively, their weighted average counterparts involve a weighting by branch time resulting in lower-variance estimates (Dellicour et al., 2019).

b Depending on the study, the impact of environmental factors on dispersal of viral lineages were investigated using different approaches. (Talbi et al., 2010) Phylodynamic studies showed that introduction through infected dog movement is the major force of rabies spread towards disease-free areas, as Indonesia [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF]Dibia et al., 2015;Mahardika et al., 2014) and the Philippines (Tohma et al., 2014;[START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF] have recently experienced, and also represents a driver of rabies spread in endemic areas where frequent reintroductions counteract local rabies elimination after vaccination campaigns (Bourhy et al., 2016;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]. In these settings, phylodynamic analysis constitutes a powerful tool to confirm introduction events (Bourhy et al., 2016;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]Talbi et al., 2010;Mollentze et al., 2013;Hayman et al., 2011;Tohma et al., 2014). Multiple mathematical models have also shown that frequent reintroductions drive rabies persistence in endemic areas (Ferguson et al., 2015;Laager et al., 2019;Mollentze et al., 2014;Cori et al., 2018).

Population structure constitutes another driving force of rabies maintenance as explored in simulation studies integrating dog ecology data in Australian [START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Hudson et al., 2019b;Hudson et al., 2019a;Brookes et al., 2019), Japanese (Kadowaki et al., 2018), Tanzania [START_REF] Beyer | The implications of metapopulation dynamics on the design of vaccination campaigns[END_REF]Beyer et al., 2011) and Chadian (Laager et al., 2018) settings. Rabies-induced behavioral changes were shown to contribute to rabies persistence in small dog populations (Brookes et al., 2019) as well as differential roaming behavior, contact rates between dog strata and the structure of contact networks [START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Leung and Davis, 2017;Laager et al., 2018;Kadowaki et al., 2018;Brookes et al., 2019).

The contribution of wildlife to canine rabies spread and maintenance is rarely addressed in phylodynamic studies because viruses isolated from wildlife specimens often correspond to dog-related lineages (Tohma et al., 2014;Hayman et al., 2011;Yao et al., 2015;Zhang et al., 2017;Wang et al., 2019) or because of insufficient sampling efforts when it comes to wildlife (Yu et al. 2012; Table A1). Nevertheless, specific RABV lineages were shown to circulate both in wildlife and domestic dogs in the Middle East and Tanzania with complex interspecies transmissions (Horton et al., 2015;Troupin et al., 2016;Brunker et al., 2018b;Dellicour et al., 2019). A phylodynamic study at the global scale showed that host shifts from dogs to wildlife with adaptation to the new host were common in RABV history (Troupin et al., 2016), which may explain why different lineages circulate in dogs and wild foxes in Brazil (Carnieli et al., 2013), in dogs and ferret badgers in Asia (Huang et al., 2019) and in dogs and mongooses in South Africa (Troupin et al., 2016) with rare interspecies transmission events. By incorporating direct interspecies transmission, mathematical modeling studies showed that dog population contributes to sustained rabies circulation in wildlife instead of the other way around (Huang et al., 2019;Fitzpatrick et al., 2012). Similarly, the proximity to wildlife was shown to not impact rabies spread in dogs in the model of [START_REF] Beyer | The implications of metapopulation dynamics on the design of vaccination campaigns[END_REF].

Finally, mathematical models and phylodynamics provide convenient estimates of a range of parameters on rabies dispersal dynamics (lineage dispersal velocities, diffusion coefficients; in Table 1), rabies evolutionary processes and dog ecology. For example, the evolutionary rate was homogeneously estimated to be between 1 × 10 -4 and 5 × 10 -4 substitutions per site per year across RABV genes and lineages, except for the Asian lineage which is estimated to evolve faster (Fig. 10A). The time to the most recent common ancestor (TMRCA) is also frequently estimated in phylodynamic studies (Table A2) which is generally more recent than suggested by historical records. R, the expected number of secondary infections, is often estimated by fitting case data to mathematical models (Fig. 10B) or by computing its value based on the choice of parameters value (Table A7). Its estimate ranges from 0.80 to 3.36 according to the setting but it is generally estimated to be between 1 and 2, corresponding to a low-grade transmission with frequent stochastic extinctions. Other parameters such as the dog-to-dog transmission rate, the introduction rate or the dog carrying capacity are also frequently estimated (Table A7).

Effective control strategies

Interdisciplinary and modeling studies generally assessed the impact of past or potential control strategies to eliminate dog rabies. The specifications of the explored control strategies depended on the economic situation of the country in which the study was supposed to be performed, as well as the model type. Dog vaccination was the most studied control measure (n = 28; [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF]Kitala et al. 2002;Coleman and Dye 1996;Zhang et al. 2012;Fitzpatrick et al. 2012;[START_REF] Beyer | The implications of metapopulation dynamics on the design of vaccination campaigns[END_REF][START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Ferguson et al. 2015;Chen et al. 2015;Sparkes et al. 2016;Leung and Davis 2017;Laager et al. 2018;Kadowaki et al. 2018;Laager et al. 2019;Beyene et al. 2019;[START_REF] Abdul Taib | Model Simulation for the Spread of Rabies in Sarawak, Malaysia[END_REF]Huang et al. 2019;Hudson et al. 2019a;Brookes et al. 2019;Carroll et al. 2010;Ortega et al. 2000;Hampson et al. 2007;Zinsstag et al. 2009;Zhang et al. 2011;Beyer et al. 2011;[START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF], whereas culling (n = 7; Dürr and Ward 2015; Sparkes et al. 2016;Hudson et al. 2019b;Carroll et al. 2010;Zinsstag et al. 2009;Zhang et al. 2011;[START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF], dog confinement or movement ban (n = 4;[START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Ferguson et al. 2015;Kadowaki et al. 2018;Hudson et al. 2019b), control of dog birth rate (n = 4; Abdul [START_REF] Taib | Model simulation for the spread of rabies in Sarawak, Malaysia[END_REF]Carroll et al. 2010;Zhang et al. 2011;[START_REF] Zhang | Spatial spread of rabies in China[END_REF]) and community behavior (n = 1; Ferguson et al. 2015) were rarely modelled. Culling was shown to be effective in two compartmental model studies (Carroll et al., 2010;[START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF] while vaccination was generally found to be the most effective strategy. Vaccination coverage strongly depends on the setting: 90% or complete dog vaccination coverages are recommended in rabies-free areas with

RABV lineage Reference

Genetic sequences Reproduction ratio high surveillance and control capacities whereas lower coverages associated with complementary strategies are recommended in endemic areas (Table 2). Nevertheless, the efficacy of vaccination strategies is mitigated by new introductions due to neighboring transmission or long-distance movements mediated by humans (Colombi et al., 2020;Townsend et al., 2013a;Ferguson et al., 2015;Laager et al., 2019;Bourhy et al., 2016;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]Knobel et al., 2013), notably in low vaccinated pop-ulations (Chen et al., 2015). In this case, reactive vaccination strategies [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF] or dog movement bans (Colombi et al., 2020) constitute alternative effective measures. However, Ferguson et al. (2015) evaluated the impact of new introductions in vaccinated areas, and concluded that vaccination coverages were robust to rabies introduction in their specific setting. Similarly, Beyer et al. (2011) suggested that the spatial structure of dog population had more impact than rabies introduction on the efficacy of vaccination campaigns. In terms of vaccination coverage, successful vaccination campaigns should target homogeneous coverage since hidden pockets of rabies transmission might jeopardize control efforts [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF]Kitala et al., 2002;Townsend et al., 2013a;Ferguson et al., 2015). In terms of campaign frequency, the efficacy of pluriannual compared to annual vaccination campaigns is difficult to evaluate as it results from many factors including the number of vaccination pulses, the time interval between each pulse, dog birth rate and the introduction rate of infectious animals (Kitala et al., 2002;[START_REF] Beyer | The implications of metapopulation dynamics on the design of vaccination campaigns[END_REF]Carroll et al., 2010). The optimal control strategy inherently depends on the epidemiological context (endemic or introduction in previously rabies-free areas), the setting (local surveillance and vaccination capacities), the assumptions of the dog rabies model and the control strategies tested by the researchers. Here, we report the strategies recommended by the authors which include quantitative and qualitative criteria such as the estimated impact of public awareness on rabid dog detection and management. Three studies (Carroll et al., 2010;Leung and Davis, 2017;Townsend et al., 2013a) are not grounded in a specific geographical area. Using simulated scenarios, they test the impact of control strategies according to the time to detection (Townsend et al., 2013a), dog population structure (Leung and Davis, 2017) and the use of immunocontraceptives (Carroll et al., 2010). Recent studies [START_REF] Beyer | The implications of metapopulation dynamics on the design of vaccination campaigns[END_REF]Leung and Davis, 2017;Laager et al., 2018;Kadowaki et al., 2018;Hudson et al., 2019b;Hudson et al., 2019a) proposed targeting at-risk dog populations, such as explorers and roaming dogs, to improve the efficacy of vaccination campaigns (Table 2). However, the sensitivity analysis of Laager et al. (2019) showed that population structure did not impact the efficacy of vaccination strategies. There are conflicting results concerning stray dog vaccination which was either less efficient than owned dog vaccination [START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF] or dependent on population composition (Leung and Davis, 2017).

Several studies also suggested an impact of dog birth rate reduction on the incidence of rabies (Abdul [START_REF] Taib | Model simulation for the spread of rabies in Sarawak, Malaysia[END_REF]Huang et al., 2019;Carroll et al., 2010;Zhang et al., 2011;Kitala et al., 2002;Zhang et al., 2012). However, the cost and feasibility of dog population management strategies such as sterilization render this unfeasible in many settings (Taylor et al., 2017b). Dog confinement, which is generally spontaneously put in place by local communities during rabies outbreaks, may improve elimination prospects but, when implemented, the level of confinement is not sufficient to reach elimination (Colombi et al., 2020;[START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Ferguson et al., 2015). Concerning the rabies burden in humans, some studies recalled the importance of public awareness (Table 2) and proper PEP coverage to reduce the number of human cases, even though it does not impact rabies circulation in dogs (Zhang et al., 2012;Laager et al., 2018;Kadowaki et al., 2018;Huang et al., 2019). All these findings confirmed and justified the strategic plan that provides a phased, all-inclusive, intersectoral approach to eliminate human deaths from rabies recently launched by United Against Rabies, in a collaboration between four partners: WHO, FAO, OIE and GARC (Cleaveland and Hampson, 2017).

Discussion

Insights on rabies epidemiology and control

In this review, we assessed the respective contributions of mathematical modeling and phylodynamics to the understanding of rabies spread and control in dog populations. Contrary to phylodynamic studies, mathematical modeling approaches were multi-faceted and mainly addressed the efficacy of control strategies and, less frequently, the drivers of rabies spread. They revealed the crucial role of frequent introductions and the potential role of dog population structure in disease dispersal and maintenance, as well as the overwhelming efficacy of dog vaccination campaigns over other control strategies. Certain studies also estimated key parameters of rabies dynamics and dog ecology, such as dog birth rate or dog carrying capacity. On the other hand, phylodynamic studies mostly focused on the description of viral dynamics at the global, regional, and local scales, and recently tested which environmental factors are impacting RABV spread. These approaches consistently unraveled the occurrence of long-distance movements suspected to be human-mediated and confirmed the role of humans in rabies dispersal dynamics in Africa and the Middle East. A third kind of studies either combined phylodynamics and mathematical modeling or presented new models integrating epidemiological and genetic data. In the former approach, hypotheses on rabies spread were generated and tested in the same epidemiological context, and thus, confirmed the impact of introductions and human movements in a low-grade transmission process characterized by small clusters and frequent stochastic extinctions. The latter approaches aimed at reconstructing local transmission chains or clusters, opening new horizons on data integration and the study of rabies (Fig. 11). Unfortunately, a large number of endemic countries is still not, or poorly studied. Data collection and/or model formulation are still needed in Russia, and most of Africa, and South-East Asia.

Figure 11: Visual summary of the uses of epidemiological data, environmental data and RABV genetic sequences for the study of rabies dynamics and control. Epidemiological data, environmental data, RABV genetic sequences and social sciences data are highlighted in cyan, yellow, pink, and brown, respectively. The section corresponding to models combining epidemiological data and RABV genetic sequences only is colored in grey since no study that meets this criterion has been identified using our search strategy. Models and their contributions to the understanding of rabies spread and control are detailed in the colored tags. Models using multiple types of data are colored with the intersection color of the corresponding data types. In our text corpus, few studies combined epidemiological, ecological, and genetic data in a unified framework.

The limitations of our review should be acknowledged. In preliminary analyses, we noticed a high variability in record selection according to the combination of search terms, and certainly due to the ambiguous use of specific terms such as phylodynamics in the literature. Since the studies selected in this review are mainly in line with previous reviews (Brunker et al., 2018a;Rattanavipapong et al., 2019;Fisher et al., 2018), we argue that we retrieved a large part of the available studies on rabies dynamics and control.

Open questions in rabies epidemiology and control

In this review, we summarized the findings of mathematical modeling and phylodynamics on the factors that impact rabies spread. Nevertheless, the full picture of rabies epidemiology remains unclear. First, the role of dog roaming behavior, and dog contact networks in dog rabies spread should be further investigated. In this review, we identified seven studies (Sparkes et al., 2016;Leung and Davis, 2017;Laager et al., 2018;[START_REF] Wilson-Aggarwal | High-resolution contact networks of free-ranging domestic dogs Canis familiaris and implications for transmission of infection[END_REF]Hudson et al., 2019a;Brookes et al., 2019;Carroll et al., 2010), all situated in Australia and Africa, showing that highly connected dogs or free roaming dogs participate in a large part in the spread of the disease. By specifically targeting this type of dogs, vaccination campaigns could be more effective according to Leung and Davis (2017), Laager et al. (2018), andHudson et al. (2019a). Yet only one study combined contact data with epidemiological data (Laager et al., 2018). The ecological and behavioral drivers of rabies circulation in domestic dogs are still not fully understood. If stray dogs do constitute a major driver of rabies dispersal, this could have direct implications on the field concerning stray dog population management for example.

Additionally, the role of wildlife and other host species remains unclear (Rupprecht et al., 2019). Even though the circulation of dog rabies seems predominant in dog populations, there are too few studies addressing the dynamics of RABV in wildlife and dogs. Furthermore, the interactions between dogs and other carnivore species are expected to change from location to location. Indeed, the interactions between dog populations and wild carnivores depend on the abundance of wild populations and the frequency of contacts between the dog reservoir and wildlife (Fitzpatrick et al., 2012;Huang et al., 2019). Better understanding the role of wildlife could also have direct implications on local policies such as increasing public awareness, notably in rural areas or strengthening wildlife surveillance systems for rabies.

At a broader scale, the spatial dynamics of rabies are still poorly understood. Urban areas were first thought to be hubs of rabies transmission but recent studies have shown that rabies could be eliminated temporarily at the city-level through mass dog vaccination campaigns (Laager et al., 2019;Bourhy et al., 2016;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]. These case studies suggest that urban areas are not hubs of rabies transmission but part of the complex spatial heterogeneity of dog ecology and dog movement. By exploring the dynamics of dog rabies circulation in urban, peri urban and rural areas, rabies research could see an improved understanding of rabies ecology. This could have direct implications on the design of vaccination campaigns, by prioritizing vaccination campaigns in hubs of rabies transmission, followed by locations with intermediate and low transmission.

Finally, there is extensive evidence of the efficacy of dog vaccination to control the spread of rabies in both human and dog populations. We showed in this review that higher coverages are recommended in rabies-free areas than in endemic areas, however, the practicalities of vaccination campaigns are rarely addressed. As a neglected tropical disease, rabies control programs are designed and deployed in resource-limited contexts. Thus, high, and even intermediate vaccination coverages cannot be achieved at once over a large area. The periodicity, the spatial prioritization, the targeted populations, and the association with other control strategies (dog population management, dog movement ban. . . ) are interesting modalities that could be tested in models and could substantially improve resource allocation.

Future directions of mathematical modeling and phylodynamics for rabies research

There is an evident lack of extensive and adequate databases possibly due to restricted data collection, data accessibility and/or data analysis capacity in resource-limited settings ("Aiming for elimination of dog-mediated human rabies cases by 2030" 2016; Hampson et al., 2019a). This constitutes the main weakness of mathematical modeling and phylodynamic studies that we identified in this review (Table 3). Epidemiological and ecological (census data, population structure, contact networks) data are needed to account for local specificities in terms of modeling interactions between rabies virus (RABV), dog reservoir, domestic animals, wildlife reservoir and human populations. Similarly, there is a need for longer RABV genetic sequences and more thorough sampling to discriminate fine-scale migration events and better characterize the interactions between RABV lineages (Brunker et al., 2015;Brunker et al., 2018a;[START_REF] Brunker | Rapid in-country sequencing of whole virus genomes to inform rabies elimination programmes[END_REF]. Improving operational data collection is nevertheless challenging.

Genomic surveillance relies on laboratory infrastructures, supply chains and expertise, all of which are costly and generally lacking in low-and middle-income countries. New portable sequencing technologies combined with bioinformatics workflows could accelerate capacity building through portability and affordability [START_REF] Brunker | Rapid in-country sequencing of whole virus genomes to inform rabies elimination programmes[END_REF][START_REF] Gigante | Portable Rabies Virus Sequencing in Canine Rabies Endemic Countries Using the Oxford Nanopore MinION[END_REF]. In parallel, potential sampling bias effects should not be overlooked (Ishikawa et al., 2019;Lemey et al., 2009a) since they may hide a part of dis- • Integration of the waning of vaccine-induced immunity

• No direct comparison of rabies dynamics due to the diversity of models ease dynamics such as silent spread in deprived rural areas. Additionally, many endemic countries with high human incidence (Russia, Malaysia, Cambodia, Burma, Niger, Mozambique, etc.) [START_REF] Hampson | Estimating the Global Burden of Endemic Canine Rabies[END_REF] remain largely unstudied using quantitative approaches. This represents an opportunity for data collection, rabies dynamics characterization and control strategy optimization. Besides filling knowledge gaps, improving the availability of epidemiological, ecological, and genetic data offers an opportunity to strengthen countries' veterinary surveillance capacities (Welburn et al., 2017) and enhance the impact assessment of control strategies, two pillars of the 2030 strategic elimination plan.

Other data types such as social sciences data could help identify knowledge gaps and refine control measures to be tested further using mathematical models. For example, there is little quantitative evidence of the impact of community response on the efficacy of control measures (Rupprecht et al., 2019), although it is key to human rabies prevention (Hasanov et al., 2018;Bardosh, 2014) and it is expected to change over rabies outbreaks and affect rabies dynamics. By bridging the two disciplines, alternative control strategies that are both effective and adapted to community preferences could be designed (Degeling et al. 2018;Fig. 11).

Finally, novel methodologies combining genetic, epidemiological, and environmental data in a comprehensive analysis framework are promising tools for the rabies field. Indeed, the interdisciplinary studies identified in this review exploited the complementarity of genetic and epidemiological information to efficiently generate and test hypotheses on the mechanisms of rabies dynamics (Talbi et al., 2010;Mollentze et al., 2014;Cori et al., 2018;[START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF][START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF], and the limitations of control strategies (Bourhy et al., 2016;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]. These new avenues represent a significant improvement on past studies and a promising opportunity for canine rabies research in the frame of a One Health concept that aims to achieve better public health outcomes through cross-sector collaboration.

Conclusions

In this review, we highlighted the need for more epidemiological, ecological, and genetic data to better characterize rabies dynamics and to get practical information on the drivers of disease transmission.

We think that the development of new methodologies integrating genetic and epidemiological data, or the combined use of mathematical models and phylodynamics, constitutes a promising approach that could ultimately contribute to the improvement of the efficacy of control measures including vaccination campaigns and help optimizing the allocation of resources in a context of limited funding.

Chapter 2

Phylodynamics to characterize RABV endemic circulation in Cambodia

In epidemiology, endemicity characterises sustained pathogen circulation in a geographical area, which involves a circulation that is not being maintained by external introduction. Because it could potentially shape the design of public health interventions, there is an interest in fully uncovering the endemic pattern of a disease. Here, we use a phylogeographic approach to investigate the endemic signature of RABV circulation in Cambodia. Cambodia is located in one of the most affected regions in the world, but RABV circulation between and within Southeast Asian countries remains understudied in the area. Our analyses are based on a new comprehensive data set of 199 RABV genomes collected between 2014 and 2017 as well as previously published Southeast Asian RABV sequences. We show that most Cambodian sequences belong to a distinct clade that has been circulating almost exclusively in Cambodia. Our results thus point toward rabies circulation in Cambodia that does not rely on external introductions, which could have concrete implications in terms of mitigation strategy in the region. More globally, our study illustrates how phylogeographic investigations can be performed to assess viral endemicity in a context of relatively limited data.

Introduction

From an epidemiological perspective, endemicity corresponds to the sustained circulation of a pathogen in a geographical area (Disease [START_REF] Control | Principles of Epidemiology in Public Health Practice, Third Edition: An Introduction[END_REF], implying that it does not need external introductions. Determining how the circulation of a pathogen is maintained at a local scale can have direct epidemiological implications on its surveillance and control strategies. For instance, the evaluation of the origin of dog rabies cases, either due to importations from neighboring areas or due to cryptic local transmission chains, has been crucial to demonstrate that vaccination campaigns at the city level can interrupt rabies transmission for several months, as exemplified in N'Djamena [START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF] and Bangui (Bourhy et al., 2016). In that context, phylogeographic approaches extracting information from pathogen genomic sequences constitute powerful tools to discriminate importation from local circulation of viral lineages. Phylogeographic investigations can however be impacted by heterogeneous sampling effort and sampling bias [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF][START_REF] Kalkauskas | Sampling bias and model choice in continuous phylogeography: Getting lost on a random walk[END_REF][START_REF] Liu | The impact of sampling bias on viral phylogeographic reconstruction[END_REF]Layan et al., 2022), confronting researchers with the challenge being to mitigate or to take into account their effects on the outcomes and conclusions of those analyses [START_REF] Faria | Establishment and cryptic transmission of Zika virus in Brazil and the Americas[END_REF][START_REF] Vrancken | Comparative Circulation Dynamics of the Five Main HIV Types in China[END_REF][START_REF] Guindon | Accounting for spatial sampling patterns in Bayesian phylogeography[END_REF].

Rabies is a fatal zoonosis affecting mammals with dogs constituting the main reservoir of its causal agent, the rabies virus (RABV). It has been estimated that dog-related rabies causes approximately 59,000 human deaths per year worldwide [START_REF] Hampson | Estimating the Global Burden of Endemic Canine Rabies[END_REF] despite the existence of effective dog and human vaccination, as well as human postexposure prophylaxis (World Health Organization (WHO), 2018).

The global burden mostly affects African and Asian countries where resources are limited to sustain long-term control efforts. In such contexts, extensive surveillance data are often scarce and molecular epidemiological approaches can therefore constitute useful and complementary tools to unravel the dynamics of viral circulation [START_REF] Layan | Mathematical modelling and phylodynamics for the study of dog rabies dynamics and control: A scoping review[END_REF]. Over the past decade, several studies have explored the patterns of RABV circulation in diverse endemic settings. While circulation is spatially-clustered in northern African countries and likely driven by human-mediated dispersal events (Talbi et al., 2010;Dellicour et al., 2017), multiple viral lineages co-circulate in Iran due to the co-occurrence of dog and wildlife reservoirs and the geographical location of Iran being at the crossroads of Asian, Middle-East, and European countries (Dellicour et al., 2019). In Tanzania, RABV circulation is restricted to dogs and maintained at the local scale by well-interconnected dog populations (Brunker et al., 2018b). The mechanisms underlying viral maintenance are context-specific and may involve frequent introductions from neighboring countries, long-distance human-mediated movements, wildlife reservoirs, sustained trans-mission in highly and heterogeneously mixing dog populations, etc. Understanding these mechanisms could assist countries in prioritizing long-term surveillance efforts or adopting new regulations on dog trade and movement.

Cambodia has one of the highest dog bite and human rabies incidences in the world [START_REF] Ly | Rabies Situation in Cambodia[END_REF][START_REF] Ponsich | A prospective study on the incidence of dog bites and management in a rural Cambodian, rabies-endemic setting[END_REF][START_REF] Chevalier | Large scale dog population demography, dog management and bite risk factors analysis: A crucial step towards rabies control in Cambodia[END_REF], with a rabies circulation that remains uncontrolled due to the lack of a national prevention and surveillance program, which together maintains a cycle of neglect [START_REF] Li | Descriptive assessment of rabies post-exposure prophylaxis procurement, distribution, monitoring, and reporting in four Asian countries: Bangladesh, Bhutan, Cambodia, and Sri Lanka, 2017-2018[END_REF]. Fortunately, Cambodia has integrated the Asian Rabies Control Network (ARACON) in 2018 [START_REF] Coetzer | Formation of the Asian Rabies Control Network (ARACON): A common approach towards a global good[END_REF], and recent actions by stakeholders of rabies surveillance and control have been implemented to move towards the elimination goal. For example, a recent study has evaluated the implementation of a hospital-based dog bite case management [START_REF] Tazawa | Evaluation of the Risk of Rabies in Human Victims through Implementation of Integrated Bite Case Management System in Phnom Penh, Cambodia[END_REF]. To improve vaccination accessibility, the Institut Pasteur du Cambodge (IPC) has recently created two additional vaccination centers in Battambang ( 2018) and Kampong Cham (2019), specifically targeting poor and rural populations, and organized a large communication campaign to raise awareness about rabies transmission and prevention (www.pasteur-kh.org/rabies-prevention-centers). IPC has also been instrumental for the development and promotion of a shortened rabies post exposure regimen that is now recommended by WHO [START_REF] Cantaert | A 1-week intradermal dose-sparing regimen for rabies post-exposure prophylaxis (RESIST-2): an observational cohort study[END_REF][START_REF] Tarantola | Intradermal rabies post-exposure prophylaxis can be abridged with no measurable impact on clinical outcome in Cambodia, 2003-2014[END_REF]. Still, several knowledge gaps persist concerning the epidemiological situation in Cambodia due to the scarcity of epidemiological and RABV genetic data. To our best knowledge, only one study has described dog-related RABV lineages in Cambodia [START_REF] Mey | Evidence of two distinct phylogenetic lineages of dog rabies virus circulating in Cambodia[END_REF], which mostly belong to the SEA-1 lineage (Troupin et al., 2016) along with RABV sequences isolated in Thailand, Vietnam, and Laos. This first phylogenetic study suggests that there is a substantial circulation of dog RABV between Southeast Asian countries.

While rabies is known to sustainably circulate in Cambodia, the importance of external RABV introduction events from surrounding countries as well as the dispersal dynamics of the virus at the country scale have not yet been investigated. In the present study, we propose to implement and apply phylogeographic approaches to characterize those aspects and evaluate the endemicity pattern of RABV in Cambodia, with the goal to improve our understanding of the important public health burden associated with rabies in that region. For this purpose, we generate and analyze a new data set of RABV genomes isolated from infected dogs in Cambodia. Specifically, we aim to exploit this comprehensive data set to (i) assess the contribution of introduction events from neighboring countries, (ii) evaluate the dynamics of spatial spread at the country level, (iii) formally compare the dispersal capacity of the virus with other regions of the World, and (iv) test the impact of key environmental factors on local viral circulation.

Methods

Samples collection

As part of the rabies surveillance in Cambodia, brain samples from suspected rabid dogs were sent to the Virology unit at IPC where rabies diagnosis activity has been performed routinely since 1998 [START_REF] Mey | Evidence of two distinct phylogenetic lineages of dog rabies virus circulating in Cambodia[END_REF]). Dog's heads were usually referred to the IPC lab from people who were consulting for post-exposure prophylaxis treatments following animal bite. The animal samples were tested by a standard direct fluorescent antibody test (DFAT) as previously described [START_REF] Duong | Laboratory diagnostics in dog-mediated rabies: an overview of performance and a proposed strategy for various settings[END_REF]. Positive brain samples collected from 2012 to 2017 were selected for sequencing as described below. Before submitting samples for sequencing, all selected samples were tested using a RT-qPCR for detecting RABV [START_REF] Dacheux | Dual Combined Real-Time Reverse Transcription Polymerase Chain Reaction Assay for the Diagnosis of Lyssavirus Infection[END_REF].

Procedure to select samples to sequence

627 positive brain samples were collected between 2012 and 2017 across Cambodia by the IPC, with the possibility to sequence 208 of them. At the beginning of this study, all 33 samples collected in 2017 had already been sequenced, and we subsequently aimed at selecting 2012-2016 samples while maximizing the spatio-temporal coverage in the perspective of phylogeographic analyses. For this purpose, we implemented a Markov process to select 35 samples per year while maximizing the sum D of great-circle distances along the edges of a Delaunay triangulation network connecting all selected samples. The algorithm started by selecting all samples along the spatial limits of the minimum convex hull polygon built around all the samples, as well as a random set of sequences within that polygon. At each iteration i, the algorithm then changed one selected sample per year, randomly replaced by another sample collected the same year, and re-computes the sum D i on the resulting Delaunay triangulation network. Similarly to the SAMOVA algorithm developed by [START_REF] Dupanloup | A simulated annealing approach to define the genetic structure of populations[END_REF] for population genetic clustering analyses, the new selection is accepted with probability p = 1 if D increased since the last iteration, and with the following probability if D did not increase:

p = e (D i -D i-1 )S A (2.1)
where S is the number of iterations performed so far in the process, and A is an arbitrary constant controlling the speed of what is called a "cooling process", here implemented to avoid becoming trapped at a local optimum [START_REF] Dupanloup | A simulated annealing approach to define the genetic structure of populations[END_REF]. The Markov process was run for 100,000 iterations, and we performed 1,000 independent repetitions of the algorithm starting each time with a different initial subsampling.

Full genome sequencing

Total RNA extraction done on brain samples was performed according to [START_REF] Marston | Next generation sequencing of viral RNA genomes[END_REF] with modifications. Briefly, brain samples were crushed into 1 ml of TRI Reagent (Sigma). After addition of 200 µl of chloroform and centrifugation at 12,000 rpm for 15 min at 4°C, the aqueous phase was collected and added to an equal volume of ethanol 70% before RNA extraction and purification using RNeasy Mini Kit (Qiagen). Genomic host DNA was depleted from purified RNA by a DNAse I treatment using the DNA-free Kit (Ambion) and following the manufacturer's instructions. Depleted RNA was finally purified using Agencourt RNAclean XP beads (Beckman Coulter) at a ratio of 1:1.8, following the manufacturer's instructions and eluted with 20 µl of nuclease-free water.

Genome sequences were obtained using next generation sequencing (NGS) as previously described (Dacheux et al., 2019;[START_REF] Luo | Characterization of Novel Rhabdoviruses in Chinese Bats[END_REF] with minor modifications. After RNA extraction, a ribosomal RNA depletion step was first carried out with 2-4 µg of RNA and 1 µl of Terminator 5'-Phosphate-Dependent Exonuclease (Epicentre Biotechnologies), in addition to 2 µl of buffer A and 0.5 µl of RNAsin Ribonuclease inhibitor (Promega). After being adjusted to 20 µl with nuclease-free water, the mix was incubated for 1h at 30°C. The depleted RNA was then purified using Agencourt RNAclean XP beads (Beckman Coulter) at a ratio of 1:1.8, following the manufacturer's instructions. Reverse transcription in complementary DNA (cDNA) of purified RNA was then done using the SuperScript III First-Strand Synthesis SuperMix kit (Invitrogen) according to the manufacturer's instructions. For this step, 8 µl of RNA was first incubated at 65°C for 5 min with 1 µl of Annealing Buffer (Invitrogen) and 80µl) of dsDNA was finally purified for each virus, using a ratio of 1:1.8 of AMPure XP beads (Beckman the R package "adephylo" [START_REF] Pavoine | Testing for phylogenetic signal in phenotypic traits: New matrices of phylogenetic proximities[END_REF]. We compared the prior and posterior distributions in Appendix B.

Spatially-explicit phylogeographic reconstruction

Continuous phylogeographic analyses were performed with the relaxed random walk (RRW) diffusion model [START_REF] Lemey | Phylogeography takes a relaxed random walk in continuous space and time[END_REF][START_REF] Pybus | Unifying the spatial epidemiology and molecular evolution of emerging epidemics[END_REF] implemented in BEAST 1.10 (Suchard et al., 2018) coupled with the high-performance computing library BEAGLE 3 [START_REF] Ayres | BEAGLE 3: Improved Performance, Scaling, and Usability for a High-Performance Computing Library for Statistical Phylogenetics[END_REF]. Branch-specific evolutionary rates and the nucleotide substitution process were again modeled according to a relaxed molecular clock with an underlying log-normal distribution and to a GTR+Γ4 parameterization, respectively. We used a gamma distribution to model the among-branch heterogeneity in diffusion velocity, and a flexible skygrid coalescence model for the tree topology, the latter enabling the inference of changes in the effective viral population size over time. The Markov chain Monte-Carlo (MCMC) algorithm was run for 15 × 10 7 generations for the analysis based on the full genome data set and for 4 × 10 8 generations for the analysis based on the N gene sequence data set, sampling every 15 × 10 4 generations in both cases.

We again used the program Tracer 1.7 to assess the convergence/mixing properties (and to ensure that ESS values associated with relevant parameters were all >200), as well as the program TreeAnnotator 1.10 to obtain and annotate the MCC tree. We used the R package "seraphim" (Dellicour et al., 2016a) to extract the spatiotemporal information embedded within posterior trees, to visualize the continuous phylogeographic reconstructions, and to estimate the weighted lineage dispersal velocity (WLDV), the latter being defined as follows:

v weighted = ∑ n i=1 d i ∑ n i=1 t i (2.2)
where d i is the geographic distance traveled along the phylogeny branch, and t i the duration of that branch, respectively. As detailed in the Results section, we also computed WLDV estimates while considering increasing cut-off values defining the maximal geographic distance that can be traveled by a phylogenetic branch to be included in the estimation.

Landscape phylogeographic analyses

We applied two previously described analytical procedures to investigate the impact of environmental factors on the dispersal location (Dellicour et al., 2019) and velocity (Dellicour et al., 2017) of viral lineages. Both analytical procedures are based on the comparison between 1,000 spatially-annotated trees sampled from the post-burn-in posterior distribution of trees inferred by a continuous phylogeographic analysis, hereafter referred to as "inferred trees", and the same tree topologies along which we simulated a RRW diffusion process [START_REF] Dellicour | Epidemiological hypothesis testing using a phylogeographic and phylodynamic framework[END_REF], hereafter referred to as "simulated trees". These RRW simulations were performed with the "simulatorRRW1" function of the R package "seraphim" and based on the sampled precision matrix parameters estimated by the phylogeographic analyses (Dellicour et al., 2018a). For each tree, the RRW simulation started from the position inferred at the root node and was constrained such that the simulated node positions remained within the study area, which was here defined by the minimum convex hull built around all node positions, avoiding non-accessible sea areas.

The purpose of these simulations is to obtain spatially-annotated trees corresponding to the trees inferred by continuous phylogeography but along which we generated a new diffusion process that has not been impacted by environmental factors.

We first investigated whether viral lineages tended to avoid or preferentially circulate within areas associated with particular environmental conditions. For this purpose, we extracted and subsequently averaged the environmental values at the tree node positions to obtain, for each environmental factor, a posterior distribution of mean environmental values at tree node positions. We then compared values obtained through inferred trees and their corresponding simulated trees using an approximated Bayes factor (BF) support [START_REF] Suchard | Models for Estimating Bayes Factors with Applications to Phylogeny and Tests of Monophyly[END_REF]: BF = p e /(1-p e ) 0.5/(1-0.5) . To test if a particular environmental factor e tended to attract viral lineages, p e was defined as the frequency at which the environmental values from inferred trees were greater than values from simulated trees; and to test if a particular environmental factor e tended to repulse viral lineages, p e was defined as the frequency at which the environmental values from inferred trees were lower than values from simulated trees. We considered BF values > 20 as strong statistical supports [START_REF] Kass | Bayes Factors[END_REF].

Second, we investigated to what extent viral lineage dispersal velocity was impacted by environmental factors acting as conductance or resistance factors. For each branch in the inferred and simulated trees we calculated an "environmental distance" using the path model implemented in the program Circuitscape [START_REF] Mcrae | Isolation by Resistance[END_REF]. This path model is based on circuit theory and allows accommodating uncertainty in the travel route. An environmental distance was first computed from each environmental raster, and then from a uniform "null" raster whose cell values are all set to 1. The environmental distance is a spatial distance that is weighted according to the values of the underlying environmental raster, and therefore constitutes a proxy for geographical distance when computed on the null raster. Each environmental variable was considered twice: once as a potential conductance factor that facilitates movement, and once as a potential resistance factor that impedes it. For each environmental variable, we also generated and tested several distinct rasters by transforming the original raster cell values with the following formula:

v t = 1 + k(v o /v max )
, where v t and v o are the transformed and original cell values, and v max the maximum cell value recorded in the raster. The rescaling parameter k here allows the definition and testing of different strengths of raster cell conductance or resistance, relative to the conductance/resistance of a cell with a minimum value set to 1, which corresponds to the null raster. For each environmental variable, we generated three distinct rasters using the following values for rescaling factor k: k = 10, 100, and 1000. For these analyses, we estimated the statistic Q defined as the difference between the coefficient of determinations obtained (i) when branch durations are regressed against the environmental distances computed on an environmental, and (ii) when branch durations are regressed against the environmental distances computed on the null raster. We estimated a Q statistic for each environmental raster and each of the 1,000 trees sampled from the posterior distribution. An environmental factor was only considered as potentially explanatory if both its distribution of regression coefficients and its associated distribution of Q values were positive [START_REF] Jacquot | Bluetongue virus spread in Europe is a consequence of climatic, landscape and vertebrate host factors as revealed by phylogeographic inference[END_REF], i.e. with at least 90% of positive values. In this case, the statistical support associated with the resulting Q distribution was compared with the corresponding null distribution of Q values obtained when computing environmental distances for phylogenetic branches of simulated trees. Similar to the procedure used for the investigation of the impact of environmental factors on the dispersal locations of viral lineages, the comparison between inferred and simulated distributions of Q values was formalized by approximating a Bayes factor support.

Results

Samples selection and sequencing

We selected and sequenced 208 RABV specimens from the 627 brain isolates of confirmed infected dog cases collected by the IPC between 2012 and 2017. To select the samples to sequence, we developed and applied a Markov process aiming at maximizing the spatio-temporal coverage of the resulting sampling, thus optimizing it for phylogeographic investigations of the dispersal of viral lineages across the study area (Fig. B1).The final data set included 199 new full genome sequences as the PCR amplification or next-generation sequencing (NGS) was unsuccessful for nine specimens. Throughout the study, we either analyzed this full genome data set or a data set made of all Cambodian RABV nucleoprotein (N) genes available in GenBank and for which we managed to retrieve GPS coordinates associated with the sampling location. While the full genome data set offers the best phylogenetic and molecular clock signal, the N gene data consists of a larger number of sequences (n = 354) with a broader spatial and temporal coverage.

Investigating the endemic signature of RABV circulation in Cambodia

We first conducted a maximum likelihood phylogenetic inference to visualize the position of Cambodian lineages within an overall RABV phylogeny (Fig. B2). This analysis was based on our data set of Cambodian N gene sequences as well as a balanced subset of RABV N gene sequences retrieved from GenBank and collected in all continents. In the resulting tree, Cambodian sequences appear uniquely related to the Southeast Asian lineages, suggesting that, contrary to Vietnam [START_REF] Gigante | Portable Rabies Virus Sequencing in Canine Rabies Endemic Countries Using the Oxford Nanopore MinION[END_REF], neither the Cosmopolitan lineage nor the Chinese lineages circulate in Cambodia (Fig. B2).

We subsequently performed a discrete phylogeographic analysis to delineate Cambodian RABV clades resulting from a distinct introduction event into the country (Fig. 12). In this analysis, we included all dog related RABV N genes from Southeast Asian countries (i.e. Indonesia, Laos, Malaysia, Myanmar, Philippines, Thailand, and Vietnam) available in GenBank, and only considered two discrete locations:

"Cambodia" and "other countries", the latter encompassing all the other Southeast Asian countries. The vast majority of the Cambodian sequences (351 out of 354) were grouped within a unique large clade also containing three sequences sampled in Vietnam. We estimated that this clade was introduced in Cambodia around 1971, with a 95% highest posterior density (HPD) ranging from 1963 to 1979 (Fig. 12B-C).

Furthermore, we identified that, within our sampling, only three other Cambodian sequences resulted from distinct introduction events into the country (Fig. 12B). Our discrete phylogeographic analysis indicated that those three sequences resulted from two different introduction events in Cambodia that did not seem to have led to substantial onward local transmission (Fig. 12C). These results clearly point towards an endemic RABV circulation in Cambodia, i.e. a circulation that does not seem maintained or fueled by external introductions.

As a result of the comprehensive data set of genomic sequences generated in the present study, Cambodia is oversampled compared to its surrounding countries, which might affect the outcome and conclusions of the discrete phylogeographic analysis aiming at identifying distinct introduction events. In other words, the lower number of RABV genomes available for the surrounding countries could potentially lead to an underestimation of the lineage introductions into Cambodia. In that context, we performed further investigations to assess if the large clade of Cambodian sequences delineated in the discrete phylogeographic inference could indeed correspond to a clade reflecting local rabies circulation not or barely fed by viral exchanges from neighbouring countries. For this purpose, we visually compared the patristic distances computed for each pair of sequences coming (i) from the same country (except Cambodia), (ii) from two different countries (except Cambodia), as well as (iii) for all pairs of sequences belonging to the major Cambodian clade (Fig. 12A). The purpose of this comparison was to assess if the pairwise patristic distances computed within the major Cambodian clade corresponded to the range of intra-country patristic distances computed for the surrounding countries. Our results confirmed that this is the case and the distribution of inter-countries patristic distance did not overlap with the patristic distances computed within that clade (Fig. 12A). Interestingly however, we noticed small overlaps between the distribution of intra-country and inter-countries patristic distances. First, a small proportion of inter-countries patristic distances were lower than 300, which corresponded to a range of distance values mostly computed for intra-country patristic distances. Second, a small proportion of intra-country patristic distances were close or higher than 500, this time mostly corresponding to a range of distance values computed for inter-countries patristic distances (Fig. 12A). While in the first case it corresponded to pairs of sequences collected in different countries but relatively close to each other in the phylogenetic tree, in the second case it corresponded to pairwise patristic distances between samples collected in the same country but belonging to distinct clades within the tree. In the latter case, it corresponded to pairs of sequences resulting from distinct transmission chains that entered into the country by independent introduction events from aboard.

Unravelling the dispersal dynamics of RABV in Cambodia

We performed a continuous phylogeographic inference to analyze the dispersal dynamics of RABV lineages within Cambodia. In this analysis, we only included the Cambodian sequences belonging to the main Cambodian clade identified by our discrete phylogeographic analysis (Fig. 12B). The continuous phylogeographic reconstructions obtained from the analysis of full genomes and N genes are presented in Fig. 13A and 13B respectively. Compared to the full genome data set, the N genes data set covered a larger geographical area with more sequences at the Thai border, as well as a larger time period with sequences isolated between January 1998 and December 2017. For both continuous phylogeographic analyses, the uncertainty associated with the inference of ancestral locations was reported by overlapping shaded polygons colored according to their temporal occurrence. The same color scale was used to color the tree nodes according to their time of occurrence (inferred for the internal nodes and corresponding to the collection date for tip nodes). For the N genes data set, the uncertainty polygons were much smaller and even hidden by the tree nodes reported on the map. The smaller phylogeographic uncertainty associated with this data set is likely related to the higher number of samples included in the analysis. Both phylogeographic reconstructions, but the reconstruction based on the N genes in particular, highlight the Phnom Penh area as a crossroad of RABV lineage circulation. Indeed, most of the samples collected distantly from the area of Phnom Penh do not seem to be directly connected with each other within the phylogeny. In other words, those more remote samples seem to arise from distinct transmission chains emanating from the Phnom Penh area.

Secondly, we used the continuous phylogeographic reconstructions to estimate the weighted dispersal velocity of RABV lineages within Cambodia: 12.6 km/year (95% HPD = [11.0-14.3]) for the analysis based on the N genes, but only 6.7 km/year (95% HPD = [6.1-7.4]) for the analysis based on the full genomes. The fact that the two analyses led to different WLDV estimates despite a similar overall phylogeographic pattern (Fig. 13A-B), might be due to the wider geographical sampling of the N genes.

Indeed, wider sampling might increase the probability to sample long-distance lineage dispersal events that, on average, are more likely to include fast dispersal events pulling the WLDV estimate to higher values (see below for further discussion on this aspect). The phylogeographic inferences were performed using the skygrid coalescent model [START_REF] Gill | Improving Bayesian Population Dynamics Inference: A Coalescent-Based Model for Multiple Loci[END_REF] for the tree prior, which allowed us to get an estimation of the recent evolution of the effective viral population size. Our skygrid reconstructions indicated that there was a global increase of the effective RABV population size in the last 25-30 years (Fig. 13C-D).

Impact of long-distance lineage dispersal events on the estimation of dispersal velocity

With the objective to assess whether RABV lineage dispersal was slower in Cambodia relative to other geographic areas, we compared these estimates with the WLDV estimates previously obtained and reported for other RABV data sets (Fig. 14). As introduced above, we suspected that the spatial extent of a study area might have an impact on the frequency at which long-distance dispersal events were sampled, Specifically, we compare the weighted lineage dispersal velocity estimated for the following data sets: RABV in Cambodia (for both the full genomes and N genes data sets), northern Africa (Talbi et al., 2010), Tanzania (Brunker et al., 2018b), Iran (Dellicour et al., 2019), and Yunnan province in China [START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF]. (A) Evolution of the weighted lineage dispersal velocity when increasing the maximal geographic distance used as the cut-off value to select the lineage dispersal events for the estimation. Solid curves and shaded polygons represent the median and 80% highest posterior density (HPD) interval estimates, respectively. (B-D) Weighted lineage dispersal velocity estimates for different maximal geographic distance cut-off values (50, 100, and 200 km, respectively).

which in turn could affect the dispersal velocity estimate due to a higher probability of long-distance dispersal events to be associated with a higher dispersal velocity. Under this assumption, such a higher probability could potentially be explained by two non-exclusive hypotheses. First, short-distance lineage dispersal events are, on average, more likely to capture local circulation of a transmission chain, which would involve a higher probability to infer phylogenetic branches associated with a short geographic distance. Second, long-distance dispersal events could be fast because they were human-mediated, which has been suspected in the case of RABV dispersal in other regions of the world (Talbi et al., 2010;Dellicour et al., 2017).

In our comparisons of WLDV estimates, we then tried to take into consideration the spatial extent of the respective study areas. For this purpose, we implemented a comparative approach in which we estimated the WLDV metric associated with each data set while increasing a cut-off value defining the maximal geographic distance that can be traveled by a phylogenetic branch retained for the WLDV estimation (Fig. 14A). Overall, this analysis confirmed that when progressively increasing this cut-off, we indeed observe an increase in the WLDV value estimated for a given data set. However, the WLDV estimated for the full genomes data set barely increased with the cut-off value, which is likely due to the overall low frequency of long-distance lineage dispersal events inferred for that data set. Our WLDV estimates for the N genes data set appear however quite close to the estimates obtained for a RABV data set from Iran (Dellicour et al., 2019), and to some extent to the estimates obtained for a RABV data set from northern Africa (Talbi et al., 2010). For these three data sets, WLDV estimates tend to reach a WLDV plateau roughly ranging from 10 to 15 km/year when the cut-off value reaches 400 km (Fig. 14A; see also Fig. 14B-D for more direct comparisons based on specific cut-off values). In the light of those results, the dispersal velocity of RABV lineages does not seem particularly slower (nor faster) in Cambodia as compared with other regions of the world for which some equivalent estimates are currently available.

Investigating the impact of environmental factors on RABV dispersal

Finally, we took advantage of the spatially-explicit reconstructions of the dispersal history of RABV lineages in Cambodia to perform landscape phylogeographic analyses, which consisted in investigating the impact of environmental factors on the dispersal of viral lineages (Dellicour et al., 2018b). Specifically, we conducted two categories of analyses that aim at testing associations between environmental factors (Fig. 15) and (i) the dispersal velocity of viral lineages (Dellicour et al., 2017), or (ii) the dispersal location of viral lineages (Dellicour et al., 2019). The environmental factors included the main land use factors occurring in the study area (forests, savannas, grasslands, croplands, water areas), two global climate variables (mean annual temperature, annual precipitation), elevation, and human population density (see Table B1 for the source of the environmental data).

The first analyses led to some consistent results obtained when analyzing the full genomes and N genes data sets: they indicated that RABV lineages tended to avoid circulation in areas associated with relatively higher forest and savanna coverages (Bayes factors [BFs] > 20), and to preferentially circulate in areas associated with a relatively higher cropland coverage, human population density, and annual mean temperature (BFs > 20; Table B2). The analyses based on the N genes data set alone also return some support (BFs > 20) for a tendency of RABV lineages to avoid circulating in areas associated with relatively higher elevation and annual precipitation (Table B2). On a cautionary note, because their outcomes are strongly influenced by the sampling effort and pattern, those first analyses are somehow more a description of the environmental conditions related to the dispersal locations of inferred viral lineages than an actual test of the impact of those conditions on the dispersal (Dellicour et al., 2019). Consistently between the full genomes and N genes data sets, the second analyses of the dispersal velocity of viral lineages did not highlight any supported association between the environmental layers tested as either conductance or resistance factors and the heterogeneity in the lineage dispersal velocity (Tables B3 andB4). Elevation is reported in meters, mean annual temperature is reported in Celsius degrees, and annual precipitation is reported in meters per year.

Discussion

By quantifying external introductions and assessing their role relative to local transmission, the degree of endemic circulation of a disease can be determined in a given geographic area. As illustrated in the present study, phylogeographic approaches allow to objectify to what extent the local circulation of fastevolving pathogens such as RNA viruses is fueled by external introduction events. Such approaches have for instance been broadly applied to tackle similar questions in the context of the COVID-19 pandemic [START_REF] Attwood | Phylogenetic and phylodynamic approaches to understanding and combating the early SARS-CoV-2 pandemic[END_REF]. It is worth noting that modeling approaches that rely on contact tracing data can also be used to study the role of imported cases to local dynamics, but data collection requires extensive active surveillance efforts [START_REF] Lembo | Exploring reservoir dynamics: a case study of rabies in the Serengeti ecosystem[END_REF][START_REF] Hampson | Transmission Dynamics and Prospects for the Elimination of Canine Rabies[END_REF][START_REF] Mancy | Rabies shows how scale of transmission can enable acute infections to persist at low prevalence[END_REF].

From a public health perspective, continuous RABV circulation in dog populations and frequent human infections correspond to sufficient criteria to consider the disease endemic in several African and Asian countries. However, RABV circulation may not solely rely on within-country transmission, and molecular epidemiological studies have shown that RABV often crosses country borders, sometimes likely driven by human movements (Lemey et al., 2009b;Talbi et al., 2010;Zhang et al., 2017). In addition, foreign introductions can lead to the local establishment of new lineages resulting in the co-circulation of multiple independent lineages in the long-term. The Indonesian island Bali exemplifies how rare events of RABV introductions can lead to the establishment of endemic transmission [START_REF] Susilawathi | Epidemiological and clinical features of human rabies cases in Bali 2008-2010[END_REF].

Foreign introductions could also be a driver of sustained RABV circulation if transmission chains rapidly go extinct. Indeed, a recent modeling study of contact tracing data in dogs showed that RABV circulates at a very low level in dog populations in the Serengeti district in Tanzania and most transmission chains rapidly die out, which would lead to the interruption of transmission without recurrent introductions from neighboring areas [START_REF] Mancy | Rabies shows how scale of transmission can enable acute infections to persist at low prevalence[END_REF]. A similar observation was made in Bangui where control measures successfully eliminated rabies over several months but each time resurged due to introductions from neighboring areas (Bourhy et al., 2016;Colombi et al., 2020). In brief, the mechanisms of sustained circulation very likely depend on the geographical scale as well as geographic context of transmission at which it occurs.

Our results point out that RABV in Cambodia represents a remarkable case of endemicity with presumably very few external introductions feeding the local circulation of the virus. Notably, the vast majority of the Cambodian sequences analyzed in our study cluster within the same clade that we estimated to be circulating almost exclusively in Cambodia. This suggests that Cambodia has few exchanges of RABV lineages with its neighbors, a surprising pattern as Meng et al. (2011) predicted Cambodia to be an important source of rabies cases in China, Laos, and Thailand. Their results have however not been replicated

in later studies indicating that they might result from small sample size and/or biased sampling. Furthermore, our sampling does not cover the northeastern region of Cambodia close to Laos and that is home for a particular dog population mostly used for hunting and relatively isolated from the rest of the country.

We thus cannot exclude undetected introduction events from Laos to this population, and which would very certainly remain undetected in the rest of the Cambodian dog population. Nevertheless, the limited number of introduction events contrasts with the epidemiological situation in Vietnam [START_REF] Nguyen | Surveillance of Severe Acute Respiratory Infection (SARI) for Hospitalized Patients in Northern Vietnam, 2011-2014[END_REF], Laos [START_REF] Ahmed | Molecular Epidemiology of Rabies Viruses Circulating in Two Rabies Endemic Provinces of Laos, 2011-2012: Regional Diversity in Southeast Asia[END_REF], and Thailand [START_REF] Benjathummarak | Molecular genetic characterization of rabies virus glycoprotein gene sequences from rabid dogs in Bangkok and neighboring provinces in Thailand, 2013-2014[END_REF] where multiple RABV lineages co-circulate and where some viral lineages are very close to Chinese lineages. It would mean that in those countries, RABV introductions and maintenance of these introduced lineages was probably more frequent and successful. We could also have expected more successful importation events of RABV from neighboring countries to Cambodia due to dog trade for meat consumption that occurs across the whole Mekong region [START_REF] Chevalier | Large scale dog population demography, dog management and bite risk factors analysis: A crucial step towards rabies control in Cambodia[END_REF][START_REF] Vu | Rabies-infected dogs at slaughterhouses: A potential risk of rabies transmission via dog trading and butchering activities in Vietnam[END_REF]. While we might not have detected introductions through dog trade because sample collection has not focused on slaughterhouses, traded dogs are slaughtered and may not contribute to rabies transmission anyway [START_REF] Chevalier | Large scale dog population demography, dog management and bite risk factors analysis: A crucial step towards rabies control in Cambodia[END_REF]. Finally, even if we employed a procedure to maximize the spatio-temporal coverage of our sampling, we note that the resulting selection of RABV samples remains more dense in densely-populated areas, in particular the area of Phnom Penh, which at least partially reflects a surveillance bias (Fig. 12D-E). While we cannot discard the hypothesis that a higher number of samples collected near the borders shared with neighboring countries might have allowed us to identify additional introduction events, we here argue that if those undetected introduction events had implanted active transmission chains in Cambodia, we would have likely detected them with the investigations we performed.

Surprisingly, we estimate a lower lineage dispersal velocity from the continuous phylogeographic reconstruction based on the full genomes compared to the equivalent reconstruction based on the N genes. We have further investigated this difference by comparing lineage dispersal velocity across multiple studies that analyzed dog RABV sequences using the same RRW diffusion model (Talbi et al., 2010;Brunker et al., 2018b;[START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF]Dellicour et al., 2019). When the lineage dispersal velocity is estimated on lineage dispersal events of less than 50 km, estimates appear relatively similar across settings. On the contrary, lineage dispersal velocity estimates start to differ between data sets when increasing this distance cut-off value. This pattern suggests that at small spatial scales RABV roughly circulates at the same pace, which would remain coherent with a viral circulation primarily driven by infected dog movements.

Notably, the vast majority of dogs, even when owned, are free-roaming in Cambodia [START_REF] Chevalier | Large scale dog population demography, dog management and bite risk factors analysis: A crucial step towards rabies control in Cambodia[END_REF] as in other countries [START_REF] Muinde | Who let the dogs out? Exploring the spatial ecology of freeroaming domestic dogs in western Kenya[END_REF][START_REF] Warembourg | Comparative Study of Free-Roaming Domestic Dog Management and Roaming Behavior Across Four Countries: Chad, Guatemala, Indonesia, and Uganda[END_REF][START_REF] De La Puente-Arévalo | Ranging patterns and factors associated with movement in free-roaming domestic dogs in urban Malawi[END_REF][START_REF] Sparkes | Spatial and temporal activity patterns of owned, free-roaming dogs in coastal eastern Australia[END_REF]. Our results also suggest that at larger spatial scales, it becomes more difficult to compare the lineage dispersal velocity estimated from different data sets. As introduced above, larger sampling areas are expected to be associated with higher probabilities to sample long-distance dispersal events that will, on average, more likely correspond to fast dispersal events than short-distance dispersal events. Therefore, comparing the lineage dispersal velocity of data sets sampled from study areas of very different spatial extents might potentially lead to an artifactual conclusion of different dispersal velocities. Overall, we would thus recommend to use a similar approach based on maximal distance cut-off values when aiming to compare lineage dispersal velocity statistics estimated from data sets collected across various spatial scales.

While our landscape phylogeographic analyses have allowed us to characterize the environmental conditions in which the inferred lineages tended to disperse within Cambodia, they have not led to any supported evidence that one or several studied environmental factor(s) could partly explain the heterogeneity in viral lineage dispersal velocity. It could imply that the velocity of RABV dispersal in Cambodia is at least not drastically shaped by the environmental factors tested in our study, but this could also result from an insufficient sampling of lineages circulating in some Cambodian regions associated with different environmental conditions. In the latter case, insufficient sampling in these areas could, for instance, limit the statistical power of the tests aiming at detecting an association between the spatial variation of an environmental factor and the dispersal velocity of viral lineages (Dellicour et al., 2016b). More generally, phylogeographic approaches are known to be sensitive to sampling bias [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF][START_REF] Guindon | Accounting for spatial sampling patterns in Bayesian phylogeography[END_REF][START_REF] Kalkauskas | Sampling bias and model choice in continuous phylogeography: Getting lost on a random walk[END_REF][START_REF] Liu | The impact of sampling bias on viral phylogeographic reconstruction[END_REF]. One way to mitigate the impact of sampling bias on phylogeographic reconstructions is to subsample locations according to local incidence data. During the COVID-19 pandemic, this kind of subsampling approach has been widely implemented in the context of phylogeographic analyses targeting SARS-CoV-2 (Dellicour et al., 2021b;[START_REF] Hodcroft | Spread of a SARS-CoV-2 variant through Europe in the summer of 2020[END_REF][START_REF] Lemey | Untangling introductions and persistence in COVID-19 resurgence in Europe[END_REF], but it would in our case require the availability of dog rabies incidence data and sufficient numbers of genomic sequences from each location to subsample from. Unfortunately, neither condition was met in the context of the present study. While not based on incidence data, our samples selection is however based on a procedure implemented as a Markov process trying to maximize the spatio-temporal coverage of the selected samples to sequence, which corresponds to an optimal sampling pattern when aiming to capture the dispersal history of lineages through phylogeographic inference.

Even though we did not identify external introductions as drivers of RABV circulation in Cambodia, they remain likely and could still lead to re-importations of active transmission chains as observed in the neighboring countries. However, considering that dog rabies incidence in Cambodia appears to be primarily driven by within-country transmission, the deployment of an ambitious rabies control policy should focus on campaigns of free and regular dog vaccination at the national level [START_REF] Tarantola | Rabies Vaccine and Rabies Immunoglobulin in Cambodia: Use and Obstacles to Use[END_REF][START_REF] Sor | Knowledge of rabies and dog-related behaviors among people in Siem Reap Province, Cambodia[END_REF], promotion of owner awareness [START_REF] Sor | Knowledge of rabies and dog-related behaviors among people in Siem Reap Province, Cambodia[END_REF][START_REF] Chevalier | Large scale dog population demography, dog management and bite risk factors analysis: A crucial step towards rabies control in Cambodia[END_REF], improvement of surveillance and diagnostic capabilities [START_REF] Duong | Laboratory diagnostics in dog-mediated rabies: an overview of performance and a proposed strategy for various settings[END_REF], improved multisectoral collaboration in a one health approach, and expansion of post-exposure prophylaxis [START_REF] Li | Descriptive assessment of rabies post-exposure prophylaxis procurement, distribution, monitoring, and reporting in four Asian countries: Bangladesh, Bhutan, Cambodia, and Sri Lanka, 2017-2018[END_REF].

Chapter 3

Impact of vaccination on household transmission of SARS-CoV-2 in Israel

Several studies have characterized the effectiveness of vaccines against SARS-CoV-2 infections. However, estimates of their impact on transmissibility remain limited. Here, we evaluated the impact of isolation and vaccination (7 days after the second dose) on SARS-CoV-2 transmission within Israeli households. From December 2020 to April 2021, confirmed cases were identified among health-care workers of the Sheba Medical Centre and their family members. Recruited households were followed up with repeated PCR for at least 10 days after case confirmation. Data were analyzed using a data augmentation Bayesian framework. A total of 210 households with 215 index cases were enrolled; 269 out of 667 (40%) susceptible household contacts developed a SARS-CoV-2 infection. Of those, 170 (63%) developed symptoms. Compared with unvaccinated and unisolated adult/teenager (aged >12 years) contacts, vaccination reduced the risk of infection among unisolated adult/teenager contacts (relative risk (RR) = 0.21, 95% credible interval (CrI): 0.08, 0.44), and isolation reduced the risk of infection among unvaccinated adult/teenager (RR = 0.12, 95% CrI: 0.06, 0.21) and child contacts (RR = 0.17, 95% CrI: 0.08, 0.32). Infectivity was reduced in vaccinated cases (RR = 0.25, 95% CrI: 0.06, 0.77). Within households, vaccination reduces both the risk of infection and of transmission if infected. When contacts were unvaccinated, isolation also led to important reductions in the risk of transmission.

Introduction

SARS-CoV-2 is a highly transmissible virus that was first detected in Wuhan China in December 2019 [START_REF] Lu | Vaccination and SARS-CoV-2 Household Transmission 1233 virus origins and receptor binding[END_REF]Izda et al., 2021). It is the cause of COVID-19, which has spread through the world, leading to a pandemic that had infected at least 250 million people and caused more than 5 million deaths worldwide by November 10, 2021(Mathieu et al., 2021). The advent of novel COVID-19 vaccines has been an important breakthrough in the management of the pandemic. To determine how vaccination may modify epidemic dynamics, it is essential to estimate its effectiveness with respect to infection, transmission, and disease severity. Multiple studies have shown that COVID-19 vaccines are effective at reducing both the risk of infection (Dagan et al., 2021;Tande et al., 2022;Pawlowski et al., 2021;SE, 2021;Martínez-Baz et al., 2021) and the risk of developing severe symptoms (Dagan et al., 2021;Martínez-Baz et al., 2021;Haas et al., 2021;Goldberg et al., 2021) in the general population.

Documenting vaccine impact on transmission is more challenging, stemming from the difficulty of thoroughly documenting chains of transmission and accounting for the ways different types of contacts may lead to different risks of transmission [START_REF] Bi | Epidemiology and transmission of COVID-19 in 391 cases and 1286 of their close contacts in Shenzhen, China: a retrospective cohort study[END_REF]. Households represent the perfect environment to evaluate factors affecting transmission such as vaccination because the probability of SARS-CoV-2 transmission among household members is high, ranging between 14% and 32% (Madewell et al., 2020;Lei et al., 2020;[START_REF] Thompson | Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) setting-specific transmission rates: a systematic review and meta-analysis[END_REF]. Beyond the evaluation of vaccine effectiveness, understanding how vaccines affect household transmission is also important to determine how recommendations should evolve with vaccines. For example, should isolation precautions be maintained in partially vaccinated households (World Health Organization (WHO), 2021b)? A number of studies have shown that vaccines provide indirect protection against household transmission (Shah et al., 2021;[START_REF] Salo | The indirect effect of mRNA-based Covid-19 vaccination on unvaccinated household members[END_REF][START_REF] Harris | Effect of vaccination on household transmission of SARS-CoV-2 in England[END_REF]Prunas et al., 2022;[START_REF] Gier | Vaccine effectiveness against SARS-CoV-2 transmission and infections among household and other close contacts of confirmed cases, the Netherlands, February to May 2021[END_REF]. However, none of these studies evaluated how isolation affected the outcome, and for some of the studies (Shah et al., 2021;[START_REF] Salo | The indirect effect of mRNA-based Covid-19 vaccination on unvaccinated household members[END_REF][START_REF] Harris | Effect of vaccination on household transmission of SARS-CoV-2 in England[END_REF]Prunas et al., 2022), the passive nature of surveillance may have led to underestimating household transmission rates.

During the first months of 2021, Israel underwent its third pandemic wave due to the rise of the Alpha variant that quickly accounted for 90% of infections (Munitz et al., 2021). Concomitantly, vaccination was extended to all adults older than age 16 years, making Israel one of the first countries to reach high vaccination coverage in their population, with 60% of the total population being vaccinated by March 22, 2021(Mathieu et al., 2021). During this period, we followed SARS-CoV-2 transmission in the households of 12,518 HCWs of the Sheba Medical Center, the largest medical center in Israel. Here, we describe dynamics of transmission in these households and evaluate the impact vaccination and isolation measures had on these dynamics. C1). Unvaccinated HCW contacts were isolated at home, whereas vaccinated HCWs were instructed to perform a PCR test every day they reported to the hospital for work.

Material and Methods

Between December 31, 2020, andApril 26, 2021, the HCWs who were SARS-CoV-2-positive or reported a positive household member were contacted at least 10 days after detection and were offered enrollment in the study. Those who agreed, and gave their consent, answered a telephone interview.

Data and sample collection

Data collected during the phone interview included the age and gender of the HCW's household members, their vaccination status, information about prior COVID-19 infections, their COVID-19 PCR test dates and results, their symptoms (i.e., fever, cough, myalgia, headache, congestion, diarrhea, vomiting, anosmia, or ageusia), the number of rooms and bathrooms in the household, and the degree to which isolation precautions were adhered to (Section 2 in Appendix C). At the time of the study, only individuals 16 years old or older were eligible for vaccination. The household member who had the first positive PCR test was defined as the index case. When multiple household members had a positive PCR test on the same day, they were defined as co-index cases. We defined complete isolation as complete separation in sleeping and eating between household contacts and index case(s) (i.e., they did not spend any time in the same room) and whether a separate bathroom was provided for the index case(s). Partial isolation was defined if one of the above was violated, but masks were continuously used, and eating was consistently separate.

For HCWs, nasopharyngeal swabs were collected by trained personnel, and reverse-transcriptase quantitative PCR analysis was performed using the Allplex 2019-nCov RT-qPCR assay (Seegene Inc., Seoul, South Korea) and expressed by cycle threshold (Ct). Other household members reported the results of their COVID-19 test(s) performed by their health-care providers.

Clinical outcome

Confirmed SARS-CoV-2 infections were defined by a positive PCR test (i.e., with a Ct value lower than 40). Symptomatic cases were defined as confirmed cases with the presence of at least 1 symptom from among the following: fever, cough, myalgia, headache, congestion, diarrhea, vomiting, anosmia, or ageusia. Contacts who reported at least 1 of the above-mentioned symptoms but were not confirmed because they performed no PCR test (n = 6) or a single test at inclusion (n = 2) were also considered as symptomatic cases. Asymptomatic cases were defined as confirmed cases who did not report any symptom over the follow-up period of the household.

Statistical analysis

We evaluated transmission in households using 2 metrics: the secondary attack rate (SAR), defined as the proportion of susceptible household contacts that are infected after the index case is detected (Liu et al., 2020), and the person-to-person probability of transmission, defined as the per-capita probability that an infected individual transmits to a susceptible household contact. The first metric includes tertiary (i.e., household contacts infected by a household member that is not the index case) and community cases (i.e., household contacts infected in the community) contrary to the second metric. In both cases, we assumed that individuals who reported past infection of SARS-CoV-2 confirmed by PCR over the year preceding the detection of the household index case (n = 20) were protected from infection and therefore, did not count as susceptible household contacts.

Baseline characteristics of the index cases and household contacts were described according to their vaccination status. All individuals older than 12 years were considered as adults/teenagers. We calculated the SAR for different categories of household contacts: unisolated and unvaccinated adults/teenagers, unisolated and vaccinated adults/teenagers, isolated and unvaccinated adults/teenagers, vaccinated and isolated adults/teenagers, unisolated children, and isolated children. Here, isolation corresponds to complete or partial isolation between household contacts and the index case. We also defined the SAR of vaccinated and unvaccinated index cases as the proportion of infected household contacts in households with vaccinated or unvaccinated index cases, respectively. In a sensitivity analysis, the SAR calculation was restricted to households in which a single index case was identified (Table C2). We also report the 95% confidence interval of the SAR. We developed a statistical model to evaluate the effect of age, isolation precautions, BNT162b2 vaccination, and household size on SARS-CoV-2 transmission dynamics in households (Section 4 in Appendix C). The model uses the sequence of symptom onset dates and positive molecular test dates to estimate the person-to-person risk of transmission within the household while accounting for the community hazard of infection (i.e., household contacts infected outside the household) and the possibility of tertiary transmissions (i.e., household contacts infected by a member of the household that is not the index case) (Cauchemez et al., 2004). The person-to-person risk of transmission is decomposed into the baseline person-to-person risk of infection depending on household size, the relative infectivity of the infector depending on their vaccination status (reference group: unvaccinated cases), and the relative susceptibility of the infectee depending on their age, isolation behavior, and vaccination status. The relative susceptibility is estimated separately for unisolated children, isolated children, isolated and unvaccinated adults/teenagers, unisolated and vaccinated adults/teenagers, and adults/teenagers that are both isolated and vaccinated, considering the group of adults/teenagers that are unisolated and unvaccinated as the reference group. None of the children were vaccinated at the time of the study. This formulation accommodates the potential confounding effects between the 3 variables characterizing household contacts (i.e., being vaccinated, being isolated, or being a child). We assumed that individuals whose isolation behavior was missing (n = 6) did not comply with isolation precautions.

Model parameters were estimated using Bayesian Markov chain Monte Carlo sampling with data augmentation (Cauchemez et al., 2004) (Section 5 in Appendix C). Data were augmented with the probable date of infection of confirmed cases. For symptomatic cases, the date of infection was reconstructed from the date of symptom onset, using the probabilistic distribution of the incubation period (McAloon et al., 2020). For asymptomatic cases, we assumed that the date of infection could occur up to 10 days prior to their molecular detection based on a meta-analysis (Cevik et al., 2021).

Since the study was conducted during the vaccine rollout, participants were enrolled at varying stages of their vaccination process. We assumed that vaccines reach their full effect 7 days after receiving a second dose (Dagan et al., 2021;Haas et al., 2021;Goldberg et al., 2021). Cases were therefore considered vaccinated if their symptom onset (or if unknown, the date of their first positive PCR test) occurred ≥ 7 days after the second dose. Similarly, household contacts were considered vaccinated if their exposure to the index case (starting with symptom onset or, in its absence, from the date of first positive PCR of the index case) occurred ≥ 7 days after the second dose. In a sensitivity analysis, we investigated how parameter estimates changed under the assumption that vaccination is effective ≥ 15 days after the first dose. We also assessed how estimates changed when the analysis was restricted to households in which all negative contacts had performed at least 1 or 2 PCR tests in the 10 days following the detection of the index case. In the baseline scenario, we assumed that asymptomatic cases are 40% less infectious than symptomatic cases based on a meta-analysis (Byambasuren et al., 2020), and we investigated whether assuming the same level of infectivity in asymptomatic and symptomatic cases modified our estimates.

Finally, in our baseline analysis, we chose a log-normal with log-mean = 0 and log-standard deviation = 1 prior distribution for the relative infectivity and relative susceptibility parameters and explored smaller and larger values (log-standard deviation = 0.7 or 2) in a sensitivity analysis.

We compared the observed and expected distributions of the number of cases per household size to assess the goodness-of-fit of the model (Table C3). We report the posterior median and the 95% credible interval (CrI) of estimated parameters. We also report the posterior probability that isolated and vaccinated adult/teenager contacts are less susceptible than vaccinated adult/teenager contacts that do not isolate.

To measure the strength of evidence of a reduced susceptibility in isolated contacts among vaccinated ones, we report the associated Bayes factor. Here, it directly corresponds to the posterior odds of a reduced susceptibility in isolated contacts among vaccinated ones. Additional details are available in Sections 1 to 6 in Appendix C.

Ethics

The study was approved by the Sheba Medical Center institutional review board committee (approval #8130-21).

Results

All 12,518 HCWs employed by the Sheba Medical Center were eligible to join the study. Between December 19 and April 28, 2021, 91% of the Sheba Medical Center personnel received both doses of the BNT162b2 vaccine, and a rapid and significant decrease in newly detected cases was observed among HCWs.

From December 31, 2020, to April 26, 2021, 276 SARS-CoV-2 cases were identified among HCWs of the Sheba Medical Center and their household members (Fig. 16). Of these, 212 agreed to participate, gave their consent, and were enrolled in the study with their household members. Two households were excluded due to missing vaccination status, dates of PCR test, and/or symptom onset. In total, we analyzed data from 210 households with 215 index cases, including 4 co-index cases, and their 687 household contacts. The median household size was 4 (interquartile range, 3-5). Mean age was 32 years among index cases (Table 4) and 27 years among household contacts (Table 5). Age was missing for 5 adult/teenager contacts, and isolation behavior was missing for 6 contacts. There was a slight overrepresentation of females among index cases (58%), and 191 index cases (89%) were adults/teenagers, of whom 15 (8%) were vaccinated. None of the 24 child index cases were vaccinated. Among the 494 adult/teenager household contacts, 125 (25%) were vaccinated. Of these, 83 (17%) also complied with isolation precautions. Among the 369 unvaccinated adult/teenager contacts, 259 (70%) isolated during the study. None of the 193 child household contacts were vaccinated and 47% of them (n = 90) isolated during the study period (Table 5). In the following, we refer to susceptible contacts (i.e., contacts that did not report SARS-CoV-2 infection over the preceding year) as contacts.

A total of 269 out of 667 (40%) household contacts developed a SARS-CoV-2 infection. Of those, 170 (63%) developed symptoms (Table 5). The SAR varied with the characteristics of the contacts.

Among the 105 adult/teenager contacts who were unisolated and unvaccinated, 80 (76%) were infected by SARS-CoV-2 (Table 6). This proportion dropped to 28% (11 out of 40) among those who were unisolated and vaccinated, 29% (71 out of 245) among those who were isolated but unvaccinated, and 11% (9 out of 83) among those who were isolated and vaccinated; 65% (66 out of 101) of child contacts who were unisolated got infected by SARS-CoV-2. This proportion declined to 33% (29 out of 87) for isolated child contacts. The proportion of asymptomatic cases varied from 26% (46 out of 174) among adult/teenager contact cases to 56% (53 out of 95) among child contact cases (Table 5).

The SAR also varied with the vaccination status of the index case regardless of the contacts' characteristics. Among the 622 household contacts whose index case was unvaccinated, 261 (42%) developed a SARS-CoV-2 infection (Table 6). This proportion dropped to 19% (8 out of 42) among household contacts whose index case was vaccinated. Finally, the SAR was relatively invariant with household size: 31%, 40%, 32%, and 32% for households of size 2, 3, 4, and 5, respectively (Fig. C1). Our statistical model makes it possible to perform a multivariate analysis of the drivers of SARS-CoV-2 transmission in households. We estimate that, relative to adult/teenager contacts who were unisolated and unvaccinated, the relative risk of being infected was 0.21 (95% CrI: 0.08, 0.44) among adult/teenager household contacts who were vaccinated but unisolated (Fig. 17A, Table C4). It was 0.12 (95% CrI: 0.06, 0.21) among household contacts who did isolate and were unvaccinated, and 0.07 (95% CrI: 0.03, 0.16) among household contacts who were both isolated and vaccinated. Isolation might reduce the risk of infection among vaccinated contacts (96% posterior probability, Bayes factor = 23) with a relative risk of 0.34 (95% CrI: 0.11, 1.14). Relative to adult/teenager contacts who were unisolated and unvaccinated, the relative risk of infection was 0.50 (95% CrI: 0.32, 0.77) for child contacts that did not isolate, and 0.17 (95% CrI: 0.08, 0.31) for those that did. We estimate that the risk of transmission from vaccinated cases was 0.25 (95% CrI: 0.06, 0.77) times that of unvaccinated cases (Fig. 17B and Table C4).

Overall, we estimate that, in a household of size 4, the person-to-person probability of SARS-CoV-2 transmission is 61% (95% CrI : 48, 72) between an unvaccinated case and an unvaccinated and unisolated adult/teenager. This probability drops to 4% (95% CrI: 1, 16) between 2 vaccinated adults/teenagers who do not follow isolation rules (Fig. 18 and Table C5). The person-to-person probability of transmission Abbreviations: CI, confidence interval; SAR, secondary attack rate. a Isolation is missing for 1 child contact and for 5 adult contacts. b The last 2 rows correspond to the SAR among the household contacts of vaccinated (n = 14 households) and unvaccinated index cases (n = 195 households). One household was excluded from this analysis because its co-index cases did not have the same vaccination status.

from an unvaccinated case to a child who does not isolate is 37% (95% CrI : 27, 48). This probability drops to 11% (95% CrI: 3, 31) if the case is vaccinated and to 14% (95% CrI: 7, 25) if the child contact is isolated.

In general, our estimates of relative susceptibility and relative infectivity were robust to model assumptions (Fig. 19). When the analysis was restricted to households in which all contacts performed at least 1 or 3 PCR tests in the 10 days following the recruitment of the index case, the relative susceptibility of vaccinated adult/teenager contacts who did not isolate was slightly higher compared with the baseline scenario. It increased from 0.21 (95% CrI: 0.08, 0.44) in the baseline scenario to 0.28 (95% CrI: 0.09, 0.66) in the analysis with at least 1 PCR and 0.32 (95% CrI: 0.09, 0.83) with at least 2 PCR tests (Table C4). In the alternative scenarios, the number of individuals included was substantially lower, increasing CrIs (Figs. C3 and C4 and Tables C6 to C9). Similarly, the relative susceptibility of vaccinated adult/teenager contacts who did isolate increased from 0.07 (95% CrI: 0.03, 0.16) in the baseline scenario to 0.12 (95% CrI: 0.04, 0.28) in the analysis with at least 1 PCR, and 0.13 (95% CrI: 0.04, 0.32) in the one with at least 2 PCR tests. Consequently, the posterior probability that isolated and vaccinated adult/teenager contacts were less susceptible than vaccinated adult/teenager contacts that did not isolate dropped from 96% to 88% with 1 PCR and 89% with 2 PCR tests. Still, the statistical support was high with a Bayes factor equal to 7 and 8, respectively. Relative infectivity and relative susceptibility were slightly sensitive to their prior distribution (Table C10). When the log-standard deviation increased, estimates were pulled towards lower values.

Discussion

We evaluated the impact of BNT162b2 vaccination on case infectivity and the mitigating effect of age, isolation from the index case, and BNT162b2 vaccination on susceptibility to infection in household settings. Our approach accounts for infections in the community, potential tertiary infections within the households, the reduced infectivity of asymptomatic cases, potential misidentification of the index case(s), and varying follow-up periods between households.

In our analysis, the SAR in unvaccinated adult/teenager contacts who did not isolate was estimated at around 76%, which is substantially higher than previous estimates obtained in household settings (Madewell et al., 2020;Lei et al., 2020;[START_REF] Thompson | Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) setting-specific transmission rates: a systematic review and meta-analysis[END_REF][START_REF] Harris | Effect of vaccination on household transmission of SARS-CoV-2 in England[END_REF][START_REF] Jing | Household secondary attack rate of COVID-19 and associated determinants in Guangzhou, China: a retrospective cohort study[END_REF][START_REF] Li | Household transmission of SARS-CoV-2 and risk factors for susceptibility and infectivity in Wuhan: a retrospective observational study[END_REF]. In meta-analyses (Madewell et al., 2020;Lei et al., 2020;[START_REF] Thompson | Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) setting-specific transmission rates: a systematic review and meta-analysis[END_REF], the average SAR ranged between 14% and 32%; however, in some studies, it could be as high as 90% (Lei et al., 2020). Most of these studies date back to the time when historical lineages were still dominant.

In contrast, our study took place when the Alpha variant represented up to 90% of infections in Israel Person-to-person probability of transmission within households according to the characteristics of the case and of the contact, Ramat Gan, Israel, 2020-2021. Estimated person-to-person probability of transmission within households of size 4, decomposed by the age, isolation behavior, and vaccination status of the contact as well as the vaccination status of the case. The posterior median and its associated 95% Bayesian credible interval are reported. (Munitz et al., 2021). Our higher estimate could be at least partly explained by the fact that the Alpha variant is substantially more transmissible than historical lineages (Munitz et al., 2021;[START_REF] Kissler | Viral dynamics of SARS-CoV-2 variants in vaccinated and unvaccinated individuals[END_REF][START_REF] Davies | Effects of non-pharmaceutical interventions on COVID-19 cases, deaths, and demand for hospital services in the UK: a modelling study[END_REF][START_REF] Volz | Assessing transmissibility of SARS-CoV-2 lineage B.1.1.7 in England[END_REF].

In agreement with previous reports, we found that children are less susceptible to SARS-CoV-2 infections than adults/teenagers (Madewell et al., 2020;Lei et al., 2020;[START_REF] Thompson | Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) setting-specific transmission rates: a systematic review and meta-analysis[END_REF][START_REF] Viner | Susceptibility to SARS-CoV-2 infection among children and adolescents compared with adults[END_REF].

We further estimated that, 7 days after their second dose, vaccinated adults/teenagers benefit from a 79% reduction in the risk of infection compared with unvaccinated adults/teenagers. We show, consistent with previous studies (Munitz et al., 2021;[START_REF] Pritchard | Impact of vaccination on new SARS-CoV-2 infections in the United Kingdom[END_REF], that BNT162b2 vaccination is highly effective against infection by the Alpha variant. In general population studies, vaccine effectiveness for symptomatic infections ranged from 57% 14 days after the first dose (Dagan et al., 2021) to 89% (Dagan et al., 2021), and 97% 7 days after the second dose (Haas et al., 2021). For asymptomatic infections, vaccine effectiveness against infection was 79% 10 days after the first dose (Tande et al., 2022) and 94% 14 days after the second dose (SE, 2021). Our estimate of vaccine effectiveness in household settings is lower than those obtained in the general population. This is consistent with estimates obtained in households (Prunas et al., 2022;[START_REF] Gier | Vaccine effectiveness against SARS-CoV-2 transmission and infections among household and other close contacts of confirmed cases, the Netherlands, February to May 2021[END_REF][START_REF] Pritchard | Impact of vaccination on new SARS-CoV-2 infections in the United Kingdom[END_REF] and might in part be explained by In the baseline scenario (black circle), we assumed that vaccination was effective from 7 days after the second dose, the relative infectivity of asymptomatic cases compared with symptomatic cases was equal to 60%, and the log-standard deviation of the relative infectivity and relative susceptibility prior distributions was equal to 1. Sensitivity analysis scenarios: yellow square, vaccination is effective ≥ 15 days after the dose; orange triangle, 1 polymerase chain reaction (PCR) test for all negative contacts; red star, 2 PCR tests for all negative contacts; pink diamond, 100% infectivity of asymptomatic cases; blue inverted triangle, relative parameter prior with log-standard deviation = 0.7; blue pentagon, relative parameter prior with log-standard deviation = 2. The posterior median and its associated 95% Bayesian credible interval are reported.

the elevated contact rates in households that may favor transmission. Additionally, studies in the general population are less suitable to detect all asymptomatic cases compared with the household setting. This might lead general population studies to overestimate vaccine effectiveness against asymptomatic infections if vaccinated contacts are less often tested than unvaccinated ones. On another note, we estimate a vaccine effectiveness against transmission of 75% (95% CrI: 23, 94), which is in line with other studies in household settings [START_REF] Harris | Effect of vaccination on household transmission of SARS-CoV-2 in England[END_REF]Prunas et al., 2022;[START_REF] Gier | Vaccine effectiveness against SARS-CoV-2 transmission and infections among household and other close contacts of confirmed cases, the Netherlands, February to May 2021[END_REF].

To our knowledge, this is the first study estimating the effect of isolation on SARS-CoV-2 transmission in households that are partially vaccinated. We showed that isolation precautions markedly reduce the overall infection risk in both adult/teenager and child contacts even when considering partial physical distancing measures. We estimated a similar reduction of infection in adult/teenager contacts that were vaccinated but did not isolate. There was a signal in the data that isolation also benefited vaccinated individuals, although credible intervals were larger, and further investigations are required to confirm this finding.

Our study has several limitations. First, household studies such as ours may be affected by multiple sources of bias. On the one hand, we may overestimate the SAR if we are more likely to detect households with multiple cases. On the other hand, we might underestimate it if some asymptomatic, or paucisymptomatic, cases are missed during follow-up. Second, we estimated an important reduction of infectivity in vaccinated cases with 2 doses compared with unvaccinated cases as previously shown [START_REF] Harris | Effect of vaccination on household transmission of SARS-CoV-2 in England[END_REF]Prunas et al., 2022;[START_REF] Gier | Vaccine effectiveness against SARS-CoV-2 transmission and infections among household and other close contacts of confirmed cases, the Netherlands, February to May 2021[END_REF][START_REF] Regev-Yochay | Decreased infectivity following BNT162b2 vaccination: a prospective cohort study in Israel[END_REF]. However, this is associated with important uncertainty due to the small number of cases (15 vaccinated index cases and 21 vaccinated secondary cases). Thus, more data are needed to reduce the size of credible intervals. Third, we assumed that vaccination was effective from 7 days after the second dose (or 15 days after the first dose in our sensitivity analysis; see Table C11). In practice, the effect of the vaccine is likely to be progressive, which might push down estimates of effectiveness since individuals with early partial protection would be considered to be unvaccinated. However, excluding households with the early-vaccinated index cases did not affect our estimates (Fig. C5 and Table C12). The limited number of households does not make it possible to dissociate early vs. full protection conferred by the vaccine nor to investigate the infectivity of children relative to adults/teenagers. Fourth, testing instructions were different for vaccinated and unvaccinated household contacts, as well as HCWs and non-HCWs. Most vaccinated contacts were HCWs at the Sheba Medical Center who complied with testing instructions to go back to work, leading to high testing rates in vaccinated individuals, with 67% having at least 2 PCR tests and 70% having 1 positive PCR or at least 2 PCR tests in the 10 days following case detection (Table C1). Among unvaccinated contacts, 49% had at least 2 PCR tests and 79% had 1 positive PCR or at least 2 PCR tests in the 10 days following case detection. This higher testing rate is notably due to the high proportion of single positive tests (30%). These differential testing behaviors and positivity rates between vaccinated, unvaccinated, HCW, and non-HCW contacts make it difficult to anticipate the directionality of a potential bias. When restricting our evaluation to households where all negative contacts were tested at least once or twice, estimates remained relatively similar to the baseline values. In the analysis with at least 2 tests for all negative contacts, we observed a slight reduction in the point estimate for vaccine effectiveness against infection that remained difficult to interpret given the very broad credible intervals (17%-91%). Sixth, the measurement of isolation precautions, vaccination status, and symptoms are based on the declaration of participants, and thus may be subject to recall bias. More importantly, the measurement of isolation precautions and vaccination status can be subject to overreporting, as they represent a socially desirable behavior. The timing and evolution of isolation precautions were not measured, and thus not integrated in our model. Nevertheless, our estimate of isolation effectiveness is consistent with a 10-day period of quarantine in modeling studies (Ashcroft et al., 2021), and our estimates of vaccination effectiveness are also consistent with the literature as mentioned above. Finally, we estimate vaccine effectiveness against infection and transmission in a context where the Alpha variant was dominant. These estimates are very likely to be different for the Delta variant (Eyre et al., 2021) that was first reported in October 2020 and rapidly became dominant worldwide (World Health Organization (WHO), 2021a).

To conclude, vaccination with 2 doses substantially reduces the risk of transmission and the risk of infection in households. Isolation from the index case while sleeping and eating provides a high level of protection to unvaccinated household members, whether they are adults/teenagers or children. Household contacts of COVID-19 patients should ideally isolate, or at least refrain from significant contact, with household cases. This may also be the case for vaccinated household members, although larger studies are required to confirm this finding.

Chapter 4

Impact and mitigation of sampling bias in discrete phylogeography

Bayesian phylogeographic inference is a powerful tool in molecular epidemiological studies that enables reconstructing the origin and subsequent geographic spread of pathogens. Such inference is, however, potentially affected by geographic sampling bias. Here, we investigated the impact of sampling bias on the spatiotemporal reconstruction of viral epidemics using Bayesian discrete phylogeographic models and explored different operational strategies to mitigate this impact. We considered the CTMC model and two structured coalescent approximations (BASTA and MASCOT). For each approach, we compared the estimated and simulated spatiotemporal histories in biased and unbiased conditions based on simulated epidemics of RABV in dogs in Morocco. While the reconstructed spatiotemporal histories were impacted by sampling bias for the three approaches, BASTA and MASCOT reconstructions were also biased when employing unbiased samples. Increasing the number of analyzed genomes led to more robust estimates at low sampling bias for CTMC. Alternative sampling strategies that maximize the spatiotemporal coverage greatly improved the inference at intermediate sampling bias for CTMC, and to a lesser extent, for BASTA and MASCOT. In contrast, allowing for time-varying population sizes in MASCOT resulted in robust inference. We further applied these approaches to two empirical data sets:

a RABV data set from the Philippines and a SARS-CoV-2 data set describing its early spread across the world. In conclusion, sampling biases are ubiquitous in phylogeographic analyses but may be accommodated by increasing sample size, balancing spatial and temporal composition in the samples, and informing structured coalescent models with reliable case count data.

Introduction

Over the past decade, Bayesian discrete phylogeographic inference has greatly benefited viral epidemiological studies in unraveling the origin and subsequent spread of viral epidemics [START_REF] Faria | Distinct rates and patterns of spread of the major HIV-1 subtypes in Central and East Africa[END_REF][START_REF] Lemey | Accommodating individual travel history and unsampled diversity in Bayesian phylogeographic inference of SARS-CoV-2[END_REF][START_REF] Lu | Adaptation, spread and transmission of SARS-CoV-2 in farmed minks and associated humans in the Netherlands[END_REF], the spatial processes driving viral spread [START_REF] Müller | Viral genomes reveal patterns of the SARS-CoV-2 outbreak in Washington State[END_REF], and environmental and human-related factors associated with viral spread [START_REF] Dudas | Virus genomes reveal factors that spread and sustained the Ebola epidemic[END_REF][START_REF] He | Phylogeography Reveals Association between Swine Trade and the Spread of Porcine Epidemic Diarrhea Virus in China and across the World[END_REF]Lemey et al., 2014). BEAST is a popular Bayesian phylodynamics software package commonly used in the analysis of time-stamped viral molecular sequences. It offers different discrete phylogeography approaches: a popular and computationally efficient discrete phylogeographic inference approach that makes use of continuous-time Markov chain (CTMC) modeling (Lemey et al., 2009a), also known as the discrete trait analysis or DTA, and the structured coalescent model under its exact and approximated forms [START_REF] Vaughan | Efficient Bayesian inference under the structured coalescent[END_REF][START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF][START_REF] Müller | MASCOT: parameter and state inference under the marginal structured coalescent approximation[END_REF]. CTMC models migration between discrete locations in the same way as nucleotide substitutions are modeled. In other words, geographical locations are modeled as a neutral trait that evolves on top of the tree from the root to the tips. As such, CTMC modeling does not explicitly model the branching process that gave rise to the tree. In contrast, the structured coalescent model -which is an extension of the coalescent model to a structured population -is a tree-generating model that explicitly models how lineages coalesce within and migrate between subpopulations from present to past. Two computationally efficient approximations of the structured coalescent model are available in BEAST2: the Bayesian structured coalescent approximation (BASTA) [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF] and the marginal approximation of the structured coalescent (MASCOT) [START_REF] Müller | MASCOT: parameter and state inference under the marginal structured coalescent approximation[END_REF]. Currently, they both assume constant prevalence through time for each deme/population, while the CTMC approach does not (Lemey et al., 2009a).

Bayesian discrete phylogeography approaches are complementary to mathematical modeling and epidemiological studies, and particularly informative when epidemiological data are scarce. In such contexts, viral genetic sequences are expected to compensate for the lack of epidemiological data. However, genetic samples may constitute a biased snapshot of the underlying viral spread, especially when isolated through passive surveillance systems. The impact of such sampling bias on discrete phylogeographic inference has been discussed and examined ever since. Indeed, CTMC estimates were suspected to be biased towards the most sampled location (Lemey et al., 2009a) and, later, sampling heterogeneity was shown to inform the posterior, and more specifically the migration parameters, which is not the case for BASTA [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF]. In BASTA, sampling evenness is not informative as such and the estimated migration rates are more correlated to the true values under simulated biased and unbiased conditions compared to CTMC [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF]. As a result, BASTA has been argued to be more robust to sampling bias [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF]. Nevertheless, the structured coalescent model is known to be sensitive to unsampled locations, known as ghost demes [START_REF] Beerli | Effect of unsampled populations on the estimation of population sizes and migration rates between sampled populations[END_REF][START_REF] Ewing | Estimating Population Parameters using the Structured Serial Coalescent with Bayesian MCMC Inference when some Demes are Hidden[END_REF][START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF]. In parallel, several studies tested alternative strategies to mitigate the potential effects of sampling bias, mostly focusing on CTMC as it was shown to be potentially less robust to sampling bias compared to the structured coalescent model. Downsampling that was tested early on but was limited to large data sets [START_REF] Yang | Bayesian phylodynamics of avian influenza A virus H9N2 in Asia with time-dependent predictors of migration[END_REF]Lemey et al., 2014) rapidly became a prerequisite in any SARS-CoV-2 data analysis study due to the large number of available sequences and the high sampling heterogeneity between countries (Hodcroft et al., 2021a). However, [START_REF] Magee | The effects of random taxa sampling schemes in Bayesian virus phylogeography[END_REF] showed that inference accuracy rapidly plateaus when using up to 25-50% of the sequence data available. Other studies aimed at improving inference accuracy by integrating additional reliable epidemiological data.

For example, CTMC was extended to incorporate information on the recent migration events using individual travel records [START_REF] Lemey | Accommodating individual travel history and unsampled diversity in Bayesian phylogeographic inference of SARS-CoV-2[END_REF][START_REF] Hong | Bayesian Phylogeographic Analysis Incorporating Predictors and Individual Travel Histories in BEAST[END_REF]. More recently, a simulation study focused on quantifying the impact of sampling bias on the predicted location of internal nodes, the prediction of migration events that lead to large local spread as well as on the estimation of migration rates in a maximum likelihood framework [START_REF] Liu | The impact of sampling bias on viral phylogeographic reconstruction[END_REF]. The authors showed that prediction accuracy actually depends on multiple factors: the underlying migration rate, the magnitude of sampling bias and the magnitude of traveler sampling. Importantly, they observed a lower relative accuracy with biased samples and when samples overrepresent travelers. Concerning the structured coalescent model, [START_REF] Müller | Inferring time-dependent migration and coalescence patterns from genetic sequence and predictor data in structured populations[END_REF] informed the deme population sizes with reliable case count data from the 2014 Ebola epidemic in Sierra Leone using MASCOT. This allows modeling time-varying population sizes instead of assuming constant population sizes over time. Sampling bias is also a concern in continuous phylogeography analyses in which other mitigation approaches were tested. Recently, (Dellicour et al., 2021b) downsampled SARS-CoV-2 genomic records from New York City based on hospitalisations rather than case counts to analyze representative samples irrespective of testing effort and strategy, [START_REF] Kalkauskas | Sampling bias and model choice in continuous phylogeography: Getting lost on a random walk[END_REF] incorporated sequence-free samples from unsampled areas, and (Guindon and De Maio, 2021) explicitly modeled sampling strategy in the data likelihood.

Whereas numerous studies tested strategies to deal with sampling bias, the impact of sampling bias on discrete phylogeographic reconstructions remains insufficiently characterized. Here, we compare the performance of the different phylogeographic methods using simulated viral epidemics using a stochastic metapopulation model, based on RABV epidemics in dogs in Morocco. We investigated the impact of sampling bias on the spatiotemporal reconstruction of these viral epidemics using CTMC, BASTA, and MASCOT, with the latter two assuming populations to stay constant over time. Next, we explored different approaches to mitigate sampling bias, maximizing the spatial and/or temporal coverage of the sample, and informing the deme sizes under MASCOT with the true (time-varying) case count data per location. The latter is to test to what degree biases originating from assuming constant population sizes over time can be mitigated by allowing them to vary over time. Finally, we applied the three algorithms to two empirical data sets: a data set of RABV sequences isolated in the Philippines islands between 2004 and 2010, and a global data set of SARS-CoV-2 genomes of the early spread of the pandemic.

Material and Methods

2.1. Simulation study

Simulation of viral transmission chains using a metapopulation model

In order to address the impact of spatial sampling bias on discrete phylogeographic inference, we performed a detailed simulation study. Sampling bias concerns all diseases, but it is even more challenging to address in the context of zoonotic diseases for which most of the transmission process is unobserved.

We grounded our study in the context of dog rabies in North Africa where transmission processes are relatively well-documented. It was notably shown that rabies transmission relies on human movement over long distances. We simulated rabies epidemics in dog populations according to realistic scenarios using a stochastic, discrete-time and spatially-explicit model implemented in R using the Rccp package [START_REF] Eddelbuettel | Extending R with C++: A Brief Introduction to Rcpp[END_REF]. We divided the Moroccan dog population into three or seven subpopulations corresponding to arbitrary regions (see the section below on the parametrization of the mobility matrix, Fig. D22). We divided each subpopulation into three compartments: susceptible, exposed, and infectious individuals (Fig. 20A). At each discrete time step, we drew newborns and dead individuals in the susceptible compartment from Poisson distributions with respective means the birth rate b and the death rate d. We defined the force of infection Λ i,t , i.e. the per-capita rate of infection of susceptible individuals in region i on day t, as:

Λ i,t = β H i I i,t-1 + ∑ j̸ =i C S ν j→i I j,t-1 (4.1)
where β is the transmission rate of rabies scaled by H i , i.e. the human population size in region i, ν j→i is the per-capita mobility rate of individuals moving from region j to region i, I j,t-1 is the number of infectious individuals in region i on day t -1, and C S is a scale factor (see below for more information).

Exhaustive dog census data were not available and it is well known that human-mediated movement plays a major role in the spread of rabies in North Africa (Talbi et al., 2010;Dellicour et al., 2017), thus we assumed that dog populations were proportional to human populations (Table D2). We scaled the rabies transmission rate by population size to ensure that the force of infection is density-independent as previously documented on rabies [START_REF] Morters | Evidence-based control of canine rabies: a critical review of population density reduction[END_REF]. We used the scale factor C S to monitor the proportion of inter-region infections. Its value was arbitrarily chosen so that 1% of infection events occurred between regions, and the basic reproduction ratio is approximately equal to 1.05 within and between regions. At each time step, we drew the number of newly exposed individuals in each region from Poisson distributions with a mean specified by the number of susceptible individuals in region i on day t -1 (S i,t-1 ) multiplied by the force of infection in region i on day t (Λ i,t ). Once an individual e j,t entered the exposed compartment, it was uniquely identified. The location of its infector was drawn from a multinomial distribution with the following probabilities:

P(e j,t in f ected by I i,t-1 ) = ν i→ j I i,t-1 ∑ k ν k→ j I k,t-1 (4.2)
Once the location of the infector was drawn, the ID of the infector was randomly sampled from the set of infectors present in the location. All infectious individuals in each region had the same probability of infection. The incubation period of exposed individuals was drawn from a gamma distribution with shape 2 and rate 11.055 [START_REF] Hampson | Transmission Dynamics and Prospects for the Elimination of Canine Rabies[END_REF] and its infectious period was drawn from a discretized gamma distribution adapted from [START_REF] Hampson | Transmission Dynamics and Prospects for the Elimination of Canine Rabies[END_REF]) so that it could not exceed 15 days (World Health Organization (WHO), 2018). Finally, the life span was drawn from an exponential distribution with rate d. If natural death occurred before the end of the incubation or infectious periods, the individual was removed prematurely. Otherwise, the individual went through the exposed and infectious compartment before dying from rabies (Table D2).

We initiated all simulations with the introduction of a single index case in Region 3 (Fig. D22). According to [START_REF] Darkaoui | A Century Spent Combating Rabies in Morocco (1911-2015): How Much Longer?[END_REF], there are on average 400 confirmed animal cases per year in Morocco which is certainly an underestimation [START_REF] Broban | Bolstering human rabies surveillance in Africa is crucial to eliminating canine-mediated rabies[END_REF]. We assumed a 20% reporting rate of dog cases in Morocco (Taylor et al., 2017a), and thus retained epidemics with at least 60,000 cases over a 20 to 30-year period (Fig. 20C). We analyzed the results for 50 simulations.

Parametrization of the between-region mobility matrix

To avoid computational difficulties and over-parameterization of the different discrete phylogeographic models, we aggregated the fifteen official Moroccan regions retrieved from the GADM data set (http: //www.gadm.org) into three or seven locations (in two simulated scenarios, respectively) that are based on human demographics and ecological features (Fig. D22). Dog mobility was defined across locations by fitting a radiation model to a raster of human population distribution (WorldPop, n.d.) using the R package movement [START_REF] Golding | Movement: Functions for the analysis of movement data in disease modelling and mapping[END_REF]. In the radiation model, commuting is determined by the job seeking behavior modeled as an absorption and radiation process [START_REF] Simini | A universal model for mobility and migration patterns[END_REF]. The average commuting flux T i, j from location i to location j with population m i and n j , respectively is:

⟨T i, j ⟩ = T i m i n j (m i + s i, j )(m i + n j + s i, j ) (4.3)
with s i, j the total population in the circle of radius r i, j centred at i (excluding the source and destination population).

We used a model of human mobility as it has been shown that humans play a major role in dog rabies spread and maintenance in North Africa, especially across long distances (Talbi et al., 2010;Dellicour et al., 2017). We preferred the radiation model over the gravity model for two reasons: the radiation model has been shown to outcompete the gravity model at local and large scales [START_REF] Simini | A universal model for mobility and migration patterns[END_REF], and it presents the advantage of having no free parameter(s). In our study, we inferred the average daily number of commuters between raster cells of 20 km with more than 1,000 inhabitants per km 2 . The size of the cells corresponds approximately to the municipality level, and the density threshold corresponds to the urban density in Morocco. The number of commuters was then aggregated at the location level.

Evolutionary model of RABV genomes associated with cases

Simulation studies that analyze the accuracy of phylogeographical techniques often use the inference model as the simulation model [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF][START_REF] Müller | The Structured Coalescent and Its Approximations[END_REF][START_REF] Kalkauskas | Sampling bias and model choice in continuous phylogeography: Getting lost on a random walk[END_REF]. Here, we took an epidemiological perspective by simulating rabies epidemics using a metapopulation model and by inferring the spatiotemporal history of rabies from RABV sequences and not from phylogenetic trees. After simulating rabies epidemics as described above, RABV genomes associated with each case were simulated according to the HKY model [START_REF] Hasegawa | Dating of the human-ape splitting by a molecular clock of mitochondrial DNA[END_REF]. We simulated in R sequence evolution forwards-in-time along the transmission chains which were used in the same way as a phylogeny.

We opted for a simple evolutionary process in which selection, gene partition, and site heterogeneity were not considered. Parameter values are listed in Table D2. The genome of the index case is a real canine rabies genome of 13 kb length isolated in Morocco in 2013 (GenBank Accession Number KF155001.1) [START_REF] Marston | Next generation sequencing of viral RNA genomes[END_REF].

Sampling schemes of viral sequences

The aim of the study is to determine the impact of sampling bias on phylogeographic inference and how alternative sampling schemes may mitigate the effects of such sampling bias. To address the former issue, we sampled either uniformly (uniform) or with a sampling bias favoring viral sequences from highly populated locations (Regions 3 and4). In the latter scenario, sequences from Regions 1, 2, 5, 6, and 7 had a weight equal to one, whereas Regions 3 and 4 had a weight equal to 2. 5, 5, 10, 20 or and 50 (biased-2.5, biased-5, biased-10, biased-20, and biased-50, respectively, Fig. 20D). To mitigate the potential effects of sampling bias, we tested a different setup reproducing a surveillance system. In this setup, a biobank of 5,000 sequences were drawn from each epidemic with a weight of one for Regions 1, 2, 5, 6, and 7, and a weight of 10 or 20 for Region 3 and 4. Subsets of sequences were sampled from the biobank either uniformly (uniform surv.), by maximizing the spatial coverage (max per region), or by maximizing the spatiotemporal coverage (max per region and per year). For all sampling schemes, a large sample of 500 sequences and a nested sample of 150 sequences were drawn over the entire epidemic except for the first year, as we assumed that the spread of the virus would remain undetected at the start of the epidemic as observed in other settings [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF].

Discrete phylogeographic analysis in BEAST 2.2.1. Generation of BEAST XML files and phylogeography inference set up

Tailored XML template files for the BASTA and MASCOT structured coalescent models, as well as for the discrete trait analysis (CTMC) model, were edited using the lxml Python package to add sequence alignments along with their metadata. Bayesian phylogeographic analyses were performed using BEAST v1.10.5 (Suchard et al., 2018) for the CTMC model (Lemey et al., 2009a), andBEAST v2.6.4 (Bouckaert et al., 2019) for MASCOT v2.2.1 [START_REF] Müller | MASCOT: parameter and state inference under the marginal structured coalescent approximation[END_REF] and BASTA v3.0.1 [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF], making use of the BEAGLE library v3.1.1 [START_REF] Ayres | BEAGLE: An Application Programming Interface and High-Performance Computing Library for Statistical Phylogenetics[END_REF]. We assumed an HKY substitution model with a strict molecular clock. Population dynamics in the CTMC model followed a constant population size prior. We chose this prior since the model of population dynamics is not expected to impact migration history inference and the constant population size model is often chosen for the analysis of endemic diseases. For the BASTA and MASCOT structured coalescent models, all demes were set to have equal size due to numerical issues leading to a computation time of over 70 hours per million iterations (data not shown). For both models, asymmetric migration matrices were inferred and BSSVS was used to avoid over-parametrization. The detailed list of prior distributions is available in Table D3 for each inference framework.

If deme sizes are set to be equal in the structured coalescent model but the actual population dynamics vary through time, the model tends to explain population dynamics by migration dynamics. In our simulations, the incidence changed dramatically over time and location (Fig. 20C), thus the inference by the structured coalescent model is expected to improve when accounting for time-varying population dynamics. To test this hypothesis, we used monthly incidence data from our simulations as a predictor of the deme sizes by using a GLM in MASCOT [START_REF] Müller | Inferring time-dependent migration and coalescence patterns from genetic sequence and predictor data in structured populations[END_REF]. We tested this alternative parametrization (MASCOT-GLM) in the following conditions: uniform, biased-2.5, biased-5, biased-10, biased-20, biased-50, uniform surv. 10, and uniform surv. 20.

These different BEAST analyses were run for at least 20 and 40 million steps, and sampled every 2,000 and 4,000 steps for small and large alignments, respectively. In total, 8,800 XML files were run for this study, for a total of an estimated 1,500 hours of computation on multi-core CPUs across different computing infrastructures (Table D4).

Analysis of phylogeographic inference output

For each BEAST analysis, adequate mixing was assessed based on the ESS values of the continuous parameters. We calculated ESS values using a Python function adapted from Tracer v1.7.2 [START_REF] Rambaut | Posterior Summarization in Bayesian Phylogenetics Using Tracer 1.7[END_REF]. When at least one continuous parameter had an ESS value below 200, chains were resumed to reach at most 120 million iterations. Analyses that exhibited ESS values lower than 200 at this point were discarded (Tables D5 andD6). Due to the higher computational burden of BASTA, the ESS cutoff was reduced to 100. We discarded a 10% burn-in in the selected chains. The combined posterior tree distributions were summarized into MCC trees using TreeAnnotator for BASTA and the CTMC, and the Python library dendropy [START_REF] Sukumaran | DendroPy: a Python library for phylogenetic computing[END_REF] for MASCOT and MASCOT-GLM.

Summary statistics, ESS values, Bayes factors (BFs) on migration rates (Lemey et al., 2009a), root state probabilities, dates of lineage introduction, and lineage migration counts were calculated in Python before plotting the results in R using the ggplot2 package [START_REF] Wickham | ggplot2: Elegant Graphics for Data Analysis[END_REF].

Performance analysis

To assess the accuracy of the phylogenetic reconstruction, the time to the most recent common ancestor (TMRCA) of every pair of sampled tips was computed on both the MCC tree and the simulated transmission chain, and these outcomes were subsequently compared using the Pearson correlation coefficient (Fig. 20A). In addition, we evaluated the impact of sampling bias and alternative sampling strategies on the estimation of the total migration counts, lineage migration counts, and dates of first lineage introduction into each sampled location using five metrics: (4.4)

• Calibration

calibration 95% = 1 n n ∑ i=1 1 {θ i ∈HPD 95% (D i )} (4.5)
• Mean relative bias

MRB = 1 n n ∑ i=1 1 θ i ( θi -θ i ) (4.6)
• Mean relative 95% highest posterior density (HPD) width

width 95% = 1 n n ∑ i=1 1 θ i (HPD 97.5% (D i ) -HPD 2.5% (D i )) (4.7)
• Weighted interval score (WIS): a generalization of the absolute error accounting for estimation uncertainty. We present the formula of the WIS and refer to the original article for further details, notably on the interval score [START_REF] Bracher | Evaluating epidemic forecasts in an interval format[END_REF].

W IS α {0:K} (F, y) = 1 K + 1/2 × (w 0 × |y -m| + K ∑ k=1 {w k × IS α k (F, y)}) (4.8)
We denote θ i the true value of the parameter, D i the parameter posterior distribution, θi the median estimate, HPD 95% the 95% HPD, K the number of prediction intervals included in the calculation of the WIS, y the observed outcome by forecast F, m the predictive median on the (1α k ) × 100 prediction interval, IS α k the interval score on the (1α k ) × 100 prediction interval and w k its weight. The mean relative bias and the mean relative 95% HPD width are defined when the true value is not zero. However, the total migration counts and the lineage migration counts for some pairs of locations can be null in our simulations whereas the algorithms infer a non-null median. These cases were not considered in the calculation of the mean relative bias and the mean relative 95% HPD width. We reported their numbers in the caption of the corresponding figures.

Data analysis 2.3.1. RABV expansion in the Philippines

We extended our comparative analysis of the CTMC, BASTA, and MASCOT by analyzing a set of RABV genetic sequences using the three approaches. In total, 233 sequences corresponding to the RABV glycoprotein gene were sampled in the Philippines from 2004 and 2010 [START_REF] Saito | Genetic Diversity and Geographic Distribution of Genetically Distinct Rabies Viruses in the Philippines[END_REF]. In the original discrete phylogeographic analysis, the authors studied viral spread across 11 out of the 17

Philippines regions and showed that the genetic diversity was highly spatially-structured, notably at the island level (Tohma et al., 2014). Here, we evaluated spread across the six sampled islands (Luzon, Catanduanes, Oriental Mindoro, Cebu, Negros Oriental, and Mindanao) to compare the reconstructions on a highly structured data set and limit the number of demes that considerably slow down BASTA and MASCOT. We assumed an HKY nucleotide substitution model with an among-site rate heterogeneity modeled by a discretized gamma distribution [START_REF] Yang | Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: Approximate methods[END_REF], and an uncorrelated relaxed molecular clock with an underlying lognormal distribution [START_REF] Drummond | Relaxed phylogenetics and dating with confidence[END_REF]. For the CTMC, we assumed a constant size coalescent model for the viral demographics as in the original analysis. For MASCOT and BASTA, current implementations assume a constant population size model for the viral demographics within demes. A detailed description of the priors is reported in Table D7. For each algorithm, we combined three post-burnin independent chains of 50 million iterations each.

The early dynamics of SARS-CoV-2 worldwide spread

Tracking viral disease spread in animal populations faces many challenges, and to our knowledge, no reliable incidence data are available for zoonoses such as rabies. In this context, MASCOT-GLM cannot readily be used. We analyzed the early worldwide spread of SARS-CoV-2 to compare the inferences of the CTMC, BASTA, MASCOT, and MASCOT-GLM. [START_REF] Lemey | Accommodating individual travel history and unsampled diversity in Bayesian phylogeographic inference of SARS-CoV-2[END_REF] Contrary to the original study, we analyzed migration between six discrete locations: Africa, Americas, Asia, China, Europe, and Oceania. For MASCOT-GLM, we used the daily number of confirmed cases at the continent level from Our World In Data [START_REF] Ritchie | Coronavirus Pandemic (COVID-19)[END_REF], or from the (World Health Organization (WHO), n.d.) as a predictor of the deme sizes. The former is referred to as MASCOT-WID, and the latter as MASCOT-WHO. We smoothed the number of new confirmed cases using a seven-day moving average. The detailed description of the priors is reported in Table D8. We combined three post-burnin independent chains of 50 or 100 million iterations for each inference.

Results

Simulation framework

We simulate RABV epidemics across three or seven locations using a stochastic metapopulation model (Fig. 20A) whose connectivity matrix is parameterized using human population mobility that we estimated by fitting the radiation model of [START_REF] Simini | A universal model for mobility and migration patterns[END_REF] to human population density data from (WorldPop, n.d.) (Fig. 20B). As each location is associated to a specific deme/population, we refer to the two simulation frameworks as the three or seven demes framework for the remainder of the text. We simulate 50 epidemics that start with the introduction of a single case and lead to at least 60,000 cases over a 30-year period (Fig. 20C). On top of the transmission chains, we simulate viral genomes for each case and then subsample starting one year after the introduction of the index case either 150 or 500 sequences in a biased or unbiased fashion (Fig. 20D). We then perform Bayesian discrete phylogeographic analysis on the geolocated and time-stamped sequence alignments before comparing the true and reconstructed evolutionary and migration histories for each discrete phylogeographic approach. Importantly, the vast majority of samples in the three demes framework contain at least one sequence of each deme which is not the case for the seven demes framework for which sampling bias often leads to unsampled locations, also called "ghost" demes.

Robust estimation of the phylogeny and genetic parameters with respect to sampling bias While the focus of our simulation study is on reconstructing the spatial spread, we first assess the potential impact of sampling bias on estimating the phylogeny itself, as well as the evolutionary parameters (Fig. 21A).

The phylogeny of the simulated pathogen is not impacted by sampling bias when using CTMC, BASTA, and MASCOT (Fig. 21A andS1). In addition, the average evolutionary rate (Fig. 21C), the stationary nucleotide frequencies (Figs. D2 to D5), and the ratio of transition-transversion rates (Fig. D6) are all well estimated at any level of sampling bias.

Spatiotemporal history reconstruction in (un)biased conditions

As the inferred spatiotemporal histories of lineages cannot be compared in a unique simple way between the different approaches, we use four types of summary statistics: (i) the total migration counts -corresponding to Markov jumps in the case of CTMC and their equivalent for BASTA and MASCOTthat account for multiple migration events along the tree branches (Fig. 22), (ii) the lineage migration counts (Fig. D7), (iii) the lineage introduction dates into the sampled locations (Fig. 23), and (iv) the root location (Fig. 24). We evaluate the performance of the phylogeographic models using five metrics:

the correlation between true and estimated values, the proportion of estimated parameters for which the true value is in the 95% highest posterior interval (HPD) that we refer to as the calibration, the mean relative bias, the mean relative 95% HPD width, and the weighted interval score (WIS). The WIS is a generalization of the absolute error accounting for estimation uncertainty [START_REF] Bracher | Evaluating epidemic forecasts in an interval format[END_REF]. The smaller the WIS, the better the inference. It is widely used to evaluate epidemic forecasts and favors estimates that are slightly biased but with a narrow confidence interval compared to estimates without bias but very large uncertainty [START_REF] Bracher | Evaluating epidemic forecasts in an interval format[END_REF].

First, we assess the reconstruction of the spatial process in the absence of sampling bias. In the unbiased/representative (uniform) scenario, CTMC correctly estimates the four types of parameters. Indeed, the correlation between the true and estimated parameter values is high, and the WIS is close to zero.

BASTA and MASCOT show no correlation for the total migration counts on uniform samples and higher WIS compared to CTMC (Fig. 22A andE) indicating biased median estimates and higher uncertainty around the point estimate. The correlation is over 0.5 when we consider the lineage migration counts under the three and seven demes frameworks. This suggests that BASTA and MASCOT only partly recover the global migration process in the absence of sampling bias (Figs. D7 andD15). Overall, CTMC outperforms BASTA and MASCOT when the sampling is representative of the true underlying transmission process, as BASTA and MASCOT only recover the big picture of the migration process.

Secondly, we evaluate how phylogeographic algorithms perform under increasing levels of bias. While CTMC satisfyingly estimates the total migration counts in the absence of sampling bias, the correlation and the calibration drop rapidly with bias and the mean relative 95% HPD width tends to decrease suggesting that bias strongly impacts CTMC estimates (Fig. 22A-C). Nevertheless, the WIS and the mean relative bias remain smaller than those of BASTA and MASCOT, even at high levels of bias. Consequently, CTMC leads to median estimates that are closer to the true values but with 95% HPDs that are too narrow. It leads to a biased picture of the geographical process with some transition events that are A-E) Impact of the increasing levels of spatial bias on the correlation, the calibration, the mean relative 95% highest posterior density (HPD) width, the mean relative bias, and the WIS between the simulated and the estimated total migration counts. (F-J) Mitigation of the impact of spatial bias on the correlation, the calibration, the mean relative 95% HPD width, the mean relative bias, and the WIS between the simulated and estimated total migration counts by using alternative sampling strategies. In the left and right columns, samples are drawn from biobanks with an underlying bias of 10 and 20, respectively. Overall, the algorithms correctly estimate the total migration counts when the correlation and the calibration are high (close to 1 and 100, respectively) and when the mean relative 95% HPD width, the mean relative bias, and the WIS are close to zero. Finally, the mean relative bias and the mean relative 95% HPD width are not defined when the true value is null. We removed 612 out of 3,600 and 380 out of 3,600 simulated migration events in the small and large samples, respectively, due to null true values.

drastically underestimated (Fig. D7). BASTA and MASCOT less accurately estimate the total migration counts with no correlation between simulated and estimated values. They are also less confident with an average 95% HPD width that is ten to thirty times higher compared to CTMC. This uncertainty is exacerbated in large samples analyzed with MASCOT in the seven demes framework, for which almost 30% (87 out of 300) of the chains have low ESS values often due to bimodal structured coalescent posterior density. Additionally, BASTA and MASCOT partly recover the global migration process (lineage migration counts) even at high levels of bias since correlation and calibration are not impacted by bias (Fig. D8). When we consider transmission dynamics between three demes, BASTA and MASCOT yield higher correlation levels than in the seven demes scenario (Figs. D15 andD16). Overall, the WIS indicate better performance of CTMC over BASTA and MASCOT.

When it comes to the estimation of lineage introduction dates, BASTA seems to outcompete CTMC and MASCOT under the three demes framework (Fig. D17) but not under the seven demes framework (Fig. 23A-E). In the three demes framework, the uncertainty around the median estimate remains high for BASTA and MASCOT, and the correlation and the calibration are barely affected by bias for BASTA, contrary to CTMC and MASCOT. In the seven demes framework, correlation is low for both BASTA and MASCOT but not affected by bias. CTMC performs poorly with a sharp decrease in both correlation and calibration in the three demes framework, and a slighter decrease in the seven demes framework.

It also tends to estimate more ancient lineage introduction dates compared to BASTA and MASCOT in both frameworks. Of note, samples of 500 sequences displayed a higher correlation than samples of 150 sequences at low and intermediate levels of bias for CTMC (conditions 2.5, 5 and 10 in Fig. 23A andS8A).

Finally, we analyze the potential impact of sampling bias on root location estimation (Fig. 24A andS18A). Of note, the location probability of the true root location is very heterogeneous among the 50 simulated epidemics when there is no or little sampling bias, notably for the two approximations of the structured coalescent model. Root location prediction by CTMC is affected by sampling bias, notably in the three demes framework (Fig. D18), which is in agreement with previous findings (De [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF]. As for the other parameters, BASTA and MASCOT perform less well compared to CTMC, at any level of bias. On the other hand, sampling bias moderately worsens their estimates. They also perform relatively better in the three demes framework.

Sample balancing mitigates the impact of sampling bias

We test alternative sampling strategies in order to mitigate the impact of sampling bias. Large and biased samples of 5,000 sequences that we refer to as biobanks were generated, then discrete phylogeographic analyses were carried out on subsamples of 150 or 500 sequences, which aimed at reproducing real life situations. For example, researchers may have access to numerous viral specimens from biobanks but cannot analyze all of them due to computational limitations, potential underlying biased sampling that may lead to spurious results, or financial limitations.

Similar to the analyses on systematically biased samples, the estimation of the total migration counts (Fig. 22F-J), lineage migration counts (Fig. D6.F-J), lineage introduction dates (Fig. 23E-H), and root location posterior probabilities (Fig. 24B-C) is strongly impacted in biased subsamples (uniform surv.) for the three approaches. By maximizing the spatial (region) or the spatiotemporal coverage (region+year), the correlation of lineage migration counts increased substantially for the CTMC even when the underlying sampling bias was high (weight=20, i.e. sequences from oversampled regions are 20 times more likely to be samples), and to a lesser extent for BASTA and MASCOT. Calibration remained high for BASTA and MASCOT, as shown earlier (Fig. 22G and Fig. 23F) while it considerably improved for CTMC. Estimates of the lineage migration counts by BASTA and MASCOT are improved in the region and region+year conditions compared to the uniform surv. condition, illustrated by a decreased mean relative 95% HPD width and decreased WIS. Still, performance remained lower than for CTMC. In the three demes framework, we obtain even stronger improvements in terms of correlation and decreased mean relative bias for BASTA and MASCOT (Fig. D15). Overall, subsampling strategies that maximize the spatial or spatiotemporal coverage considerably improved the inference of the geographical spread by the CTMC, and improved inference under BASTA and MASCOT to a lesser extent.

True incidence data as a predictor of the time-varying deme sizes mitigate sampling bias in MASCOT

Due to the lack of statistical power (data not shown), we have forced all deme sizes to be equal in BASTA and MASCOT and to be constant over time, the latter being currently the default assumption of both structured coalescent models. This hypothesis is potentially impactful given that deme sizes are directly related to the migration history in the structured coalescent model [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF][START_REF] Müller | MASCOT: parameter and state inference under the marginal structured coalescent approximation[END_REF]. To relax this assumption and allow for time-varying effective population sizes, we next use the monthly incidence data from our simulations as a predictor of the deme sizes over time in the generalized linear model (GLM) extension of MASCOT and denote the resulting model as MASCOT-GLM. This approach is only available for MASCOT, we can therefore not perform the same analysis for BASTA.

By accommodating for the time variations of deme sizes, the correlation, mean relative 95% HPD width, mean relative bias, and WIS are markedly improved with MASCOT-GLM compared to BASTA and MASCOT for the total migration counts (Fig. 22A-E), lineage migration counts (Fig. D7A-E), and lineage introduction dates (Fig. 23A-E) under biased and unbiased spatial sampling. In the absence of spatial sampling bias (uniform), the mean relative bias for the total migration counts decreases from 5% for BASTA and MASCOT to -0.2% for MASCOT-GLM (Fig. 22D), and the correlation between simulated and inferred total migration counts increases approximately from 0.2 to 0.75. Inference performance is improved for all migration parameters even under highly biased sampling conditions. For example, the mean relative bias of total migration counts remains close to zero for MASCOT-GLM, while it increases up to 38% for BASTA. In addition to the strong correlation and the low mean relative bias between simulated and estimated values, the uncertainty around the true value is low compared to BASTA and MASCOT. We obtain similar results in the biased subsamples of the surveillance sampling protocols (uniform surv.).

Analysis of the spread of RABV in the Philippines

As a case study to compare the performance of the three algorithms, we analyze the spread of RABV in dog populations between six Philippine islands (Luzon, Catanduanes, Oriental Mindoro, Cebu, Negros

Oriental, and Mindanao) using 233 sequences of the RABV glycoprotein gene isolated between 2004 and 2010 [START_REF] Saito | Genetic Diversity and Geographic Distribution of Genetically Distinct Rabies Viruses in the Philippines[END_REF]Tohma et al., 2014). Discrete phylogeography is particularly adapted here to model transmission in animal populations across an archipelago. In this data set, sampling is highly heterogeneous across the different islands: Luzon represents up to 65% of the total data set while Oriental Mindoro is represented only by a single sequence (Fig. D19). This heterogeneity is very unlikely to be representative of the underlying transmission but rather due to case underreporting outside Luzon.

Previous studies on RABV in the Philippines suggested that although the circulating lineages likely circulate independently in the main islands [START_REF] Saito | Genetic Diversity and Geographic Distribution of Genetically Distinct Rabies Viruses in the Philippines[END_REF]Tohma et al., 2014), inter-island transmission events can lead to sustained circulation in previously rabies-free islands [START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF].

Importantly, the patterns of spatial spread were evaluated using the CTMC at a finer spatial scale (Tohma et al., 2014). Here, the CTMC model also predicts a highly spatially-structured phylogeny with few migration events between islands. It reconstructs four island-specific clades located in Catanduanes, Luzon, Mindanao, and Negros Oriental with high node and location posterior support (Fig. 25A). BASTA and MASCOT also predict the Catanduanes, Mindanao, and Negros Oriental clades with high node and location posterior support (Fig. 25B-C). However, the migration history of the Luzon clade is more uncertain with potential intense migrations between Luzon and Oriental Mindoro islands, the most and least sampled islands, respectively. As shown in the simulations, CTMC might be overconfident compared to BASTA and MASCOT but the uncertainty of the two approximations of the structured coalescent model might be related to the pseudo-ghost demes, i.e. locations for which very few sequences are available. As

we don't have information regarding the number of cases over time, we could not apply MASCOT-GLM to this data set. Gray tiles correspond to transitions associated with a migration rate that is not statistically supported, i.e., with a Bayes factor lower than 3.

Analysis of the early spread of SARS-CoV-2 across the world

In the context of zoonotic diseases, surveillance systems mostly rely on disease monitoring in human populations. Thus, there are typically no reliable estimates of the number of new cases in wild animal populations and, depending on the country and the species considered, domestic animal populations.

However, for pathogens infecting the human population, such estimates are typically widely available, as is the case for SARS-CoV-2 and as has also been shown used previously when studying Dengue virus, HIV and West Nile virus [START_REF] Gill | Understanding Past Population Dynamics: Bayesian Coalescent-Based Modeling with Covariates[END_REF][START_REF] Dellicour | Epidemiological hypothesis testing using a phylogeographic and phylodynamic framework[END_REF].

To compare the phylogeographic reconstructions of the four algorithms tested above, we analyze a data set of SARS-CoV-2 genomic sequences from the early stage of the pandemic [START_REF] Lemey | Accommodating individual travel history and unsampled diversity in Bayesian phylogeographic inference of SARS-CoV-2[END_REF]. In the original study, the initial wave of SARS-CoV-2 infections was investigated using a novel travel historyaware extension of the CTMC model, which we here refer to as CTMC-TRAVEL.

We again use the CTMC model, BASTA and MASCOT as well as MASCOT-GLM to analyze the data set. MASCOT-GLM is informed using the seven-day moving average of case count data either from Our World In Data [START_REF] Ritchie | Coronavirus Pandemic (COVID-19)[END_REF] or from the (World Health Organization (WHO), n.d.). MASCOT-GLM is then referred to as MASCOT-WID and MASCOT-WHO, respectively (Fig. D20). Due to the low number of mutations accumulated in the SARS-CoV-2 genome at the start of the pandemic, the posterior support of internal nodes for each algorithm is low and the tree topology very uncertain [START_REF] Morel | Phylogenetic Analysis of SARS-CoV-2 Data Is Difficult[END_REF]. Besides, we do not intend to reconstruct the origins of SARS-CoV-2 which in any case cannot be addressed solely with phylogeographic analyses [START_REF] Pipes | Assessing Uncertainty in the Rooting of the SARS-CoV-2 Phylogeny[END_REF]. That is why our comparison focuses on the posterior support of four clades originally identified by [START_REF] Lemey | Accommodating individual travel history and unsampled diversity in Bayesian phylogeographic inference of SARS-CoV-2[END_REF] D1).

For the latter two reconstructions, most of the ancestral branches were not inferred to occur in China and, similarly to the RABV data set, these approaches predict the least sampled locations (Africa and Oceania)

to play a major role in the transmission process. For CTMC, BASTA and MASCOT, posterior distributions of the total migration counts with a Bayes factor (BF) < 3 are not depicted but marked as non-significant (NS). We identify bimodal marginal posterior distributions with a (*) and we report for each posterior distribution the median and 95% HPD. We normalize the width of the violin plots so that the cumulative density is equal to one.

We next incorporated incidence data from either Our World In Data or the WHO into MASCOT-GLM.

Interestingly, the reconstructions differed strongly between the two data sets for incidence. While MASCOT-WID predictions are uncertain with multimodal total migration counts (Fig. 26) and do not reflect the original spread from China (Fig. D21.E), MASCOT-WHO estimated migration counts that are close to the estimates of CTMC-TRAVEL (Fig. 26) and its MCC tree is in agreement with the origin of the pandemic (Fig. D21.E). Importantly, the two data sets differ strongly in how well early cases are covered (Fig. D20), with the WHO data set being more representative of the incidence over time.

Overall and as also suggested by our simulations, while the structured coalescent model, in principle, allows to mitigate sampling biases, it can itself be highly biased when the wrong population dynamics are assumed.

Discussion

Sampling bias is a key challenge in phylodynamic inference [START_REF] Frost | Eight challenges in phylodynamic inference[END_REF], as in discrete phylogeography. In its early developments, the evaluation of the impact of sampling bias on Bayesian discrete phylogeography models was restricted by the availability of whole genomes (Lemey et al., 2009a). The SARS-CoV-2 pandemic has led to a paradigm shift as genomic surveillance became part of routine surveillance systems around the world (Hodcroft et al., 2021a). Here, we evaluated the impact of sampling bias on discrete phylogeography inference using simulated and empirical data to provide insightful knowledge on how sampling bias affects such inference and how it could be mitigated.

Inference performance in absence of sampling bias

In our simulation study, genetic parameters (i.e., average evolutionary rate, stationary nucleotide frequencies, ratio of transition-transversion rates) are correctly estimated and tree topologies match the corresponding simulated transmission chains for all approaches. In addition, CTMC leads to high correlation between simulated and estimated spatiotemporal parameters as well as low relative and absolute error in absence of sampling bias. Overall, CTMC reconstructs the spatiotemporal histories well and its estimates are more accurate in large samples. BASTA and MASCOT do not correctly infer the spatiotemporal parameters in the seven demes framework but correlation between simulated and estimated total migration counts is slightly improved in the three demes framework while remaining lower than CTMC.

This could result from three different causes. First, we assumed that all deme sizes are equal and constant over time in BASTA and MASCOT, the former to avoid overparameterization and the latter being the only available assumption in current implementations. Such a parameterization is more appropriate in the case of endemic circulation with limited time-varying dynamics such as local extinctions. However, large variations in time and local extinctions occur in our simulations meaning that we had to assume incorrect population dynamics in BASTA and MASCOT. This is confirmed by the better performance of MASCOT-GLM in uniform samples that accommodates for the true population dynamics. Secondly, we would expect BASTA and MASCOT to perform better on "even" samples that contain approximately as many sequences of each sampled location [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF]. In our simulation study, uniform sampling does not imply an even representation of sampled locations. Indeed, locations where the virus has not circulated much are less represented. Such an effect is more pronounced in the seven demes framework than the three demes framework and we effectively observe poorer performances of BASTA and MASCOT in the seven demes framework. Finally, the structured coalescent model is known to be sensitive to ghost demes, i.e. unsampled locations [START_REF] Beerli | Effect of unsampled populations on the estimation of population sizes and migration rates between sampled populations[END_REF][START_REF] Ewing | Estimating Population Parameters using the Structured Serial Coalescent with Bayesian MCMC Inference when some Demes are Hidden[END_REF][START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF]. As we considered the sampling process to be naive of the number of affected locations, locations where the virus has not circulated much may remain unsampled. This is true for the seven demes framework only for which we observe poorer performance of BASTA and MASCOT compared to the three demes framework. However, the impact of ghost deme inclusion and potential misspecification on the estimation of the migration patterns remains unclear. While two studies showed that accounting for ghost demes in the structured coalescent model improves the inference of deme size [START_REF] Beerli | Effect of unsampled populations on the estimation of population sizes and migration rates between sampled populations[END_REF][START_REF] Ewing | Estimating Population Parameters using the Structured Serial Coalescent with Bayesian MCMC Inference when some Demes are Hidden[END_REF], [START_REF] Ewing | Estimating Population Parameters using the Structured Serial Coalescent with Bayesian MCMC Inference when some Demes are Hidden[END_REF] also showed that adding just a few sequences from the ghost deme leads to the overestimation of the migration rate.

Inference performance under sampling bias

We show that CTMC, BASTA, and MASCOT are impacted by spatial sampling bias in different ways.

CTMC performance is dramatically impaired with increasing levels of sampling bias. This is directly linked to the geographical sampling frequencies that inform the likelihood of CTMC [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF]. It also tends to be overconfident, and this overconfidence worsens with stronger sampling bias as previously shown [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF]. However, the impact of sampling bias can be mitigated by either using large samples at low levels of sampling bias or controlling for sampling bias by balancing sample composition (region and region+year subsamples) at intermediate levels of sampling bias. These results were well-replicated in a simpler framework of transmission between three locations which rules out the confounding effect of the simulation complexity and unsampled locations on our results (see section 4 of the Supplementary Materials).

BASTA and MASCOT do not accurately estimate the total migration counts nor the lineage introduction dates in biased and unbiased conditions. Nevertheless, the overall migration process evaluated by the lineage migration counts is relatively well captured with a correlation around 0.5 that is not impacted by sampling bias contrary to CTMC in both the three demes and seven demes scenarios. We show that the approximations of the structured coalescent model are generally less confident than CTMC which is in agreement with a previous study [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF] and their uncertainty around median estimates increases with sampling bias. We also show that sample composition impacts the inference of BASTA and MASCOT in the three demes framework since correlation levels are strongly improved and bias and uncertainty are reduced for all spatiotemporal parameters in "even" samples (region and region+year), despite the underlying surveillance bias. Still, BASTA and MASCOT estimates display lower correlation with the simulated values, higher uncertainty and higher relative and absolute bias compared to CTMC.

In the seven demes framework, the results are less clear which may be due to the presence of ghost demes. Interestingly, BASTA seems to outperform CTMC and MASCOT in the inference of the lineage introduction dates in the three demes framework. This result was however not replicated in the seven demes framework.

While structured coalescent methods potentially allow mitigating sampling biases as previously shown [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF], assuming incorrect population dynamics very likely introduces biases. Structured coalescent models currently assume constant population sizes in all demes, and often require the additional assumption of equal population sizes to reach convergence and attain proper mixing. When the true underlying population dynamics are complex with large differences between populations, the models cannot estimate the population sizes with low uncertainty and compensate for this issue in the estimation of the migration rates, so ultimately in the migration history. We addressed this issue by modeling population dynamics more accurately using a GLM approach whenever the required incidence data to do so were available. Indeed, using incidence data to inform population dynamics in MASCOT counteracts the impact of sampling bias even at high levels. This result also underlines the fact that location sampling frequencies do not inform the structured coalescent model when population dynamics are known [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF]. It also shows that the inclusion of ghost demes is not necessary when the true population dynamics are incorporated in the model. Overall, our results showcase the importance of considering the assumptions of population dynamics on the ancestral state reconstruction in structured coalescent model approximations (Table 7).

Analysis of empirical RABV and SARS-CoV-2 data sets

We further compare the approaches on real data sets of RABV and SARS-CoV-2. As dog case counts were not available for RABV, we compare only CTMC, BASTA, and MASCOT. CTMC predicts a highly spatially-structured migration process whereas BASTA and MASCOT predict a non-parsimonious sce-nario. We observe similar results for the SARS-CoV-2 data set. As we have set equal deme sizes in BASTA and MASCOT but a single tip is sampled for Oriental Mindoro in the RABV data set and Africa in the SARS-CoV-2 data set, the two algorithms compensate for location underrepresentation by estimating high backwards-in-time migration rates to the underrepresented location (Oriental Mindoro and Africa). Our results are in line with previous studies reporting strong differences between CTMC and the structured coalescent model on real data sets [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF][START_REF] Dudas | MERS-CoV spillover at the camelhuman interface[END_REF]. However, there is also evidence in the literature of a good agreement between the two types of models [START_REF] Faria | Establishment and cryptic transmission of Zika virus in Brazil and the Americas[END_REF][START_REF] Brynildsrud | Global expansion of Mycobacterium tuberculosis lineage 4 shaped by colonial migration and local adaptation[END_REF][START_REF] Yang | Bayesian phylodynamics of avian influenza A virus H9N2 in Asia with time-dependent predictors of migration[END_REF][START_REF] Mavian | Toxigenic Vibrio cholerae evolution and establishment of reservoirs in aquatic ecosystems[END_REF]. Such similarities can result from sample composition (at least ten sequences per location in [START_REF] Yang | Bayesian phylodynamics of avian influenza A virus H9N2 in Asia with time-dependent predictors of migration[END_REF]), the parameters used for comparison (probability of clade ancestral location in [START_REF] Faria | Establishment and cryptic transmission of Zika virus in Brazil and the Americas[END_REF]), prior information (information on the root location in [START_REF] Brynildsrud | Global expansion of Mycobacterium tuberculosis lineage 4 shaped by colonial migration and local adaptation[END_REF]), or the underlying transmission dynamics. Besides, these studies focused on the overall migration process which corresponds to the lineage migration counts in our simulation study and we showed that the overall migration process is roughly estimated at any level of bias. In brief, we show on real data sets that singletons may be inferred as drivers of the migration process in an unparsimonious way by structured coalescent model approximations. This result supplements a previous study on the impact of the inclusion of few ghost deme sequences on the inference of migration rates [START_REF] Ewing | Estimating Population Parameters using the Structured Serial Coalescent with Bayesian MCMC Inference when some Demes are Hidden[END_REF], however their impact remains unclear and deserves close consideration.

Interestingly, the posterior density of the structured coalescent model in BASTA is bimodal for the SARS-CoV-2 data set. Its major mode corresponds to a past migration history close to CTMC-TRAVEL and our expectations of SARS-COV-2 spread at the start of the pandemic, whereas the minor mode corresponds to the non-parsimonious scenario. Such bimodality was not observed for MASCOT in the SARS-CoV-2 analysis. This difference in estimation is not unexpected since the two structured coalescent model approximations are different. However, it is not clear which characteristics of the two algorithms would lead to different behaviors. Another possibility relies on the choice of operators that determine how well the two approximations explore the parameter and tree space in which case MAS-COT should lead to a bimodal posterior density on the long run.

Practical implications for the analysis of empirical data sets

Computation time is an important consideration in real-life situations. CTMC is a fast algorithm that can handle many sequences while facing little convergence issues, which made it the predominant approach.

For example, CTMC and its extensions have been extensively used during the SARS-CoV-2 pandemic [START_REF] Candido | Evolution and epidemic spread of SARS-CoV-2 in Brazil[END_REF]Dellicour et al., 2021b;[START_REF] Lemey | Accommodating individual travel history and unsampled diversity in Bayesian phylogeographic inference of SARS-CoV-2[END_REF][START_REF] Perez | The early SARS-CoV-2 epidemic in Senegal was driven by the local emergence of B.1.416 and the introduction of B.1.1.420 from Europe[END_REF][START_REF] Kaleta | Antibody escape and global spread of SARS-CoV-2 lineage A.27[END_REF][START_REF] Alteri | Genomic epidemiology of SARS-CoV-2 reveals multiple lineages and early spread of SARS-CoV-2 infections in Lombardy, Italy[END_REF]Dellicour et al., 2021c;[START_REF] Butera | Genomic sequencing of SARS-CoV-2 in Rwanda reveals the importance of incoming travelers on lineage diversity[END_REF]. In general, researchers analyzed large data sets whose composition was corrected or reflected case counts [START_REF] Candido | Evolution and epidemic spread of SARS-CoV-2 in Brazil[END_REF][START_REF] Lemey | Accommodating individual travel history and unsampled diversity in Bayesian phylogeographic inference of SARS-CoV-2[END_REF] or the number of hospitalizations per geographical location (Dellicour et al., 2021b). According to our results, even though the pool of available sequences is not representative of the underlying transmission process, CTMC inference should be little impacted when using even subsamples of the available sequences. However, we did not test sampling strategies based on case counts in our simulations.

With BASTA and MASCOT, computation time can become rapidly cumbersome and even impractical -also as a result of poor mixing of structured coalescent model parameters -when the number of sequences and locations increase. In such cases, these approaches are not able to discriminate which migration routes are the most important in the migration process leading to bimodal structured coalescent posterior densities, as observed for MASCOT on large samples of 500 sequences in the seven demes framework and for BASTA on the SARS-CoV-2 data set. Repeating these problematic analyses with different starting values did not redeem these issues. Other studies have reported similar issues [START_REF] Richardson | Gene exchange drives the ecological success of a multi-host bacterial pathogen[END_REF]. However, these problematic inferences can potentially be overcome by informing structured coalescent models with additional covariate data on viral population size dynamics. Indeed, as a result of adding such data, MASCOT-GLM not only outperformed the other approaches at estimating spatiotemporal parameters but also displayed improved mixing as expected with GLM approaches which improves the computational burden. However, such improvements depend on the availability and informativeness of the case count data used, notably on the early viral population size dynamics. This is illustrated in our analysis of the SARS-CoV-2 data for which the addition of WHO data led to improved chain mixing and past migration inference compared to the Our World in Data data, knowing that the dynamics are rather similar in the two data sets but they go back to January, 4th 2020 for the WHO data and to January, 23rd 2020 for the Our World in Data data.

Limitations

We acknowledge several limitations of our study. First, BASTA and MASCOT are expected to perform better on even samples, a condition that we did not directly test. In the representative (uniform) samples, location frequencies inform CTMC and thus it would be expected to be favored over BASTA and MASCOT. Still, we show that MASCOT and BASTA perform better on even (region and region+year) samples in the three demes framework even if they are derived from biased large biobanks. This result suggests that BASTA and MASCOT perform better on even samples with no ghost demes. Second, our subsampling procedure in the simulation analysis could leave some locations unsampled, which can be considered as an extreme case of sampling bias. While this happened in only a few highly biased samples in the three demes framework, it is very common in the seven demes framework even in absence of sampling bias. It is difficult to determine whether the poor performance of MASCOT and BASTA in absence of bias in the seven demes framework compared to the three demes framework is due to ghost demes or is simply due to the higher number of locations. Additionally, we cannot rule out that the effects of sampling bias we observe are due to unsampled locations/unspecified ghost demes rather than unrepresentative sampling. We did not include unsampled locations as ghost demes in such conditions. However, this is unlikely to improve migration rate estimation [START_REF] Ewing | Estimating Population Parameters using the Structured Serial Coalescent with Bayesian MCMC Inference when some Demes are Hidden[END_REF]. Third, the impact of sampling bias certainly depends on the underlying overall migration rate as shown by [START_REF] Liu | The impact of sampling bias on viral phylogeographic reconstruction[END_REF], an impact that we did not investigate here.

Another limitation concerns the incorporation of epidemiological data in phylogeographic models. Here, deme sizes in MASCOT-GLM are informed by case count data but this kind of data may not be readily available (Grubaugh et al., 2019b) and is known to be often biased due to varying testing effort and strategy, as well as differential testing behaviors by age [START_REF] Buckee | Thinking clearly about social aspects of infectious disease transmission[END_REF]. It is difficult to predict how MASCOT-GLM would perform if parameterized with biased case counts, a case that we did not address in our simulations. The comparison between the WHO and WID cases data, however, suggests that biased coverage of the true case load could bias such inference. If case count data are not reliable, one could use hospitalization data instead (Dellicour et al., 2021b). Further, a similar approach is available under the CTMC framework but we did not test it here. This framework consists in modeling the migration process with CTMC and the overall population dynamics with the GLM extension [START_REF] Gill | Understanding Past Population Dynamics: Bayesian Coalescent-Based Modeling with Covariates[END_REF] of the skygrid coalescent model [START_REF] Gill | Improving Bayesian Population Dynamics Inference: A Coalescent-Based Model for Multiple Loci[END_REF]. In this extension, case count over all locations could be used as a predictor of the viral population size over time. Yet, such an approach assumes a panmictic population and remains rare.

Finally, it is difficult to generalize our results in regards to the number of demes. Our choice of the number of locations was influenced by the RABV scenario in Morocco. While a scenario with three demes was doable, the one with seven demes turned out to be difficult to analyze, notably due to computational burden (Supplementary Materials). More research and development is needed for data sets with a large number of locations (> 15) and it currently seems unlikely that such analyses are possible at all with BASTA and MASCOT.

Perspectives

In conclusion, sampling bias can be tackled at different levels of data generation and analysis in phylogeographic analyses: sample constitution, inference model choice, and data integration (e.g. through an integrated GLM). Other studies also assess the impact of sampling bias in post hoc analyses [START_REF] Chaillon | HIV persists throughout deep tissues with repopulation from multiple anatomical sources[END_REF][START_REF] Vrancken | Comparative Circulation Dynamics of the Five Main HIV Types in China[END_REF] or explicitly model sampling patterns [START_REF] Guindon | Accounting for spatial sampling patterns in Bayesian phylogeography[END_REF].

Although the exploration of the impact of sampling bias has increased over the recent years and more robust methodologies have been developed, many aspects remain unclear, among which the impact of unsampled locations, biased epidemiological data incorporation, or the relative performances on even versus representative samples. Whenever possible, we would advise to opt for an even sampling strategy across geographical locations, compare the inferences of the different approaches or compare the inferences over multiple subsamples when analyzing real data sets. These considerations are all the more important in a world of ever-growing genome sequence generation and concern not only human viral diseases but also zoonoses and epizooties.

Chapter 5

Impact of contact heterogeneity on respiratory diseases transmission in households

Households are an ideal setting for the study of respiratory diseases transmission. Modeling studies of household transmission data have helped characterize the role of children for infections such as influenza and SARS-CoV-2. However, estimates obtained in these studies may be biased since they do not account for the heterogeneous nature of household contacts. Here, we quantified the impact of contact heterogeneity between household members on the estimation of the relative susceptibility and infectivity of children. We simulated epidemics of SARS-CoV-2-like and influenza-like infections in a synthetic database of 1,000 households assuming heterogeneous contact levels. Contacts were assumed more frequent in the father-mother pair, followed by the child-mother pair, then the child-child pair, and finally the child-father pair with the least contact frequency. Child susceptibility and infectivity were then estimated while accounting for heterogeneous contacts or not. We showed that the relative susceptibility of children was under-estimated by approximately 20% in the two disease scenarios. Concerning the relative infectivity of children, it is underestimated by 20% when children and adults had different infectivity levels. This study shows how in small communities, heterogeneous contact patterns should be evaluated and accounted for. New household studies collecting both disease and contact data are needed to cast light on the role of complex contacts on disease transmission and improve the estimation of key biological parameters.

Introduction

Households constitute an ideal setting for the study of respiratory diseases transmission. These diseases generally transmit through aerosols, a transmission route that is favored in closed indoor spaces like households, or through droplets during close contacts that are characteristic of contacts between household members [START_REF] Tsang | Household Transmission of Influenza Virus[END_REF][START_REF] Wang | Airborne transmission of respiratory viruses[END_REF]. Household transmission represents a nonnegligible part of respiratory disease transmission, and, in extreme cases like influenza infections, living with an infected individual is the most important risk factor of infection [START_REF] Longini | Estimating household and community transmission parameters for influenza[END_REF]. In addition, the study of respiratory diseases transmission is simplified in households because case contacts are well-defined which facilitates their follow-up after exposure and the estimation of the secondary attack rate (SAR), defined as the proportion of susceptible household contacts that are infected after the index case is detected.

Mathematical models of disease transmission in households have helped characterize the role of children (Cauchemez et al., 2004;[START_REF] Cauchemez | Household transmission of 2009 pandemic influenza A (H1N1) virus in the United States[END_REF][START_REF] Tsang | Indirect protection from vaccinating children against influenza in households[END_REF][START_REF] Endo | Fine-scale family structure shapes influenza transmission risk in households: Insights from primary schools in Matsumoto city, 2014/15[END_REF][START_REF] Dattner | The role of children in the spread of COVID-19: Using household data from Bnei Brak, Israel, to estimate the relative susceptibility and infectivity of children[END_REF] and vaccination [START_REF] Tsang | Indirect protection from vaccinating children against influenza in households[END_REF]Prunas et al., 2022) in the dynamics of transmission. This is generally done by estimating their relative susceptibility and infectivity compared to adults. For example, child susceptibility was shown to be half adult susceptibility for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections (Davies et al., 2020a;[START_REF] Viner | Susceptibility to SARS-CoV-2 infection among children and adolescents compared with adults[END_REF][START_REF] Dattner | The role of children in the spread of COVID-19: Using household data from Bnei Brak, Israel, to estimate the relative susceptibility and infectivity of children[END_REF][START_REF] Franco | Inferring age-specific differences in susceptibility to and infectiousness upon SARS-CoV-2 infection based on Belgian social contact data[END_REF], and twice as susceptible to influenza infections (Cauchemez et al., 2004;[START_REF] Cauchemez | Household transmission of 2009 pandemic influenza A (H1N1) virus in the United States[END_REF]. The relative infectivity and susceptibility estimated in these studies can be caused by biological factors (e.g. different levels of viral shedding when infected or different propensity to get infected when exposed), but also by the level of physical contacts in the household [START_REF] Lordan | Considerations for the Safe Operation of Schools During the Coronavirus Pandemic[END_REF]. However, so far, household transmission models have always ignored the second source of heterogeneity, implicitly assuming estimated values were indicative of different biological parameters between children and adults. To date, only one study has tested the hypothesis of homogeneous mixing in the household environment that is underlying in all these studies [START_REF] Goeyvaerts | Household members do not contact each other at random: Implications for infectious disease modelling[END_REF]. It concluded that, (i) on average, children have less contacts with their father than with other siblings, (ii) the overall rate of physical contacts between children decreases with age, and (iii) the magnitude of contacts decreases with household size. The study shows that the assumption of homogeneous mixing does not hold in the household environment. As a result, part of the estimated differences between children and adults in households is expected to be due to different mixing patterns in the household. It is important to determine by how much the complex mixing patterns in the households may bias estimates of biological susceptibility/infectivity that are derived in household studies.

Here, we aim at investigating how heterogeneous contact patterns in households could bias estimates of respiratory diseases transmission, notably the force of infection between household members, the relative susceptibility of children compared to adults, and their relative infectivity. We simulate epidemics in households using realistic contact patterns [START_REF] Goeyvaerts | Household members do not contact each other at random: Implications for infectious disease modelling[END_REF] and we estimate key transmission parameters, accounting or not for the heterogeneous nature of the contact patterns.

Methods

Household composition in the simulated data set

We constituted a synthetic database by randomly sampling with replacement 1,000 households from a subset of the households (n = 225) of the multi-center household study RECOVER [START_REF] Verberk | Transmission of SARS-CoV-2 within households: a remote prospective cohort study in European countries[END_REF]. From the RECOVER study, we retained households with two to five household members that correspond either to heterosexual couples, or to single-parent or hetero-parental two-generation families.

We excluded same-sex couples and homo-parental families because of the lack of estimates in the study by [START_REF] Goeyvaerts | Household members do not contact each other at random: Implications for infectious disease modelling[END_REF] on contact levels between partners of same-sex couples, and more specifically, between same-sex parents and their children. From the original household study RECOVER, we kept two types of information for each household member: (i) whether the individual is the index case, and (ii) the category of the individual (i.e., mother, father, or child).

Simulation of household epidemics 2.2.1. In silico follow-up protocol

We assumed that the 1,000 households from the synthetic database were recruited and followed up starting from the symptom onset of the index case, and for up to 20 days. Since our aim is to ascertain how the misspecification of contact intensity may impact the estimation of transmission rates, we decided to consider a simple inference context: in the simulated data set we analyze, all cases exhibit symptoms and testing is perfect.

Force of infection within households

In the simulations, the probability that an individual k in household h gets infected between time t and time t + dt is:

Λ k (t,t + dt) = 1 -exp α × dt + ∑ l∈I h {ξ l <t} β n/2 κ k,l µ s,k µ i,l t+dt t f (u -ξ l |s l )du (5.1)
where:

• α is the instantaneous hazard of infection in the community.

• l ∈ I h {ξ l < t} correspond to the infected individuals in household h that were infected before time t, with ξ l their infection date.

• β n/2 models the dependency between the baseline transmission rate β and the household size n.

Here, the baseline transmission rate β corresponds to the transmission rate in heterosexual couples, when n = 2, κ k,l = κ mother, f ather = 1, µs, k = µ s,adult = 1, and µi, l = µ i,adult = 1. See below for the meaning of the parameters, and the reference categories.

• κ k,l is the relative contact rate between recipient k and infector l according to the type of the pair.

We used the mother-father pair as a reference, which means that for this type of pair κ k,l = 1. For the other pairs, we used the odds-ratios estimated by [START_REF] Goeyvaerts | Household members do not contact each other at random: Implications for infectious disease modelling[END_REF] during weekdays.

Mother-child pairs were assumed to be 11% less in contact than mother-father pairs, father-child pairs 58% less in contact, and pairs of children 24% less in contact.

• µ s,k is the relative susceptibility of recipient k according to their age. For adults, µ s,adult = 1.

• µ i,l is the relative infectivity of infector l according to their age. For adults, µ i,adult = 1.

• f (tξ l |s l ) is the density probability function of the generation time conditioned on the incubation period s l of infector l. Here, the generation time is defined as the distribution of the interval between the infection time of the infector and the infection time of the recipient. We used the distribution estimated by [START_REF] Ferretti | The timing of COVID-19 transmission[END_REF] for SARS-CoV-2 infections.

If k gets infected between t and t + dt, its exact time of infection ξ k is drawn uniformly between t and t + dt, and its incubation period s k is drawn from a log-normal distribution with log-mean=1.63 and logstandard deviation=0.5, previously estimated by McAloon et al. (2020) for SARS-CoV-2 infections. If symptom onset occurs after the end of the follow-up, the individual is not detected. We simulate continuous times of infection and symptom onset. For realistic reasons, we truncated the time of symptom onset and kept only the day of symptom onset to perform the inference.

We tested two scenarios. The first one corresponds to a SARS-CoV-2-like scenario, with child sus-ceptibility being half adult susceptibility, and 20% less infectious than adults (Table 8). The second corresponds to an influenza-like scenario with children being twice as susceptible but as infectious as than adults. For each scenario, the value of the baseline transmission rate in heterosexual couples β was chosen so that the overall SAR is approximately 37% (Table 8). Finally, we simulated epidemics in the synthetic household database 100 times for each scenario.

Statistical inference

Statistical inference was performed in a Bayesian framework with data augmentation (Cauchemez et al., 2004). In the section above, we detailed the model by using adults as the reference. In the inference model, we used children as a reference because pairs of children were more numerous than pairs of adults which improved inference. We estimated the hazard of infection in the community α, the force of infection between two children in a household of size four β 4/2 κ child,child µ s,child µ i,child , the relative susceptibility 1/µ s,child and relative infectivity 1/µ i,child of adults compared to children using a simple Metropolis-Hastings algorithm. For α, we assumed an exponential prior distribution with parameter equal to 500 which means that the instantaneous incidence rate is 200/100,000 inhabitants in the population, and for β 4/2 κ child,child µ s,child µ i,child , we assumed a uniform prior distribution between 0 and 10. We used a log-normal distribution with log-mean = 0 and log-standard deviation = 1 for 1/µ s,child and 1/µ i,child .

Infection dates and symptom onset dates were augmented after each parameter iteration. Infection dates were sampled from the incubation period distribution estimated by McAloon et al. (2020), and the exact time of symptom onset was sampled uniformly over the observed day of symptom onset.

For each simulation, we launched one Markov chain Monte Carlo (MCMC) chain for 50,000 iterations.

We discarded a burn-in of 5,000 steps and applied a thinning of 20 for the estimation of the posterior distributions. Convergence was assessed visually and by calculating the effective sample size (ESS) using the "effectiveSize" function in the "coda" R package for every parameter of every MCMC chain.

ESS values exceeded 500 for all parameters in all chains. The comparison of the prior and posterior distributions of model parameters is available in Fig. E1 for the SARS-CoV-2 infection scenario and in Fig. E2 for the influenza virus infection scenario in Appendix E.

Comparison of simulated and estimated parameters

The estimates of β , µ s,child , and µ i,child were compared to the values used in the simulations using two metrics:

• the mean relative bias defined as MRB = 1 100 ∑ 100 i=1

1 θ i ( θi -θ i );
• and the 95% coverage defined as coverage 95% = 1 100 ∑ 100 i=1 1 {θ i ∈CrI 95% (D i )} .

We denote θ i the true value of the parameter, D i the parameter posterior distribution, θi the median estimate, and CrI 95% the 95% credible interval.

Results

In the COVID-19 scenario depicted in Fig. 27, the three parameters of within household transmission are well estimated when the inference model accounts for heterogeneous contact patterns between household members ("correct" inference model in Fig. 27). The transmission rate in heterosexual couples is relatively well estimated with a mean relative bias lower than 3% (Fig. 27D) and a 95% coverage of 96% (Fig. 27G). The estimation of child relative susceptibility is also satisfying with a mean relative bias around -5% (Fig. 27E) and a 95% coverage of 91% (Fig. 27H). Finally, the 20% reduction of child infectivity is well estimated with a mean relative bias of about 4% (Fig. 27F) and a high 95% coverage of 98% (Fig. 27I). The slight overestimation of the transmission rate in heterosexual couples mirrors the slight underestimation of child relative susceptibility as the two parameters are negatively correlated. When the inference model does not account for contact heterogeneity ("incorrect" inference model in Fig. 27), the estimation of the parameters of within household transmission is largely biased. The transmission rate is overestimated by 29% and the 95% CrI never contains the true value (Fig. 27D andG). Child relative susceptibility and child relative infectivity are underestimated by more than 20% (Fig. 27E-F) and their 95% coverage does not exceed 20% (Fig. 27H-I). Given that heterosexual couples have the strongest level of contact in the simulations, their net transmission rate is higher than the net transmission rate in pairs of children or between parents and children. When the inference model assumes that all household members have the same level of contact patterns, it has to compensate for the higher transmission rate in pairs of adults and the lower transmission rates between children and in parent-child pairs by increasing the transmission rate in heterosexual couples and reducing the susceptibility and infectivity of children.

The extent of the bias that we observe results from the values used to model contact heterogeneity in the simulations. We obtain very similar results for the flu scenario presented in Fig. 28. When contact heterogeneity is accounted for, the transmission rate in heterosexual couple is slightly overestimated by around 3% with a 95% coverage of 91% (Fig. 28D andG). Child relative susceptibility is underestimated by about 5% with a 95% coverage of 91% (Fig. 28E andH). In contrast, when homogeneous mixing between household members is assumed, the transmission rate in heterosexual couples is overestimated by 19% (Fig. 28D) and child relative susceptibility is underestimated by 18% (Fig. 28E) given that the 95% coverage does not exceed 40% for both parameters (Fig. 28G-H). Just like in the COVID-19 scenario, estimation bias in the incorrect inference model results from the compensation of contact heterogeneity in the simulations.

A

The results for child relative infectivity are less clear in the flu scenario in which adults and children have the same infectivity levels. Indeed, the parameter is overestimated by 8% with a 95% coverage of 85% (Fig. 28F andI) with the correct model and it is underestimated by 8% with a 95% coverage of 82% with the incorrect model (Fig. 28F andI).

Discussion

In this study, we showed that the estimates of the child relative susceptibility and child relative infectivity can be biased when heterogeneous contact patterns between household members are not accounted for in the inference. When considering the transmission of SARS-CoV-2 or influenza viruses in households with heterogeneous contacts derived from [START_REF] Goeyvaerts | Household members do not contact each other at random: Implications for infectious disease modelling[END_REF], the incorrect assumption of homogeneous mixing in the inference model leads to the underestimation of child relative susceptibility and child relative infectivity by around 20%. This underestimation compensates the lower contact rate between children and other household members compared to the contact rate in heterosexual couples in the simulated epidemics [START_REF] Goeyvaerts | Household members do not contact each other at random: Implications for infectious disease modelling[END_REF]). Biased estimates of child relative susceptibility and child relative infectivity may mislead the parameterization of disease transmission models that are often used to design intervention measures.

To circumvent this problem, it seems important to integrate information about contact patterns in household transmission models. Using the results of a household contact survey such as [START_REF] Goeyvaerts | Household members do not contact each other at random: Implications for infectious disease modelling[END_REF] to inform an observational study in a different country seems problematic since household contact patterns are expected to vary across socioeconomic levels and cultural practices. Ideally, the study design of household transmission studies should integrate the collection of epidemiological data on transmission and contact data between household members. The behavior of household members may change when one or multiple members develop symptoms, and it is therefore important to monitor variations in contact patterns during the study period. In addition, behavioral change upon symptomatic infection may depend on socioeconomic factors. For instance, physical distancing and self-isolation are not possible in crowded households [START_REF] Vopham | Social Distancing Associations with COVID-19 Infection and Mortality Are Modified by Crowding and Socioeconomic Status[END_REF]. Finally, the way contact data are collected may be influential. Contact surveys may be subject to reporting bias (selective revealing or suppression of information) because participants may under-report undesirable behaviors like not implementing physical distancing.

Alternatively, wearable electronic devices that measure close-proximity interactions are highly valuable in contexts with complex networks and for the study of infectious disease transmission [START_REF] Starnini | Robust Modeling of Human Contact Networks Across Different Scales and Proximity-Sensing Techniques[END_REF]. However, records typically do not exceed a few days due to the limited autonomy of these devices. Here, we simulated epidemics in households so that around 37% of household contacts get infected. The choice of this value for the SAR is relatively arbitrary given that estimates from empirical data vary from a few percents to 45% for the historical variant of SARS-CoV-2 (Madewell et al., 2020), and from 4% to 45% for influenza viruses [START_REF] Cauchemez | Household transmission of 2009 pandemic influenza A (H1N1) virus in the United States[END_REF][START_REF] Lau | Household Transmission of 2009 Pandemic Influenza A (H1N1): A Systematic Review and Meta-analysis[END_REF][START_REF] Glatman-Freedman | Attack Rates Assessment of the 2009 Pandemic H1N1 Influenza A in Children and Their Contacts: A Systematic Review and Meta-Analysis[END_REF][START_REF] Azman | Household transmission of influenza A and B in a school-based study of nonpharmaceutical interventions[END_REF]. Simulating epidemics with a lower SAR would reduce the number of infected pairs, and thus, the statistical power to estimate child relative susceptibility and child relative infectivity.

Besides, we made simplistic assumptions in the simulation model assuming that all infected individuals eventually develop symptoms and testing is perfect which would not have been adapted for the analysis of empirical data. We also assumed that the risk of infection in the community is the same for adults and children, although it may vary with age [START_REF] Cauchemez | Role of social networks in shaping disease transmission during a community outbreak of 2009 H1N1 pandemic influenza[END_REF][START_REF] Tsang | Indirect protection from vaccinating children against influenza in households[END_REF]. However, household studies are not designed to evaluate the risk of infection in the community, notably because participants are followed up over short time periods, and such studies are generally deployed for the study of diseases with intense transmission in households. For these reasons, the interpretation of the hazard of infection in the community should subject to caution, as its estimation is loosely reliable.

In conclusion, the heterogeneous nature of contacts in households is expected to bias estimates of key parameters that are estimated from household studies, such as the relative susceptibility and infectivity of children. It is therefore important that these complex household contact patterns are accounted for in future household studies. Data are scarce and many knowledge gaps remain concerning the changes of household contact patterns that may occur following infections. Future household transmission studies should collect that on both disease and contact patterns, raising new challenges related to the study design, and model development.

General discussion

1. Synthesis of the results

Dog rabies circulation and its control

In Chapter 1, I highlight the main mechanisms underlying rabies circulation in dog populations: small R 0 leading to short transmission chains, role of imports from neighboring endemic areas, co-circulation of viral lineages, and high inter-individual heterogeneity in behavior and transmission. A recent modeling study analyzing an extensive contact tracing data set has confirmed the intricate role of all these mechanisms in the maintenance of rabies circulation in an African and endemic setting, the Serengeti district in Tanzania [START_REF] Mancy | Rabies shows how scale of transmission can enable acute infections to persist at low prevalence[END_REF]. In Chapter 1, I also underline that there is a high variability across settings related to the role of wildlife, importations, and dog ecology. For example, the Iranian epidemiological context is underlaid by the co-circulation of independent viral lineages in dogs and wildlife that belong to very different rabies biogeographical clades (Dellicour et al., 2019). On the other hand, I show in Chapter 2 that a unique viral clade circulates in dogs, the most important reservoir of rabies in Cambodia [START_REF] Ly | Rabies Situation in Cambodia[END_REF], with presumably no or few cross-country transmission events. More intriguingly, the epidemiological situation in Cambodia contrasts with its neighbors where multiple clades, either related to Chinese lineages [START_REF] Nguyen | Molecular epidemiology of rabies virus in Vietnam (2006-2009)[END_REF], or other Southeast Asian lineages [START_REF] Ahmed | Molecular Epidemiology of Rabies Viruses Circulating in Two Rabies Endemic Provinces of Laos, 2011-2012: Regional Diversity in Southeast Asia[END_REF][START_REF] Benjathummarak | Molecular genetic characterization of rabies virus glycoprotein gene sequences from rabid dogs in Bangkok and neighboring provinces in Thailand, 2013-2014[END_REF] circulate. Besides, (illegal) dog trade, not only for dog meat consumption, concerns the entire Southeast Asian area [START_REF] Chevalier | Large scale dog population demography, dog management and bite risk factors analysis: A crucial step towards rabies control in Cambodia[END_REF] which means that dogs do cross borders and external introductions very likely occur but do not lead to sustained transmission chains. Parts of rabies transmission dynamics in Cambodia thus remain unclear, notably the role of humans, long-distance transmission events, and spatial heterogeneity.

The comparison of the contributions of epidemiological and phylodynamic modeling in Chapter 1 points to the complementarity of the two methodological approaches. Phylodynamics helped unravel largescale mechanisms of transmission, while epidemiological modeling focused more on the design and evaluation of interventions. Nevertheless, using simulations, several epidemiological modeling studies illustrated how population structure heterogeneity may participate to the maintenance of rabies despite its low transmissibility (Leung and Davis, 2017;Hudson et al., 2019b;Kadowaki et al., 2018). Recent efforts to better characterize dog populations in terms of population density [START_REF] Chevalier | Large scale dog population demography, dog management and bite risk factors analysis: A crucial step towards rabies control in Cambodia[END_REF][START_REF] Mancy | Rabies shows how scale of transmission can enable acute infections to persist at low prevalence[END_REF][START_REF] Thanapongtharm | Spatial Distribution and Population Estimation of Dogs in Thailand: Implications for Rabies Prevention and Control[END_REF], roaming behavior [START_REF] Bombara | A preliminary study to estimate contact rates between free-roaming domestic dogs using novel miniature cameras[END_REF][START_REF] Wilson-Aggarwal | Spatial and temporal dynamics of space use by free-ranging domestic dogs Canis familiaris in rural Africa[END_REF][START_REF] Kittisiam | Analyses of Contact Networks of Community Dogs on a University Campus in Nakhon Pathom, Thailand[END_REF], serological status [START_REF] Velander | Rabies Vaccination in Dogs in Laos: Owner Knowledge and Serological Status of Dogs[END_REF], and ecological interactions with humans [START_REF] Chevalier | Large scale dog population demography, dog management and bite risk factors analysis: A crucial step towards rabies control in Cambodia[END_REF][START_REF] Thanapongtharm | Spatial Distribution and Population Estimation of Dogs in Thailand: Implications for Rabies Prevention and Control[END_REF] Indeed, the vast majority of dogs are owned and owners do trade their dogs on a regular basis but in a very opportunistic way. Although, this trade mostly occurs at small spatial scales, long-distance trade can also happen which implies that humans might have mediated the long-distance transmission events unraveled in Cambodia in Chapter 2, similar to the North African context (Dellicour et al., 2017;Talbi et al., 2010). More extensive field studies are necessary to fill the gap about dog population structure and ecology, and set up more realistic models of rabies transmission in dogs Dog vaccination, a control measure that has been recommended by the WHO for several decades (World Health Organization (WHO) et al., 2018), is the most effective way of controlling rabies circulation.

However, parenteral vaccination of stray and free-roaming dog populations requires large and skilled dog-catching teams that are very costly [START_REF] Yale | Review of Oral Rabies Vaccination of Dogs and Its Application in India[END_REF], thus it is rarely implemented by local authorities despite the importance of these dog populations in RABV circulation (Leung and Davis, 2017;Hudson et al., 2019b;Kadowaki et al., 2018). The complementary use of oral rabies vaccination (ORV) in dogs represents a promising avenue to achieve high vaccination coverage in low-resource settings where the majority of dogs are free-roaming such as in India [START_REF] Yale | Review of Oral Rabies Vaccination of Dogs and Its Application in India[END_REF] and Cambodia [START_REF] Chevalier | Large scale dog population demography, dog management and bite risk factors analysis: A crucial step towards rabies control in Cambodia[END_REF]. Unfortunately, the absence of political engagement and resource mobilization in Cambodia constitute the primary barrier to the implementation of ambitious vaccination policies. As long as rabies is not a notifiable disease in Cambodia, there will be no wide access to dog vaccination nor frequent vaccination campaigns and, the advancement towards rabies elimination will remain compromised. One way to promote political engagement is to show that elimination is feasible or at least that the costs to reduce the number of cases are limited. Our results in Chapter 2 are encouraging in this sense. The relatively strict endemicity of rabies in Cambodia implies that any well-designed vaccination campaign could effectively reduce rabies burden in dogs and human on the short term. However, as local transmission is controlled, re-importations will play a greater role threatening long-term control or elimination. Additional measures such as legislation on vaccination status at importation could help prevent potentially harmful introductions but they pose numerous technical challenges.

In brief, data are necessary at the individual and country levels to better understand setting-specific dynamics of RABV in dogs and design adapted control strategies in the most cost-efficient way.

SARS-CoV-2 household dynamics and interventions to control its transmission

Despite being a close relative of SARS-CoV, SARS-CoV-2 transmits in a very different way [START_REF] Abdelrahman | Comparative Review of SARS-CoV-2, SARS-CoV, MERS-CoV, and Influenza A Respiratory Viruses[END_REF]Cevik et al., 2021) which led to many unknowns and knowledge gaps at the start of the pandemic at the beginning of 2020. At the time, estimating key transmission parameters at the individual-level was crucial to assess variations in infectiousness through time by age and symptom status. Household studies rapidly proved to be valuable and have continued to provide insightful knowledge over the entire pandemic period [START_REF] Pitzer | Household studies provide key insights on the transmission of, and susceptibility to, SARS-CoV-2[END_REF][START_REF] Yang | Understanding how fast SARS-CoV-2 variants transmit from household studies[END_REF]. In parallel, the advent of vaccination gave to public health authorities a means to control circulation while relaxing social distancing measures. Randomized controlled trials were carried out to evaluate vaccine efficacy against severe outcome [START_REF] Baden | Efficacy and Safety of the mRNA-1273 SARS-CoV-2 Vaccine[END_REF], and in a lesser extent, against infection [START_REF] Polack | Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine[END_REF].

However, these vaccine efficacy estimates do not reflect the protective power of vaccination in real life conditions that are not controlled. Besides, randomized controlled trials are not adapted to evaluate the effect of vaccines against transmission in breakthrough infections [START_REF] Lipsitch | SARS-CoV-2 breakthrough infections in vaccinated individuals: measurement, causes and impact[END_REF]. Vaccine effectiveness measures protection in real world conditions and can be estimated in observational studies such as cohort studies, household studies, case control studies, or with the screening method. a similar effect with the same order of magnitude, but they also showed that this effect is transient. Indeed, vaccine effectiveness against transmission in breakthrough infections decreases with time from vaccination. More than 90 days after the second dose, there is no more protective effect against transmission. Vaccine effectiveness against infection also decreases, but fortunately, vaccine effectiveness against severe outcome remains high [START_REF] Feikin | Duration of effectiveness of vaccines against SARS-CoV-2 infection and COVID-19 disease: results of a systematic review and meta-regression[END_REF]. Vaccine effectiveness against infection and transmission is transient due to the waning of vaccine-induced immunity, and vaccine effectiveness has been challenged during the pandemic by the emergence of new SARS-CoV-2 variants. For example, our results in Chapter 3 are applicable to the Alpha variant that represented more than 95% of the cases in Israel at the time of the study [START_REF] Ritchie | Coronavirus Pandemic (COVID-19)[END_REF], but it got rapidly replaced by the Delta variant in June 2021, itself replaced by Omicron in January 2022. Vaccine effectiveness against Delta and Omicron is lower compared to Alpha [START_REF] Andrews | Covid-19 Vaccine Effectiveness against the Omicron (B.1.1.529) Variant[END_REF][START_REF] Bernal | Early effectiveness of COVID-19 vaccination with BNT162b2 mRNA vaccine and ChA-dOx1 adenovirus vector vaccine on symptomatic disease, hospitalisations and mortality in older adults in England[END_REF]. This reduction is due to vaccine variant-mismatch because the more recent variants have accumulated mutations in the spike protein, the main target of vaccine-induced neutralizing antibodies, compared to the ancestral D614G strain used for vaccine production [START_REF] Hewins | Alpha, Beta, Delta, Omicron, and SARS-CoV-2 Breakthrough Cases: Defining Immunological Mechanisms for Vaccine Waning and Vaccine-Variant Mismatch[END_REF]. The adaptive immune evasion of SARS-CoV-2 is one of the main challenges for the control of disease dynamics on the long-term.

Nonpharmaceutical interventions like social and physical distancing proved to be highly valuable to control SARS-CoV-2 transmission at the population-level, notably during the pre-vaccine period [START_REF] Flaxman | Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe[END_REF][START_REF] Zhang | Changes in contact patterns shape the dynamics of the COVID-19 outbreak in China[END_REF]. The impact of nonpharmaceutical interventions was mainly assessed on aggregated data and rarely at the individual level, but it is possible that nonpharmaceutical interventions prevent transmission in the population when implemented by a critical mass of the population without conveying protection at the individual-level. In addition, the magnitude of the reduction of the infection risk when an individual isolates has been rarely quantified [START_REF] Fazio | Social distancing decreases an individual's likelihood of contracting COVID-19[END_REF]. In Chapter 3, I account for physical distancing because household contacts were encouraged to isolate from the index case at enrollment, and not accounting for it would bias our estimates. Besides, social behavior, notably physical contacts within households, is expected to change upon infection by both the case and its contacts.

Here, I estimate a strong effect of isolation behavior in Israeli households whose effectiveness against infection is similar to vaccines. Although these results were very promising, they need confirmation.

Unfortunately, Omicron variants have completely replaced the Alpha variant by now, and since they are much more transmissible than Alpha, physical distancing in closed settings like households will likely be less effective.

Early on in the pandemic, age disparities in cases were observed. Most cases, especially severe cases, were adults suggesting that children are less susceptible to SARS-CoV-2 infection. Many studies have tried to quantify this potential reduction [START_REF] Viner | Susceptibility to SARS-CoV-2 infection among children and adolescents compared with adults[END_REF]Davies et al., 2020a;[START_REF] Zhu | A Meta-analysis on the Role of Children in Severe Acute Respiratory Syndrome Coronavirus 2 in Household Transmission Clusters[END_REF][START_REF] Chung | Comparison of Symptoms and RNA Levels in Children and Adults With SARS-CoV-2 Infection in the Community Setting[END_REF] by analyzing case notification or ascertainment data. However, lower notifications in children may result from multiple factors: (i) lower biological susceptibility, (ii) less social mixing, and (iii) low case ascertainment of asymptomatic and paucisymptomatic cases that are more prevalent in children [START_REF] Lordan | Considerations for the Safe Operation of Schools During the Coronavirus Pandemic[END_REF]. The last two factors may have confounding effects on the estimation of child susceptibility. Besides, the role of children in the transmission at the population-level has changed over the pandemic, in particular when adults were vaccinated. After the first vaccination campaign, a large part of the adult population was vaccinated, thus the proportion of transmission occurring in schools increased and living with a child constituted a risk factor for infection [START_REF] Lessler | Household COVID-19 risk and in-person schooling[END_REF]. In our study presented in Chapter 3, I introduce a parameter for the relative susceptibility of children. Consistent with the literature, I estimate a lower susceptibility for children. To obtain more robust estimates of this parameter, it will be important to integrate to these analyses data describing contact rates between household members. Indeed, I show in Chapter 5 that ignoring contact heterogeneity in households could bias estimates of child relative susceptibility and infectivity. Some studies have also investigated the relative infectivity of children compared to adults [START_REF] Dattner | The role of children in the spread of COVID-19: Using household data from Bnei Brak, Israel, to estimate the relative susceptibility and infectivity of children[END_REF]. In Chapter 3, I do not integrate child relative infectivity because there was not enough statistical power and I wanted to avoid model overparameterization.

Importantly, most results on SARS-CoV-2 transmission during the pandemic were published as preprints or peer-reviewed papers and were rapidly outdated due to the emergence of new variants and changes in priorities. Our estimates covered the Alpha wave in Israel and could not be generalized to the Delta variant that emerged a few months later at a time when vaccine-induced immunity had already decayed at the population level. A follow-up study covering the Delta wave in Israel is undergoing.

RABV and SARS-CoV-2: epidemiological research on different timescales

The differing epidemiology of COVID-19 and rabies dictates the time-scale of their research. As underlined in Chapter 1, the transmission potential of rabies in dogs is low with an R 0 close to one. In contrast, the high transmissibility of COVID-19 leads to explosive dynamics, known as epidemic waves, which requires rapid evaluation within a few days or weeks. The short time-scale of SARS-CoV-2 research also depends on the recurrent emergence of variants with varying transmissibility. New variants should be identified and tracked in real-time, their transmission potential assessed in a timely manner, and their level of vaccine escape quantified when they replace the other variants. All of these steps may occur within a few months as exemplified by the Alpha variant studied in Chapter 3 that circulated in Israel for eight months only, from December 2020 to July 2021. RABV dynamics in relation to its genetic diversity are fairly different. As mentioned in Chapter 1, the co-circulation of RABV variants is com-mon in rabies-affected countries and, so far, no difference of transmission potential between them has been shown. In this sense, rabies research spans more on the long-term. Another aspect of rabies and COVID-19 epidemiology that influences the time-scale of their research is the role of introductions in their maintenance or geographic expansion. While a few introductions of SARS-CoV-2 are sufficient to establish self-sustaining local transmission chains [START_REF] Lemieux | Phylogenetic analysis of SARS-CoV-2 in Boston highlights the impact of superspreading events[END_REF], transmission chains resulting from RABV introductions are short and should be numerous to allow RABV maintenance [START_REF] Mancy | Rabies shows how scale of transmission can enable acute infections to persist at low prevalence[END_REF]. Rabies endemicity in Cambodia that I explore in Chapter 2 is a good example. Introductions from neighboring countries are very likely, but not sufficient in number to compete against the dominant Cambodian clade. Nevertheless, single introductions of rabies may lead in some cases like Bali to sustained transmission [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF].

Beyond their contrasting epidemiology, COVID-19 and rabies have different research agendas and financial resources which also determines the type of data that are collected, the methodological choices, and the amount of scientific production. Rabies exemplifies the lack of detailed epidemiological data which is characteristic of neglected tropical diseases, epizooties in developing countries, and zoonoses.

For such diseases, phylodynamics is a powerful approach as it requires little sampling efforts limiting the costs of data collection and generation. On the other side of the spectrum, studies on SARS-CoV-2 transmission using individual-level data are numerous. They take advantage of national health repositories or highly detailed follow-up in observational studies. Despite the large number of individual-level studies, uncertainties remain on the determinants of transmission, notably concerning partial immunity levels in populations following multiple waves of SARS-CoV-2 variants and more or less targeted vaccination campaigns.

Epidemiology, data availability, financial resources, and scientific opportunities are different for SARS-CoV-2 and RABV, but, as vaccine-preventable diseases, they share the same need for the design of effective vaccination campaigns. In the case of RABV, there is still room for improvement. Most endemic countries that have implemented regular vaccination campaigns are far from elimination and the design of national control strategies is restricted by financial constraints. For SARS-CoV-2, long-term transmission and recurrent emergence of new variants raises new challenges in terms of vaccination production, target population, and vaccination campaign frequency.

Limitations of quantitative tools for the study of infectious diseases spread

Although some of the quantitative tools have been developed a long time ago and are largely used, their limitations are not always well-characterized neither known by modelers. In this thesis, I also investigate the impact of sampling bias and model misspecification on parameter estimation in Chapters 4 and 5.

In Chapter 4, I focus on the impact of sampling bias on discrete phylogeography reconstruction and our conclusions are less clear-cut than previously thought [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF] because none of the three most popular algorithms outperforms the others nor is robust to sampling bias at the same time. CTMC modeling is a valid approach, even when spatial sampling is very biased, but it requires careful sensitivity analyses based on subsamples. Importantly, a recent study by [START_REF] Gascuel | A Darwinian Uncertainty Principle[END_REF] investigated identifiability issues in CTMC modeling, suggesting that further work is needed to precisely assess the limits of parameter identifiability in CTMC. The approximations of the structured coalescent on the other hand were previously thought to be more robust to spatial sampling bias [START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF]. However, in our study, they appear to have limited estimation capacities on real-world data. Interestingly, the addition of unbiased case count data largely improves the performances of one of the approximations of the structured coalescent model (MASCOT-GLM) that even outperforms CTMC. This work has many practical implications that go from study design to sensitivity analyses. Indeed, one can either organize genetic data collection in a way that is representative of the transmission process, prioritize sample size over representativeness to collect as many sequences as possible, perform sensitivity analyses on subsamples that maximize the spatiotemporal coverage, or analyze genetic data collected in an opportunistic way along with case count data that were collected in the least biased way. In the end, our work highlights the importance of testing and discussing the impact of sampling bias, notably on data sets obtained by opportunistic sampling.

In Chapter 5, I explore how assumptions on mixing patterns in household transmission studies impact the estimation of age-varying susceptibility and infectivity parameters. This study is particularly relevant for airborne diseases such as flu and COVID-19 whose transmission in confined spaces is primarily driven by droplets [START_REF] Lei | Routes of transmission of influenza A H1N1, SARS CoV, and norovirus in air cabin: Comparative analyses[END_REF][START_REF] Jayaweera | Transmission of COVID-19 virus by droplets and aerosols: A critical review on the unresolved dichotomy[END_REF]. In such settings, successful transmission depends on case infectivity, contact susceptibility, and contact rate between the infector and the infectee.

I show that not accounting for heterogeneous contact rates between household members leads to biased infectivity and susceptibility estimates. Our simulation study highlights the importance of collecting transmission-related data along with household contact data which, to the best of our knowledge, has not been implemented yet. Designing such a study raises many practical challenges: should household follow-up rely rather on detailed testing and symptom onset data, or seroconversion data? Seroconversion data collection being less constraining for household members and less costly, but more challenging in terms of modeling. Should all household members be surveyed to collect their contacts or only a fraction of them to increase participant adherence? When should household members detail their contacts:

at inclusion or during follow-up? How frequently should household members provide information on their contacts? etc. Importantly, SARS-CoV-2 is known to be transmitted not only by droplets during close contacts but also by aerosols (very small pathogen-laden particles in air that can stagnate when ventilation is low) that allow long-term transmission [START_REF] Jayaweera | Transmission of COVID-19 virus by droplets and aerosols: A critical review on the unresolved dichotomy[END_REF]. For the time being, models of SARS-CoV-2 transmission in households assume that droplets are the primary route of transmission and overlook the potential role of aerosols.

Comparison of epidemiological and phylodynamic modeling

In this thesis, I use epidemiological modeling on individual-level data of partially observed transmission chains and phylodynamics on genetic sequences from cases whose link between one another is unknown.

The two types of approaches allow the study of different phenomena: the former models between-host transmission while the latter models evolutionary processes that shape pathogen genetic diversity. Depending on the rate of within-host evolution relative to the timing of transmission, a phylogenetic tree does not exactly represent a transmission chain, and the pathogen effective population size might not be simply proportional to case counts. Consequently, the estimates of pathogen dispersal by the two approaches may not be easily comparable. For example, the comparison of simulated transmission chains to estimated phylogenetic trees in Chapter 4 is not trivial. Since migration rates estimated by discrete phylogeography do not correspond to the ones of the mobility matrix used in the simulations, I compare counts of migration and introduction events. Actually, model benchmarking in phylodynamics is generally done on phylogenetic trees simulated with a coalescent or birth-death model [START_REF] Gill | Improving Bayesian Population Dynamics Inference: A Coalescent-Based Model for Multiple Loci[END_REF][START_REF] Boskova | Inference of Epidemiological Dynamics Based on Simulated Phylogenies Using Birth-Death and Coalescent Models[END_REF][START_REF] De Maio | New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation[END_REF][START_REF] Müller | MASCOT: parameter and state inference under the marginal structured coalescent approximation[END_REF], rather than alignments of sequences generated from the simulation of viral genetic sequences along transmission chains themselves simulated by an epidemiological model like in Chapter 4. This relatively new approach opens a new avenue for model benchmarking in phylodynamics and allows to test algorithms in more complex situations that are closer to the analysis of real-world data. Besides, the simulated epidemics of RABV decribed in Chapter 4 could be used to assess the performances of algorithms of maximum likelihood-based ancestral character reconstruction such as the CTMC models implemented in PastML (Ishikawa et al., 2019) or

TreeTime [START_REF] Sagulenko | TreeTime: Maximum-likelihood phylodynamic analysis[END_REF].

In the field of epidemiological modeling, models are often very refined and adapted to a specific context. Until recently, source codes were not systematically in open access but a culture shift is currently operating, notably under the requirements of scientific journals to foster open science and analysis reproducibility. Besides, new tools such as Odin [START_REF] Fitzjohn | odin: ODE Generation and Integration[END_REF] or RStan (Stan Development Team, 2020) now facilitate inference even for complex epidemiological models. In contrast, phylodynamics relies on more complex and less flexible models and inference is generally performed using packages like BEAST. In addition to accelerating data analysis and result generation, the use of packages allows non-experts to apply complex methodologies to their own data sets but this comes at the expense of potential misuse or misinterpretation. Although the core hypotheses in phylodynamics are quite rigid, models of population dynamics [START_REF] Gill | Understanding Past Population Dynamics: Bayesian Coalescent-Based Modeling with Covariates[END_REF] and phylogeographic models (Lemey et al., 2014;[START_REF] Müller | Inferring time-dependent migration and coalescence patterns from genetic sequence and predictor data in structured populations[END_REF] have been extended to integrate covariates related to demography, mobility, case counts, climate etc. Inversely, the use of genetic sequences to inform epidemiological models remains challenging. When it comes to individual-level data, epidemiological modeling is an ideal framework related because of its flexibility while accounting for individual heterogeneities in phylodynamics requires the development of new analytical tools.

Still, epidemiological modeling and phylodynamics share common features among which the inference framework. Indeed, Bayesian statistics are generally preferred over maximum likelihood inference, and the Metropolis-Hastings MCMC algorithm as exemplified in this thesis is the most widely used inference algorithm. Furthermore, both approaches can be affected by bias that can occur at the different stages of the analysis, from data collection and preparation, to model choice and specification, or prior choice. Simulation studies provide important insights to assess the impact of such biases and identify the limits of parameter identifiability. In this thesis, simulation studies have helped better characterizing the impact of sampling bias in discrete phylogeography (Chapter 4) and of incorrect mixing assumption (Chapter 5). The development of digital tools to collect, store, and share epidemiological and genetic data have paved the way to big data in epidemiology. This raises new technical challenges related to data storage, optimization of computational times, and inference approach, as Bayesian inference might be computationally impractical on very large data sets.

Perspectives

On SARS-CoV-2 and RABV

Many questions remain regarding RABV spread in dog populations. The role of dog demography, dog movement, dog social structure, dog ecology, and interactions with humans very likely depends on the cultural practices that vary across countries, but also within countries. For example, the epidemiology of rabies in the Northeastern part of Cambodia, close to the Lao and Vietnamese borders, is expected to be very different from that in the rest of the country because hunting practices, dog density, and relationship to dogs are extremely different (Chapter 2). Field studies to collect dog behavior and dog ecology data are key to better understand rabies dynamics and epidemiological data are still needed in most endemic countries. In parallel, RABV genetic data that are already available on GenBank could be exploited in large-scale phylogenetic studies to explore dog rabies transmission across countries in a cost-effective way. This would provide a first overview of the worldwide spread of the virus that should be completed by the above-mentioned finer-scale studies.

SARS-CoV-2 transmission is now well-characterized although there is room left for studies deepening knowledge on the impact of the mosaicism of population immunity on SARS-CoV-2 transmission. The immune profile of individuals against SARS-CoV-2 is now highly heterogeneous within and across countries because it depends on the biological features of the individuals, their personal infection history, and the types and number of vaccine doses they received that greatly varies across countries. On top of that, immunity against SARS-CoV-2 wanes with time from infection or vaccination. Consequently, there is now no clear reference group to estimate vaccination efficacy and vaccine effectiveness. Besides, epidemiological studies that are generally used to evaluate herd immunity at the population level such as cross-sectional serosurveys are not sufficient to assess the mosaicism of population immunity. The level of protection at the individual-level should not focus on individual infection and vaccination histories but on biological correlates like antibody titers. Assessing the quantitative relationship between protection and biological correlates and using this information to interprete serosurvey results will help assess herd immunity.

On methodological approaches

As demonstrated in this thesis, epidemiological modeling is particularly adapted to the integration of host-related determinants, like susceptibility, infectivity, and behavior. Nevertheless, all modeling frameworks are not suitable to account for complex host behaviors that vary in space and time. Network mod-els constitute a good candidate and have already been used to design infection prevention measures in hospital settings using a simulation approach [START_REF] Smith | Optimizing COVID-19 surveillance in long-term care facilities: a modelling study[END_REF], using contact data recorded by using proximity sensors. This approach could be extended to households to measure more precisely heterogeneous contact patterns.

Contrary to epidemiological modeling, phylodynamics is still a relatively new field in which model limitations are still to be defined. While phylogeography is highly valuable, the impact of sampling bias cannot be overlooked and methodological advances that incorporate sampling procedure or uncertainty concerning sample representativeness are to be developed. Besides, theoretical work has shown that CTMC fails at estimating state change counts and root location at the same time [START_REF] Gascuel | A Darwinian Uncertainty Principle[END_REF]. Similar questions related to parameter identifiability concern the structured coalescent in discrete phylogeography and the RRW model in continuous phylogeography. Additional data such as case counts for the structured coalescent model (Chapter 4), or sequence-free cases for the RRW model [START_REF] Kalkauskas | Sampling bias and model choice in continuous phylogeography: Getting lost on a random walk[END_REF] were shown to improve phylogeography inference, but they lead to other sampling issues that also need attention. Another prospect for phylodynamics relates to its predictive power and its use to evaluate control measure which has been only little explored so far [START_REF] Dellicour | Epidemiological hypothesis testing using a phylogeographic and phylodynamic framework[END_REF].

As previously underlined, epidemiological modeling and phylodynamics provide complementary insights on the transmission process. That is why, interdisciplinary studies that exploit the potential of both approaches have emerged, notably for RABV and SARS-CoV-2. We have identified so far two types of interdisciplinary studies that either propose a new unified modeling framework that integrates epidemiological and genetic data [START_REF] Salje | Reconstructing unseen transmission events to infer dengue dynamics from viral sequences[END_REF] -however, only few approaches currently exist and they require extensive model testing and validation -, or that combine multiple modeling approaches and sources of data. In the latter case, investigators benefit from epidemiological modeling, phylodynamics, and basic epidemiological investigation, but tremendous efforts of coordination and communication between the different fields of expertise might complexify scientific production.

Conclusion

In this thesis, I show that quantitative studies in epidemiology encompass a wide range of concepts, techniques, and data. At both ends of the spectrum, we find epidemiological modeling that can incorporate refined information on disease transmission at the individual level and phylodynamics that makes use of genetic sequences embedding coarse information on transmission at the population level. The complementary insights of these two approaches help understanding disease transmission and often guide decision making, as shown in the context of SARS-CoV-2 and RABV. Ultimately, the development of modeling frameworks that unify epidemiological and genetic data is an exciting and promising prospect for epidemiology. 1948; 1987 -1988; 1985 -1986; 1946 -1953 Table A2: Description of the phylogeographic models with an emphasis on data source and potential sources of bias. Table A3: Description of the mathematical models with their key quantitative results. .week -1

Supplementary Tables

): • Development of new methodologies (Mollentze et al., 2014;Cori et al., 2018). Impact of underreporting (Mollentze et al., 2014;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]Laager et al., 2019).

Mains findings

Rabies spread was studied at multiple geographical scales (transborder area, country, district, city, neighborhood). Studies at small spatial scales supported that local scale elimination is achievable on the short term (Laager et al., 2019;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]Bourhy et al., 2016), but introduction events participate in rabies maintenance (Laager et al., 2019;Mollentze et al., 2014;Cori et al., 2018;Beyer et al., 2011) and impede control efforts (Bourhy et al., 2016;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]. Rabies was shown to circulate at low intensity within two cities, Bangui (Bourhy et al., 2016) and N'Djaména (Laager et al., 2019;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]Zinsstag et al., 2009), but connections between urban areas are expected to accentuate rabies spread (Colombi et al., 2020). Indeed, human-mediated movements strongly impact rabies dispersal within countries in North Africa (Dellicour et al., 2017;Talbi et al., 2010) and the Central African Republic (Colombi et al., 2020). According to the setting, they may counteract the effects of control measures.

Spatial and individual heterogeneity were not sufficient to explain rabies maintenance in settings with low circulation (Laager et al., 2019;[START_REF] Wilson-Aggarwal | High-resolution contact networks of free-ranging domestic dogs Canis familiaris and implications for transmission of infection[END_REF] and there is no current evidence of the role of wildlife in the maintenance of rabies (Beyer et al., 2011;Fitzpatrick et al., 2012). At the continental scale, there are both co-circulating RABV lineages (Lemey et al., 2009a;Brunker et al., 2015;Talbi et al., 2009;Hayman et al., 2011;Brunker et al., 2018b) and spatial clustering of RABV lineages (Lemey et al., 2009a;Mollentze et al., 2013;Brunker et al., 2015;Talbi et al., 2009;Brunker et al., 2018b) which points at the role of human-mediated movements.

The dog vaccination coverage recommended by the WHO (70%) has been generally shown to be sufficient to reach dog rabies elimination (Zinsstag et al., 2009;Kitala et al., 2002;Fitzpatrick et al., 2012), except in Ethiopia where a 90% vaccination coverage was recommended (Beyene et al., 2019). Vaccination strategies targeting at-risk dog populations are more effective [START_REF] Beyer | The implications of metapopulation dynamics on the design of vaccination campaigns[END_REF]. The role of underreporting is not clear (Laager et al., 2019;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]Mollentze et al., 2014) but heterogeneous vaccination coverage is shown to disrupt vaccination [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF].

Asia

Current situation

• Disease-free in Japan.

• Recent introductions in Indonesia and Philippines.

• Endemic in China and continental South-East Asia.

Models

• Mostly deterministic models implemented to analyze dog rabies in China (Zhang et al., 2012;[START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF]Zhang et al., 2011;Chen et al., 2015;Huang et al., 2019), Malaysia (Coleman and Dye, 1996;[START_REF] Abdul Taib | Model Simulation for the Spread of Rabies in Sarawak, Malaysia[END_REF] and Indonesia (Coleman and Dye, 1996).

• Agent-based models [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF]Kadowaki et al., 2018;Ferguson et al., 2015).

• Phylogeography (Zhang et al., 2017;Meng et al., 2011;Guo et al., 2013;Wang et al., 2019;Tohma et al., 2014;Dibia et al., 2015;[START_REF] Ma | Re-emerging of rabies in Shaanxi province, China, from 2009 to 2015[END_REF]Yu et al., 2012;Yao et al., 2015).

• Interdisciplinary studies [START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF].

Data

Human rabies cases from passive surveillance, dog rabies cases from active (China) or passive surveillance, contact tracing, dog vaccination data, dog density from surveys, dog movements from household surveys, historical records of dog rabies epidemics in Osaka and of dog and human censuses, RABV genetic sequences from dogs, wildlife and humans.

Modelling aims

• Better understanding of the spatial and temporal dynamics of rabies spread (Zhang et al., 2011;Zhang et al., 2012;Chen et al., 2015;[START_REF] Abdul Taib | Model Simulation for the Spread of Rabies in Sarawak, Malaysia[END_REF]Zhang et al., 2017;Meng et al., 2011;Guo et al., 2013;Wang et al., 2019;Tohma et al., 2014;Dibia et al., 2015;[START_REF] Ma | Re-emerging of rabies in Shaanxi province, China, from 2009 to 2015[END_REF]Yu et al., 2012;Yao et al., 2015;[START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF].

• Identification of circulating lineages (Wang et al., 2019;Dibia et al., 2015;[START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF] and environmental factors impacting rabies spread (Yao et al., 2015;[START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF].

• Spatiotemporal dynamics and interactions of canine and wildlife RABV lineages (Huang et al., 2019;Yu et al., 2012).

• Feasible and effective control strategies (Coleman and Dye, 1996;Huang et al., 2019;Ferguson et al., 2015;[START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF]Zhang et al., 2011;[START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF]Zhang et al., 2012).

• Impact of human-mediated movement [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF]Ferguson et al., 2015) and vaccination coverage [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF] on the efficacy of control strategies.

• Modelling dynamics following an introduction and assessment of the efficacy of current contingency plans (Kadowaki et al., 2018).

• Estimation of the time from introduction to detection according to the value of R [START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF].

Main findings

Rabies introductions in the disease-free islands of the Philippines result from single introductions from neighboring rabies-endemic islands followed by local transmission (Tohma et al., 2014;[START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF].

At the continental scale, RABV lineages are spatially clustered (Guo et al., 2013;Wang et al., 2019) but transboundary movements markedly influence rabies spread (Guo et al., 2013). China is endemic for rabies and multiple RABV lineages co-circulate across the country, notably Asian, Arctic-like and Cosmopolitan lineages (Meng et al., 2011;Yu et al., 2012;Yao et al., 2015). It is thought to be one of the main sources of RABV lineages in Asia (Meng et al., 2011;Guo et al., 2013).

A decade after achieving rabies elimination, it resurged in Yunnan and is currently circulating uncontrolled. This Chinese province corresponds to a crossroads area where multiple RABV lineages circu-late, probably resulting from multiple transboundary movements (Zhang et al., 2017;[START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF].

Moreover, rabies dispersal velocity is weakly associated with forest coverage, croplands and accessible areas [START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF]. Whereas human-mediated movement is not statistically associated with rabies velocity in the Yunnan province [START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF], it is suspected to have played a role in rabies dispersal in the Shaanxi province [START_REF] Ma | Re-emerging of rabies in Shaanxi province, China, from 2009 to 2015[END_REF]. More studies are needed to unravel the interactions between RABV, reservoir ecology and humans in Asia.

In general, rabies is estimated to spread at low grade with an R lower than two [START_REF] Townsend | Designing Programs for Eliminating Canine Rabies from Islands: Bali, Indonesia as a Case Study[END_REF]Zhang et al., 2011;[START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF]Zhang et al., 2012;Chen et al., 2015;Huang et al., 2019;[START_REF] Abdul Taib | Model Simulation for the Spread of Rabies in Sarawak, Malaysia[END_REF]. Occasional long distance migrations which were documented in the Philippines [START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF], Indonesia (Dibia et al., 2015) and China (Chen et al., 2015;Yao et al., 2015;Guo et al., 2013) might contribute to disease persistence.

The role of wildlife has been poorly studied and remains unclear in endemic areas (Huang et al., 2019;Yu et al., 2012).

Dog vaccination is the most effective strategy (Zhang et al., 2011;[START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF]Huang et al., 2019;[START_REF] Abdul Taib | Model Simulation for the Spread of Rabies in Sarawak, Malaysia[END_REF] and may be improved by complementary measures such as domestic and stray dog management (Zhang et al., 2011;[START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF]Zhang et al., 2012), dog confinement (Ferguson et al., 2015), or increasing public awareness (Zhang et al., 2012;Huang et al., 2019;Kadowaki et al., 2018). Homogeneous vaccination coverage was shown to yield better elimination prospects (Townsend et al., 2013a;Chen et al., 2015;Ferguson et al., 2015) which might be due to its robustness to humanmediated movements (Townsend et al., 2013a). In Japan, Kadowaki et al. (2018) showed that the current contingency plan is adapted to the rapid detection, control and elimination of rabies after an introduction. The authors emphasized the benefits of dog owner awareness and the control of stray dogs in the improvement of the plan (Kadowaki et al., 2018).

The time to detection is also a crucial factor in the success of rabies elimination after introduction. The faster the disease is detected, the higher the odds of eradicating it (Townsend et al., 2013a). For example, it's estimated that the surveillance system detected rabies circulation one year after its introduction in the Luzon island group in the Philippines [START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF]. This delay would have been greater with a lower reporting capacity [START_REF] Tohma | Molecular and mathematical modeling analyses of inter-island transmission of rabies into a previously rabies-free island in the Philippines[END_REF].

Middle East

Current situation

Endemic

Models

Phylogeography (Dellicour et al., 2019;Horton et al., 2015) Data RABV genetic sequences from dogs, wildlife, and humans.

Modelling aims

• Spatiotemporal dynamics and interactions of canine and wildlife RABV lineages (Dellicour et al., 2019;Horton et al., 2015).

• Identification of circulating lineages and environmental factors impacting rabies spread (Dellicour et al., 2019).

Main findings

Many lineages circulate that are phylogenetically related to Asian, Arctic/Artic-like, or Cosmopolitan lineages resulting from sustained circulation in dogs and wildlife after introduction (Dellicour et al., 2019;Horton et al., 2015). There is a strong spatial segregation of RABV lineages circulating in Iran.

Overall, their spread is not driven by road connectivity, but humans presumably play a role since lineages tend to disperse towards and remain in highly populated areas. Lineages were less likely to spread towards grasslands and to occur in areas with barren vegetation. These results may be influenced by biased sampling towards populated areas however (Dellicour et al., 2019).

Wildlife seems to play a role in rabies maintenance in dog populations (Dellicour et al., 2019;Horton et al., 2015) but data are not sufficiently available to study host shift and dynamics between reservoirs.

South America Current situation

Endemic for bat rabies and localized resurgences of rabies in dogs.

Models

• Fuzzy compartmental model (Ortega et al., 2000).

• Phylogeography (Carnieli et al., 2013;Carnieli et al., 2011).

Data

Serological data and RABV genetic sequences from dogs and wildlife.

Modelling aims

• Implementation of a fuzzy logic approach to model rabies spread (Ortega et al., 2000).

• Spatiotemporal dynamics of wild fox (Carnieli et al., 2013) and dog (Carnieli et al., 2013;Carnieli et al., 2011) RABV lineages.

Main findings

Despite extensive dog vaccination campaigns, multiple dog-related RABV lineages circulate in Brazil with a relatively recent common ancestor estimated in the 1950s (Carnieli et al., 2013;Carnieli et al., 2011). Dog lineages are generally spatially clustered (Carnieli et al., 2013;Carnieli et al., 2011) and lineages circulating in wild foxes and dogs are phylogenetically and dynamically independent (Carnieli et al., 2013). 4 9 3 8 3 0 4 7 4 2 9 0 . 5 0 1 9 7 4 4 1 5 5 1 3 3 6 3 9 9 8 1 3 0 3 1 4 1 2 4 1 . 5 0 1 4 5 5 9 6 8 2 0 3 4 2 7 1 0 1 1 6 7 4 1 1 5 0 . 5 0 1 4 6 4 6 2 4 8 8 0 4 1 9 7 5 4 3 2 3 0 0 5 4 1 6 . 5 0 1 7 1 1 6 1 1 3 2 1 0 3 9 2 f (δ t |d, s) is the density of the generation time defined as the distribution of the interval between the infection time ξ i of the infector i and the infection time ξ j of the recipient j conditioned on the symptom onset or date of detection, and the presence of symptoms of i.

3 1 . 1 1 k r o l h T - r u o K l r o r K - m u r h C y a v S - g n e i R y a v S - a i d o b m a C 8 2 - 1 0 - 4 0 0 2 g o D 2 0 3 6 6 3 M K 6 8 3 . 5 0 1 7 5 2 . 1 1 y e r m a d g n o R - m o n h p g n u e o h C - m o n h p a B - g n e V y e r P - a i d o b m a C 6 0 - 9 0 - 0 0 0 2 g o D 5 7 2 6 6 3 M K 7 0 7 . 4 0 1 8 5 5 . 1 1 h t i h c P y e r P - u e L g n o r m a S - e l u o n s g n A - l a d n a K - a i d o b m a C 6 1 - 8 0 - 0 0 0 2 g o D 5 3 3 6 6 3 M K 8 2 1 . 5 0 1 5 6 8 . 1 1 o a B a r K y o r h C - r a a k o R - s a e M g n u K - m a h C g n o p m a K - a i d o b m a C 5 2 - 1 0 - 9 9 9 1 g o D 9 0 3 6 6 3 M K A N A N a i d o b m a C 9 9 9 1 s i r a i l i m a f - s i n a C - g o D 2 5 2 8 4 1 X K 7 0 1 . 5 0 1 5 2 3 . 2 1 l i p m A l o u T - o a l a r S - y a r a B - m o h T g K - a i d o b m a C 6 1 - 2 0 - 9 0 0 2 g o D 8 8 2 6 6 3 M K 9 3 9 . 4 0 1 3 3 5 . 1 1 2 v o p m A r a b h C - y e h c
d K g n e o B - a i d o b m a C 3 0 - 1 0 - 3 1 0 2 g o D 2 0 X
N A N o c i R o t r e u P 7 9 9 1 e s o o g n o M 8 3 5 3 1 5 Q J A N A N o c i R o t r e u P 4 0 0 2 e s o o g n o M 5 9 4 8 2 2 J F A N A N o c i R o t r e u P 6 9 9 1 e s o o g n o M 8 2 5 3 1 5 Q J A N A N o c i R o t r e u P 7 9 9 1 e s o o g n o M 4 3 5 3 1 5 Q J A N A N i t i a H 8 1 0 2 s i r a i l i m a f - s u p u l - s i n a C 9 2 1 5 5 0 W M A N A N y n a m r e G 2 0 0 2 s e p l u v - s e p l u V 2 3 6 6 8 8 U E A N A N y n a m r e G 5 0 0 2 s e p l u v - s e p l u V 5 3 6 6 8 8 U E A N A N y n a m r e G 4 0 0 2 s e p l u v - s e p l u V 4 3 6 6 8 8 U E A N A N a i n e v o l S 2 1 0 2 e a d i n a C 3 1 6 2 2 5 C K A N A N y n a m r e G 1 0 0 2 s e p l u v - s e p l u V 1 3 6 6 8 8 U E A N A N a i r t s u A 6 0 0 2 s e p l u v - s e p l u V 6 3 6 6 8 8 U E A N A N o c c o r o M 3 9 9 1 A N 2 2 3 2 9 9 U G A N A N l i z a r B 5 1 0 2 s i r a i l i m a f - s u p u l - s i n a C 0 0 1 6 5 9 K M A N A N l i z a r B 5 1 0 2 s i r a i l i m a f - s u p u l - s i n a C 1 0 1 6 5 9 K M A N A N l i z a r B 5 1 0 2 s i r a i l i m a f -s u p u l -s i n a C
For symptomatic cases, f is derived from the corrected infectivity profile estimated by Ashcroft et al.

(2020), a shifted Γ distribution with shape=97.2, rate=3.7 and shift=25.6. The shift of the distribution corresponds to the symptom onset of i. According to McAloon et al., 2020, less than 2% of the symptomatic cases develop symptoms over the three days following their infection (McAloon et al., 2020). We assumed that incubation periods are of 3 days minimum and that the infectious period starts 3 days before the symptom onset, independent of the duration of the incubation period. For asymptomatic infectors, f is derived from the same estimate of the infectivity profile so that infectors are infectious starting from 2 days after their infection time and their infectivity peaks approximately 5 days after their infection.

Instantaneous risk of infection of a household member

The risk of infection of individual j in household k at time ξ is the sum of the hazard of infection within the community and the hazards of infection by infected household members:

λ j,k (ξ ) = α + ∑ i∈I k {ξ i <ξ } h i→ j,k (ξ ) (C.2)
where α is the instantaneous risk of infection in the community. It is assumed constant over the follow-up of households and the entire period of the study.

Likelihood function

Denote θ the vector of the transmission model parameters. The likelihood of the transmission process within the household conditional on the first date of infection ξ 1 in the household is:

P(ξ |θ ) = ∏ i∈I f (d i -ξ i ) ∏ i∈I-{1} λ i (ξ i )e - ξ i ξ 1 λ i (u)du ∏ j∈S e - t end ξ 1 λ j (u)du (C.3)
where f (d iξ i ) is the density of the incubation period for symptomatic cases or the density of the RT-qPCR detection period after infection for asymptomatic cases. The distribution of the incubation period was defined as a truncated log-normal distribution with log-mean=1.63 and log-sd=0.25 as estimated by McAloon et al., 2020(McAloon et al., 2020). As previously mentioned, less than 2% of the symptomatic cases develop symptoms over the three days following their infection according to this distribution. We assumed that the incubation period lasts at least 3 days and does not exceed 30 days. For the RT-qPCR detection period, we assumed a Uniform(0,10) distribution.

Household contacts that reported a SARS-CoV-2 infection in the year preceding follow-up (n = 20) were considered protected from re-infection, and thus, did not contribute to the likelihood of the transmission process. A-E) Impact of the increasing levels of spatial bias on the correlation, the calibration, the mean relative 95% HPD width, the mean relative bias, and the WIS between the simulated and the estimated lineage migration counts. (F-J) Mitigation of the impact of spatial bias on the correlation, the calibration, the mean relative 95% HPD width, the mean relative bias, and the WIS between the simulated and estimated lineage migration counts by using alternative sampling strategies. The mean relative bias and the mean relative 95% HPD width are not defined when the true value is null. We removed 3,126 out of 13,200 and 1,410 out of 9,588 simulated migration events in the small and large samples, respectively, due to null true values. The examples depicted here correspond to one simulation inferred by the model that accounts for heterogeneous contact patterns ("correct"), and the model that assumes homogeneous mixing within households ("incorrect"). From left to right, the panels depict the hazard of infection in the community α, the infection rate in an heterosexual couple β 4/2 κ child,child µ sus,child µ in f ,child , the relative susceptibility of adults µ sus,adult , and the relative infectivity of adults µ in f ,adult . The examples depicted here correspond to one simulation inferred by the model that accounts for heterogeneous contact patterns ("correct"), and the model that assumes homogeneous mixing within households ("incorrect"). From left to right, the panels depict the hazard of infection in the community α, the infection rate in an heterosexual couple β 4/2 κ child,child µ sus,child µ in f ,child , the relative susceptibility of adults µ sus,adult , and the relative infectivity of adults µ in f ,adult . ment de nouvelles méthodes.

Ces exemples de l'utilisation de la modélisation épidémiologique et de la phylodynamique soulignent leur complémentarité. La modélisation épidémiologique est tout particulièrement adaptée à l'identification des facteurs individuels et environnementaux qui influent sur le processus épidémique, mais aussi à la prédiction à court et long terme et enfin à la conception et l'évaluation de mesures de contrôle. La phylodynamique quant à elle permet d'intégrer les déterminant liés aux pathogènes et, en confirmant des chaînes de transmission, apporte un éclairage sur la contribution de la transmission locale comparée aux importations. Il est intéressant de noter que la pandémie de la maladie à coronavirus 2019 a été marquée par une certaine démocratisation des études interdisciplinaires qui combinent des données épidémiologiques individuelles et populationnelles à des séquences génétiques, le tout analysé par des techniques diverses de statistiques classiques, modélisation épidémiologique et/ou phylodynamique.

De nombreux défis subsistent concernant l'utilisation de la modélisation épidemiologique et de la phylodynamique. Ces défis sont liés à la prise en compte des biais d'échantillonnage dans le processus d'inférence et à la spécification des modèles. Un échantillon est biaisé lorsque sa composition ne reflète pas la dynamique d'une épidémie. Les biais d'échantillonnage sont particulièrement courant en phylodynamique car l'échantillonnage des séquences de pathogène se fait surtout de manière opportuniste et, quand il est planifié, des disparités spatiales subsistent. Les modèles de phylogéographie sont connus pour être sensibles à ces biais mais l'impact de ces biais et les moyens d'en atténuer les effets restent peu compris. Dans un tout autre registre, l'épidémiologie de la transmission des maladies respiratoires a largement bénéficié des études de leur transmission dans les ménages. Toutefois, les modèles de transmission dans les ménages font l'hypothèse que l'ensemble des membres du ménage entrent en contact à la même fréquence. Plusieurs études ont montré que cette hypothèse n'est pas vérifiée ce qui pourrait biaiser les estimations de susceptibilité et d'infectivité relative des membres du ménage en fonction de leur âge, sexe etc...

Objectifs de la thèse

Cette thèse a pour objectif principal d'explorer les contributions des données épidémiologiques individuelles dans les ménages et des séquences génétiques des pathogènes qui se trouvent aux deux extrémités du spectre de granularité des données dans la compréhension de la transmission des maladies infectieuses dans les populations. Ces données sont analysées par modélisation épidémiologique et phylodynamique respectivement. Le deuxième objectif de cette thèse est d'étudier les limites de ces deux approches, plus précisément, l'impact des biais d'échantillonnage sur les inférences de phylogéographie discrète et l'impact de contact hétérogènes dans les ménages sur l'estimation des paramètres de susceptibilité et d'infectivité relative des enfants par rapport aux adultes. Ces objectifs sont traités par le prisme de deux cas d'étude, le virus de la rage (RABV) et le SARS-CoV-2. La rage est une zoonose (maladie qui se transmet naturellement de l'animal à l'homme) tropicale négligée dont le réservoir principal sont les chiens domestiques, responsables de 99% des cas de rage humaine. Un vaccin contre la rage est disponible chez l'homme et l'animal mais elle reste endémique en Afrique et en Asie ce qui est dû en partie au manque de moyens financiers et d'implication politique. Par ailleurs, de nombreuses zones d'ombre subsistent concernant les dynamiques de transmission de la rage chez le chien. À l'opposé, les moyens qui ont été déployés pendant la pandémie de COVID-19 ont été sans précédent et la production

Résultats

Les études de modélisation épidémiologique se concentrent en priorité sur l'évaluation des mesures de contrôle alors que l'identification des déterminants de la transmission est l'objectif premier des études de phylodynamique. La modélisation épidémiologique a permis de montrer que la vaccination est la stratégie de contrôle la plus efficace et doit atteindre une couverture vaccinale élevée dans les régions indemnes mais à haut risque d'introduction, alors qu'une couverture intermédiaire est suffisante dans les régions endémiques. La phylodynamique et les études interdisciplinaires ont mis en évidence le rôle central de l'hétérogénéité spatiale dans le maintien de la circulation de la rage. L'ensemble des méthodes utilisées sont limitées par la quantité des données et les biais d'échantillonnage sont généralement inconnus. De manière intéressante, les études interdisciplinaires donnent un cadre qui permet de formuler et tester des hypothèses sur les processus de transmission.

Limites de l'étude

L'identification des articles scientifiques, bien que se basant sur une procédure codifiée, est sensible à la combinaison de mots-clés utilisée. Puisque les résultats obtenus dans cette revue sont en accord avec les résultats de revues précédentes, nous pensons que nous n'avons pas manqué d'étude quantitative majeure sur la transmission de la rage.

Conclusion

Abstract

Background

Rabies is a fatal yet vaccine-preventable disease. In the last two decades, domestic dog populations have been shown to constitute the predominant reservoir of rabies in developing countries, causing 99% of human rabies cases. Despite substantial control efforts, dog rabies is still widely endemic and is spreading across previously rabies-free areas. Developing a detailed understanding of dog rabies dynamics and the impact of vaccination is essential to optimize existing control strategies and developing new ones. In this scoping review, we aimed at disentangling the respective contributions of mathematical models and phylodynamic approaches to advancing the understanding of rabies dynamics and control in domestic dog populations. We also addressed the methodological limitations of both approaches and the remaining issues related to studying rabies spread and how this could be applied to rabies control.

Methodology/principal findings

We reviewed how mathematical modelling of disease dynamics and phylodynamics have been developed and used to characterize dog rabies dynamics and control. Through a detailed search of the PubMed, Web of Science, and Scopus databases, we identified a total of n = 59 relevant studies using mathematical models (n = 30), phylodynamic inference (n = 22) and interdisciplinary approaches (n = 7). We found that despite often relying on scarce rabies epidemiological data, mathematical models investigated multiple aspects of rabies dynamics and control. These models confirmed the overwhelming efficacy of massive dog vaccination campaigns in all settings and unraveled the role of dog population structure and frequent introductions in dog rabies maintenance. Phylodynamic approaches successfully disentangled the evolutionary and environmental determinants of rabies dispersal and consistently reported support for the role of reintroduction events and human-

Introduction

Background

Rabies is a viral zoonosis affecting the central nervous system of mammals that is almost always fatal to humans. Domestic dogs represent the main reservoir of rabies virus (RABV) worldwide. They are responsible for 99% of human rabies cases [1]. In-depth understanding of dog ecology and host-pathogen interactions is necessary to characterize rabies dynamics and design appropriate control measures. Rabies is a vaccine-preventable disease in both human and canine populations, and dog vaccination is the most cost-effective control measure [2].

Strong evidence is available for the efficacy of dog rabies elimination programs in endemic areas [3][4][5][6][7], notably in South America where massive dog vaccination campaigns in the 1980s alleviated the burden of canine rabies. Regardless, there has been only little improvement of the global burden since the successes in South America. Dog rabies is still endemic in Africa, Asia, and the Middle East [8,9].

In 2015, the World Health Organization (WHO), the Global Alliance for Rabies Control (GARC), the World Organization for Animal Health (OIE) and the Food and Agriculture Organization of the United Nations (FAO) launched a comprehensive framework targeting the global elimination of dog-mediated human rabies by 2030 [10]. Effective One Health interventions such as the improvement of the current prophylaxis in both humans [11,12] and dogs should enable reaching this goal.

Despite valuable efforts in several endemic countries [9,13,14], control strategies have not stopped rabies from circulating due to inadequate political, economic, and social responses. Weak interest from veterinary services, lack of sustainable resources and political neglect [15] prevent most endemic countries to reach the 70% vaccination coverage recommended by the WHO [9]. Moreover, rabies infections continue to spread, notably in previously rabies-free areas in countries such as Indonesia [16][17][18] and the Philippines [19,20]. In this resource-limited context, in-depth knowledge of the mechanisms underlying rabies dynamics (environmental drivers of spread, impact of dog density, impact of dog behavior, etc.) would be a key asset to limiting the spread of this vaccine-preventable disease, notably by aiding to design more effective vaccination campaigns that are robust to resurgence in the long-term. The development of novel methodologies to better understand rabies epidemiology and transmission dynamics therefore constitutes a promising avenue of research.

Objectives

In this scoping review, we focused on the insights of two quantitative approaches applied to the study of rabies: mathematical modelling of infectious diseases and phylodynamics. The former is a field of research that exploits epidemiological data to unravel the spread of diseases in populations, assess the impact of interventions, support policy making, and optimize control strategies. The latter studies the interactions between epidemiological, immunological, and evolutionary processes from the analysis of viral genetic sequence data [21]. Within phylodynamics, phylogeographic inference specifically aims at reconstructing the dispersal history and dynamics of viral lineages in space and time. Here, we assessed the uses and respective contributions of both approaches, as well as their limitations and the remaining knowledge gaps concerning rabies dispersal and control in domestic dog populations.

Methods

Search strategy

This review follows the guidelines of the PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analyses Extension for Scoping Reviews) statement for scoping reviews [22]. In this review, we screened PubMed, Web of Science and Scopus databases on the 2nd of June, 2020 using the following combination of terms ["rabies" AND ("dog" OR "canine") AND ("modelling" OR "modeling" OR "phylogeography" OR "phylodynamics") AND "dynamics"] along with the "all fields" option and without restriction on publication year. The "all fields" option enabled to apply the search terms for their appearance in the title, abstract PLOS NEGLECTED TROPICAL DISEASES and keywords. Only English-written papers published in scientific journals were considered. All data were searched and screened by the same researcher (ML). The search strategy identified 65, 94 and 768 publications in PubMed, Web of Science and Scopus databases respectively, which corresponded to 797 unique records. In addition, references of selected publications were screened manually, leading to the identification and inclusion of two additional studies [23,24]. Finally, the paper of Colombi et al. [25], which was not identified in the databases nor in the references, was also included (Fig 1).

Selection of studies

In total, 797 records were included and processed manually in a multi-stage procedure. At each selection step, a conservative approach was taken to ensure the best sensitivity level. Firstly, studies were selected based on their title using the following inclusion criteria: mathematical models of dog and human rabies assessing the impact of control strategies, the risk of rabies importation, the drivers of rabies spread or models estimating epidemiological parameters, cost-effectiveness studies, phylodynamic studies including RABV isolated from dogs, and broad studies on new phylodynamic or mathematical models. Indeed, rabies has often been used as a model disease in phylodynamics and mathematical modelling, and a reference to rabies might not appear directly in the title or the abstract. The following exclusion criteria were used: reviews, studies strictly on wildlife rabies, dog ecology and population dynamics, conservation biology, and evolutionary analyses for diagnostic purposes. Secondly, studies were selected based on their abstract with a refined set of exclusion criteria to exclude statistical

PLOS NEGLECTED TROPICAL DISEASES

analyses of epidemiological data, cost-effectiveness studies with no focus on rabies dynamics, experimental rabies cross-species transmission which did not incorporate a modelling aspect and studies on the evolutionary processes of RABV. Finally, studies went through a full-text reading step to verify that their content matched our selection criteria. At this step, theoretical models which were not grounded in a specific epidemiological context were excluded (Fig 1).

Data extraction and analysis

Selected studies were classified into three categories based on their methodology: mathematical models, phylodynamic and interdisciplinary studies. Most phylodynamic studies identified in this review correspond to phylogeographic analyses, where the main focus is on inferring the spread of a pathogen over time using location data associated with the available sequence data. The interdisciplinary category covers studies either integrating epidemiological and genetic data in a unified modelling framework or mixing modelling approaches with phylodynamics. Data were systematically charted in an Excel spreadsheet designed to retrieve: i) the main modelling strategy with its assumptions; ii) the data source; iii) remarks about potential bias of the data in relation to the underlying evolutionary and epidemiological processes; iv) the qualitative and quantitative results concerning the dynamics of dog rabies; and v) if performed, the sensitivity analysis determining the robustness of the methodology to parameter values or potential biases.

Results

General characteristics of selected studies

Our selection procedure identified 59 studies that meet our selection criteria with 30 mathematical models [16,, 22 phylodynamic studies [17,19,[START_REF] Bourhy | The origin and phylogeography of dog rabies virus[END_REF][START_REF] Lemey | Bayesian phylogeography finds its roots[END_REF][START_REF] Talbi | Evolutionary history and dynamics of dog rabies virus in western and central Africa[END_REF][START_REF] Meng | Evolutionary dynamics of rabies viruses highlights the importance of China rabies transmission in Asia[END_REF][START_REF] Hayman | Evolutionary history of rabies in Ghana[END_REF][START_REF] Carnieli | Phylogeography of rabies virus isolated from dogs in Brazil between 1985 and 2006[END_REF][START_REF] Yu | The spatial and temporal dynamics of rabies in China[END_REF][START_REF] Mollentze | Dog rabies in southern Africa: Regional surveillance and phylogeographical analyses are an important component of control and elimination strategies[END_REF][START_REF] Guo | National Borders Effectively Halt the Spread of Rabies: The Current Rabies Epidemic in China Is Dislocated from Cases in Neighboring Countries[END_REF][START_REF] Carnieli | Phylogeographic dispersion and diversification of rabies virus lineages associated with dogs and crab-eating foxes (Cerdocyon thous) in Brazil[END_REF][START_REF] Horton | Complex Epidemiology of a Zoonotic Disease in a Culturally Diverse Region: Phylogeography of Rabies Virus in the Middle East[END_REF][START_REF] Brunker | Elucidating the phylodynamics of endemic rabies virus in eastern Africa using whole-genome sequencing[END_REF][START_REF] Yao | The Spatiotemporal Expansion of Human Rabies and Its Probable Explanation in Mainland China, 2004-2013[END_REF][START_REF] Troupin | Large-Scale Phylogenomic Analysis Reveals the Complex Evolutionary History of Rabies Virus in Multiple Carnivore Hosts[END_REF][START_REF] Zhang | Cross-border spread, lineage displacement and evolutionary rate estimation of rabies virus in Yunnan Province, China[END_REF][START_REF] Ma | Re-emerging of rabies in Shaanxi province, China, from 2009 to 2015[END_REF][START_REF] Dellicour | Using Viral Gene Sequences to Compare and Explain the Heterogeneous Spatial Dynamics of Virus Epidemics[END_REF][START_REF] Brunker | Landscape attributes governing local transmission of an endemic zoonosis: Rabies virus in domestic dogs[END_REF][START_REF] Wang | Phylodynamic and transmission pattern of rabies virus in China and its neighboring countries[END_REF][START_REF] Dellicour | Using phylogeographic approaches to analyse the dispersal history, velocity and direction of viral lineages-Application to rabies virus spread in Iran[END_REF], and 7 interdisciplinary studies [20,[START_REF] Talbi | Phylodynamics and Humanmediated dispersal of a zoonotic virus[END_REF][START_REF] Mollentze | A bayesian approach for inferring the dynamics of partially observed endemic infectious diseases from space-time-genetic data[END_REF][START_REF] Bourhy | Revealing the Micro-scale Signature of Endemic Zoonotic Disease Transmission in an African Urban Setting[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF][START_REF] Cori | A graph-based evidence synthesis approach to detecting outbreak clusters: An application to dog rabies[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF], all published between 1996 and 2020 (Figs 1 and2A and2B). Mathematical models were first published followed by phylodynamic and interdisciplinary studies (Fig 2B). This timeline can be explained by the recent developments of Bayesian phylodynamic, and in particular phylogeographic, models in BEAST [START_REF] Baele | Emerging concepts of data integration in pathogen phylodynamics[END_REF][START_REF] Suchard | Bayesian phylogenetic and phylodynamic data integration using BEAST 1.10[END_REF][START_REF] Bouckaert | BEAST 2.5: An Advanced Software Platform for Bayesian Evolutionary Analysis[END_REF]. Africa and Asia are the most studied continents in the three methodological categories, while China accounts for most of the Asian studies (Fig 2C). Oceania is not represented in the interdisciplinary and phylodynamic categories since it is a rabies-free area (Fig 2A).

Topics addressed by the studies

Phylodynamic studies are homogeneous in terms of methodologies (essentially phylogeographic studies) and research goals. They predominantly focus on unraveling the dispersal dynamics of rabies at the regional and country levels (n = 16) [17,19,[START_REF] Bourhy | The origin and phylogeography of dog rabies virus[END_REF][START_REF] Lemey | Bayesian phylogeography finds its roots[END_REF][START_REF] Talbi | Evolutionary history and dynamics of dog rabies virus in western and central Africa[END_REF][START_REF] Meng | Evolutionary dynamics of rabies viruses highlights the importance of China rabies transmission in Asia[END_REF][START_REF] Hayman | Evolutionary history of rabies in Ghana[END_REF][START_REF] Carnieli | Phylogeography of rabies virus isolated from dogs in Brazil between 1985 and 2006[END_REF][START_REF] Yu | The spatial and temporal dynamics of rabies in China[END_REF][START_REF] Carnieli | Phylogeographic dispersion and diversification of rabies virus lineages associated with dogs and crab-eating foxes (Cerdocyon thous) in Brazil[END_REF][START_REF] Brunker | Elucidating the phylodynamics of endemic rabies virus in eastern Africa using whole-genome sequencing[END_REF][START_REF] Yao | The Spatiotemporal Expansion of Human Rabies and Its Probable Explanation in Mainland China, 2004-2013[END_REF][START_REF] Ma | Re-emerging of rabies in Shaanxi province, China, from 2009 to 2015[END_REF][START_REF] Dellicour | Using Viral Gene Sequences to Compare and Explain the Heterogeneous Spatial Dynamics of Virus Epidemics[END_REF][START_REF] Wang | Phylodynamic and transmission pattern of rabies virus in China and its neighboring countries[END_REF][START_REF] Dellicour | Using phylogeographic approaches to analyse the dispersal history, velocity and direction of viral lineages-Application to rabies virus spread in Iran[END_REF]. In four of them, the authors deciphered the role of lineage introduction in rabies maintenance or emergence [START_REF] Mollentze | Dog rabies in southern Africa: Regional surveillance and phylogeographical analyses are an important component of control and elimination strategies[END_REF][START_REF] Guo | National Borders Effectively Halt the Spread of Rabies: The Current Rabies Epidemic in China Is Dislocated from Cases in Neighboring Countries[END_REF][START_REF] Horton | Complex Epidemiology of a Zoonotic Disease in a Culturally Diverse Region: Phylogeography of Rabies Virus in the Middle East[END_REF][START_REF] Zhang | Cross-border spread, lineage displacement and evolutionary rate estimation of rabies virus in Yunnan Province, China[END_REF]. In recent years, researchers have been trying to identify external factors impacting the spatial dynamics of RABV spread (n = 5) [START_REF] Brunker | Elucidating the phylodynamics of endemic rabies virus in eastern Africa using whole-genome sequencing[END_REF][START_REF] Yao | The Spatiotemporal Expansion of Human Rabies and Its Probable Explanation in Mainland China, 2004-2013[END_REF][START_REF] Dellicour | Using Viral Gene Sequences to Compare and Explain the Heterogeneous Spatial Dynamics of Virus Epidemics[END_REF][START_REF] Brunker | Landscape attributes governing local transmission of an endemic zoonosis: Rabies virus in domestic dogs[END_REF]71] (Fig 2D and S1 Table). Contrary to phylodynamic studies, the modelling category gathers a diverse panel of models with aims that cover the implementation of new mathematical methodologies (n = 2) [START_REF] Hudson | Using roaming behaviours of dogs to estimate contact rates: The predicted effect on rabies spread[END_REF][START_REF] Ortega | Fuzzy dynamical systems in epidemic modeling[END_REF], the characterization of rabies dynamics (n = 11) [26,27,31,32,[START_REF] Taib | Model simulation for the spread of rabies in Sarawak, Malaysia[END_REF][START_REF] Huang | Modeling the Transmission Dynamics of Rabies for Dog, Chinese Ferret Badger and Human Interactions in Zhejiang Province, China[END_REF][START_REF] Brookes | Rabies-induced behavioural changes are key to rabies persistence in dog populations: Investigation using a network-based model[END_REF][START_REF] Hampson | Synchronous cycles of domestic dog rabies in sub-Saharan Africa and the impact of control efforts[END_REF][START_REF] Zinsstag | Transmission dynamics and economics of rabies control in dogs and humans in an African city[END_REF][START_REF] Zhang | Analysis of rabies in China: transmission dynamics and control[END_REF][START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF], the identification of factors driving the resurgence or maintenance of rabies (n = 9) [16,23,25,[33][34][35]37,[START_REF] Ozella | High-resolution contact networks of free-ranging domestic dogs Canis familiaris and implications for transmission of infection[END_REF][START_REF] Hudson | Modelling targeted rabies vaccination strategies for a domestic dog population with heterogeneous roaming patterns[END_REF], the assessment of control strategies efficacy (n = 18) [16,23,24,[27][28][29]31,[33][34][35][36][START_REF] Hudson | Using roaming behaviours of dogs to estimate contact rates: The predicted effect on rabies spread[END_REF][START_REF] Hudson | Modelling targeted rabies vaccination strategies for a domestic dog population with heterogeneous roaming patterns[END_REF][START_REF] Brookes | Rabies-induced behavioural changes are key to rabies persistence in dog populations: Investigation using a network-based model[END_REF][START_REF] Carroll | The use of immunocontraception to improve rabies eradication in urban dog populations[END_REF][START_REF] Zhang | Analysis of rabies in China: transmission dynamics and control[END_REF][START_REF] Beyer | Metapopulation dynamics of rabies and the efficacy of vaccination[END_REF][START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF], the risk assessment of rabies introduction and the evaluation of outbreak preparedness in rabies-free areas (n = 3) [30,36,[START_REF] Hudson | Using roaming behaviours of dogs to estimate contact rates: The predicted effect on rabies spread[END_REF], and cost-effectiveness studies (n = 2) [START_REF] Beyene | Impact of One-Health framework on vaccination cost-effectiveness: A case study of rabies in Ethiopia[END_REF]48] (Fig 2D and S1 Table). Finally, interdisciplinary studies mainly focused on PLOS NEGLECTED TROPICAL DISEASES rabies dynamics in endemic areas (n = 6) [20,[START_REF] Talbi | Phylodynamics and Humanmediated dispersal of a zoonotic virus[END_REF][START_REF] Mollentze | A bayesian approach for inferring the dynamics of partially observed endemic infectious diseases from space-time-genetic data[END_REF][START_REF] Bourhy | Revealing the Micro-scale Signature of Endemic Zoonotic Disease Transmission in an African Urban Setting[END_REF][START_REF] Cori | A graph-based evidence synthesis approach to detecting outbreak clusters: An application to dog rabies[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF] and the identification of environmental factors influencing rabies spread and maintenance such as recurrent reintroductions (n = 3) [START_REF] Talbi | Phylodynamics and Humanmediated dispersal of a zoonotic virus[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF]. Two of these used genetic and epidemiological data of dog rabies in a unified modelling approach [START_REF] Mollentze | A bayesian approach for inferring the dynamics of partially observed endemic infectious diseases from space-time-genetic data[END_REF][START_REF] Cori | A graph-based evidence synthesis approach to detecting outbreak clusters: An application to dog rabies[END_REF], whereas the others analyzed sequences through regular phylogenetic approaches and completed their analysis with a mathematical model [20,[START_REF] Talbi | Phylodynamics and Humanmediated dispersal of a zoonotic virus[END_REF][START_REF] Bourhy | Revealing the Micro-scale Signature of Endemic Zoonotic Disease Transmission in an African Urban Setting[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]77] (Fig 2D and S1 Table).

Potential sources of bias in the data

Data source (active/passive surveillance), resolution (number and length of RABV sequences, incidence per country/region, etc.) and representativity influence the level of evidence of the For phylodynamic studies, countries were not considered if their genetic data were included only in regular phylogenetic tree reconstructions. Similarly, two studies which described rabies dynamics at the global scale [START_REF] Bourhy | The origin and phylogeography of dog rabies virus[END_REF][START_REF] Troupin | Large-Scale Phylogenomic Analysis Reveals the Complex Evolutionary History of Rabies Virus in Multiple Carnivore Hosts[END_REF] were not considered in this figure. In our collected records, China accounts for most Asian studies. Spain appears on the map because Ceuta and Melilla, which are Spanish enclaves in North Africa, are represented in two datasets of RABV genetic sequences [START_REF] Dellicour | Using Viral Gene Sequences to Compare and Explain the Heterogeneous Spatial Dynamics of Virus Epidemics[END_REF][START_REF] Talbi | Phylodynamics and Humanmediated dispersal of a zoonotic virus[END_REF]. (D) Number of studies per topic and methodological category. The World Bank, https://datacatalog.worldbank.org/dataset/world-bank-official-boundaries, CC-BY 4.0. https://doi.org/10.1371/journal.pntd.0009449.g002

PLOS NEGLECTED TROPICAL DISEASES

studies on the underlying epidemiological and evolutionary processes. In particular, recorded cases collected through passive surveillance systems are expected to underestimate the disease burden and to be potentially spatiotemporally biased [8,[START_REF] De La Puente-Leo ´n | Spatial Inequality Hides the Burden of Dog Bites and the Risk of Dog-Mediated Human Rabies[END_REF]. Similarly, genetic sequences collected from publicly available databases such as GenBank often lack precise metadata (e.g., sampling time and location) and/or are of short length.

In our text corpus of phylodynamic and interdisciplinary studies, passive surveillance systems and GenBank represent the main sources of RABV genetic sequence data (S2-S4 Tables). By combining these two data sources, researchers have generally managed to increase the spatiotemporal coverage of their dataset. This however does not guarantee a good representativity of the epidemic process. Active surveillance was mostly used to collect dog specimens from animal markets in China (n = 2) [START_REF] Yu | The spatial and temporal dynamics of rabies in China[END_REF][START_REF] Guo | National Borders Effectively Halt the Spread of Rabies: The Current Rabies Epidemic in China Is Dislocated from Cases in Neighboring Countries[END_REF] and thorough contact tracing after biting events in China and Tanzania (n = 2) [START_REF] Brunker | Elucidating the phylodynamics of endemic rabies virus in eastern Africa using whole-genome sequencing[END_REF][START_REF] Zhang | Cross-border spread, lineage displacement and evolutionary rate estimation of rabies virus in Yunnan Province, China[END_REF]. On average, the datasets analyzed in these studies contained 183 sequences spanning from approximatively 3% to 100% of the RABV genome length. Short sequences containing the N gene constitute the most common type of data. They are less informative than whole genomes which were only generated and analyzed in recent years across four studies [START_REF] Brunker | Elucidating the phylodynamics of endemic rabies virus in eastern Africa using whole-genome sequencing[END_REF][START_REF] Troupin | Large-Scale Phylogenomic Analysis Reveals the Complex Evolutionary History of Rabies Virus in Multiple Carnivore Hosts[END_REF][START_REF] Brunker | Landscape attributes governing local transmission of an endemic zoonosis: Rabies virus in domestic dogs[END_REF][START_REF] Dellicour | Using phylogeographic approaches to analyse the dispersal history, velocity and direction of viral lineages-Application to rabies virus spread in Iran[END_REF] (S2 Table ).

In studies from the modelling and interdisciplinary categories, authors generally simulated rabies epidemics (n = 24) [20,23,25,[28][29][30][31][32][33][34][35][36][START_REF] Ozella | High-resolution contact networks of free-ranging domestic dogs Canis familiaris and implications for transmission of infection[END_REF][START_REF] Taib | Model simulation for the spread of rabies in Sarawak, Malaysia[END_REF][START_REF] Hudson | Using roaming behaviours of dogs to estimate contact rates: The predicted effect on rabies spread[END_REF][START_REF] Hudson | Modelling targeted rabies vaccination strategies for a domestic dog population with heterogeneous roaming patterns[END_REF][START_REF] Brookes | Rabies-induced behavioural changes are key to rabies persistence in dog populations: Investigation using a network-based model[END_REF][START_REF] Carroll | The use of immunocontraception to improve rabies eradication in urban dog populations[END_REF][START_REF] Ortega | Fuzzy dynamical systems in epidemic modeling[END_REF][START_REF] Hampson | Synchronous cycles of domestic dog rabies in sub-Saharan Africa and the impact of control efforts[END_REF][START_REF] Zhang | Analysis of rabies in China: transmission dynamics and control[END_REF][START_REF] Beyer | Metapopulation dynamics of rabies and the efficacy of vaccination[END_REF][START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF][START_REF] Talbi | Phylodynamics and Humanmediated dispersal of a zoonotic virus[END_REF], and thus predominantly relied on publicly available estimates of the natural history of rabies, dog demographics and dog ecology (S3 and S4 Tables). When models were fitted to incidence data (n = 13) [16,24,26,27,37,[START_REF] Beyene | Impact of One-Health framework on vaccination cost-effectiveness: A case study of rabies in Ethiopia[END_REF][START_REF] Huang | Modeling the Transmission Dynamics of Rabies for Dog, Chinese Ferret Badger and Human Interactions in Zhejiang Province, China[END_REF][START_REF] Zinsstag | Transmission dynamics and economics of rabies control in dogs and humans in an African city[END_REF][START_REF] Mollentze | A bayesian approach for inferring the dynamics of partially observed endemic infectious diseases from space-time-genetic data[END_REF][START_REF] Bourhy | Revealing the Micro-scale Signature of Endemic Zoonotic Disease Transmission in an African Urban Setting[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF][START_REF] Cori | A graph-based evidence synthesis approach to detecting outbreak clusters: An application to dog rabies[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF], human and/or dog case data from passive surveillance systems were used, or bite incidence data from thorough active surveillance. In general, there was a lack of data on dog rabies cases (available in 10 studies; [16,24,26,27,37,[START_REF] Zinsstag | Transmission dynamics and economics of rabies control in dogs and humans in an African city[END_REF][START_REF] Mollentze | A bayesian approach for inferring the dynamics of partially observed endemic infectious diseases from space-time-genetic data[END_REF][START_REF] Bourhy | Revealing the Micro-scale Signature of Endemic Zoonotic Disease Transmission in an African Urban Setting[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF][START_REF] Cori | A graph-based evidence synthesis approach to detecting outbreak clusters: An application to dog rabies[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF]) and estimates on dog demographics and ecology integrating the local specificities of host ecology were available in only seven studies [27,37,[START_REF] Beyene | Impact of One-Health framework on vaccination cost-effectiveness: A case study of rabies in Ethiopia[END_REF][START_REF] Huang | Modeling the Transmission Dynamics of Rabies for Dog, Chinese Ferret Badger and Human Interactions in Zhejiang Province, China[END_REF][START_REF] Zinsstag | Transmission dynamics and economics of rabies control in dogs and humans in an African city[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF]. Access to local data is crucial since differences in rabies spread [27] and dog carrying capacities [START_REF] Beyene | Impact of One-Health framework on vaccination cost-effectiveness: A case study of rabies in Ethiopia[END_REF] were estimated between areas of the same country. We would expect these differences to be more pronounced across different countries. To overcome the lack of epidemiological data on dog rabies, one study used serological data (from vaccination campaigns) to model the dynamics of rabies [START_REF] Ortega | Fuzzy dynamical systems in epidemic modeling[END_REF], and another study [36] based its analyses on historical records in Japan from the 1950s. Similarly, most Australian studies [30,[START_REF] Hudson | Using roaming behaviours of dogs to estimate contact rates: The predicted effect on rabies spread[END_REF][START_REF] Hudson | Modelling targeted rabies vaccination strategies for a domestic dog population with heterogeneous roaming patterns[END_REF][START_REF] Brookes | Rabies-induced behavioural changes are key to rabies persistence in dog populations: Investigation using a network-based model[END_REF] took the perspective of dog ecology data since Australia is free of rabies. This way, the authors explored the impact of dog population structure and dog roaming behavior on rabies dynamics.

Description of the models

In studies using phylodynamic approaches, the geographical dispersal of rabies was studied using either parsimony (n = 4) [START_REF] Bourhy | The origin and phylogeography of dog rabies virus[END_REF][START_REF] Talbi | Evolutionary history and dynamics of dog rabies virus in western and central Africa[END_REF][START_REF] Meng | Evolutionary dynamics of rabies viruses highlights the importance of China rabies transmission in Asia[END_REF][START_REF] Yu | The spatial and temporal dynamics of rabies in China[END_REF], Bayesian discrete phylogeography (n = 18) [17,19,20,[START_REF] Lemey | Bayesian phylogeography finds its roots[END_REF][START_REF] Hayman | Evolutionary history of rabies in Ghana[END_REF][START_REF] Carnieli | Phylogeography of rabies virus isolated from dogs in Brazil between 1985 and 2006[END_REF][START_REF] Mollentze | Dog rabies in southern Africa: Regional surveillance and phylogeographical analyses are an important component of control and elimination strategies[END_REF][START_REF] Guo | National Borders Effectively Halt the Spread of Rabies: The Current Rabies Epidemic in China Is Dislocated from Cases in Neighboring Countries[END_REF][START_REF] Horton | Complex Epidemiology of a Zoonotic Disease in a Culturally Diverse Region: Phylogeography of Rabies Virus in the Middle East[END_REF][START_REF] Brunker | Elucidating the phylodynamics of endemic rabies virus in eastern Africa using whole-genome sequencing[END_REF][START_REF] Yao | The Spatiotemporal Expansion of Human Rabies and Its Probable Explanation in Mainland China, 2004-2013[END_REF][START_REF] Zhang | Cross-border spread, lineage displacement and evolutionary rate estimation of rabies virus in Yunnan Province, China[END_REF][START_REF] Ma | Re-emerging of rabies in Shaanxi province, China, from 2009 to 2015[END_REF][START_REF] Wang | Phylodynamic and transmission pattern of rabies virus in China and its neighboring countries[END_REF][START_REF] Dellicour | Using phylogeographic approaches to analyse the dispersal history, velocity and direction of viral lineages-Application to rabies virus spread in Iran[END_REF][START_REF] Talbi | Phylodynamics and Humanmediated dispersal of a zoonotic virus[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF][START_REF] Brunker | Genomic sequencing, evolution and molecular epidemiology of rabies virus[END_REF], or Bayesian continuous phylogeography (n = 6) [START_REF] Carnieli | Phylogeographic dispersion and diversification of rabies virus lineages associated with dogs and crab-eating foxes (Cerdocyon thous) in Brazil[END_REF][START_REF] Dellicour | Using Viral Gene Sequences to Compare and Explain the Heterogeneous Spatial Dynamics of Virus Epidemics[END_REF][START_REF] Brunker | Landscape attributes governing local transmission of an endemic zoonosis: Rabies virus in domestic dogs[END_REF][START_REF] Dellicour | Using phylogeographic approaches to analyse the dispersal history, velocity and direction of viral lineages-Application to rabies virus spread in Iran[END_REF][START_REF] Bourhy | Revealing the Micro-scale Signature of Endemic Zoonotic Disease Transmission in an African Urban Setting[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF] (S2-S4 Tables). All Bayesian phylogeographic studies were carried out in BEAST 1 [START_REF] Suchard | Bayesian phylogenetic and phylodynamic data integration using BEAST 1.10[END_REF] with discrete trait analysis (DTA) to perform a phylogeographic reconstruction based on discrete/discretized sampling locations (e.g. provinces or countries) or with continuous trait analysis to perform a phylogeographic reconstruction based on spatiallyexplicit sampling location data (latitude and longitude coordinates). Several methodologies take advantage of such phylogeographic inferences to investigate the impact of external factors on the dispersal of viruses: a generalized linear model (GLM) extension of DTA developed by Lemey et al. [83] to test predictors of dispersal transition frequencies among discrete locations which was implemented by Brunker et al. [69]; and post hoc statistical approaches developed by Dellicour et al. [71,[START_REF] Dellicour | Explaining the geographic spread of emerging epidemics: A framework for comparing viral phylogenies and environmental landscape data[END_REF][START_REF] Dellicour | Phylodynamic assessment of intervention strategies for the West African Ebola virus outbreak[END_REF] to investigate the impact of environmental factors on the dispersal PLOS NEGLECTED TROPICAL DISEASES velocity, direction, or frequency of viral lineages in continuous phylogeographic frameworks which were applied in four rabies studies [START_REF] Dellicour | Using Viral Gene Sequences to Compare and Explain the Heterogeneous Spatial Dynamics of Virus Epidemics[END_REF][START_REF] Brunker | Landscape attributes governing local transmission of an endemic zoonosis: Rabies virus in domestic dogs[END_REF][START_REF] Dellicour | Using phylogeographic approaches to analyse the dispersal history, velocity and direction of viral lineages-Application to rabies virus spread in Iran[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF]. Finally, Zinsstag et al. [75] were the only authors to implement a birth-death model in BEAST 2 [80] to reconstruct the effective reproduction ratio (R) along vaccination campaigns and compare it to estimates obtained with a modelling approach (S4 Table ).

Compared to phylodynamics, mathematical models display a large diversity of specifications and parametrizations. Compartmental models (n = 18) [20,23,24,26,27,33,34,[START_REF] Beyene | Impact of One-Health framework on vaccination cost-effectiveness: A case study of rabies in Ethiopia[END_REF][START_REF] Taib | Model simulation for the spread of rabies in Sarawak, Malaysia[END_REF][START_REF] Huang | Modeling the Transmission Dynamics of Rabies for Dog, Chinese Ferret Badger and Human Interactions in Zhejiang Province, China[END_REF][START_REF] Carroll | The use of immunocontraception to improve rabies eradication in urban dog populations[END_REF][START_REF] Ortega | Fuzzy dynamical systems in epidemic modeling[END_REF][START_REF] Hampson | Synchronous cycles of domestic dog rabies in sub-Saharan Africa and the impact of control efforts[END_REF][START_REF] Zinsstag | Transmission dynamics and economics of rabies control in dogs and humans in an African city[END_REF][START_REF] Zhang | Analysis of rabies in China: transmission dynamics and control[END_REF][START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF] are the most represented models, followed by agent-based (n = 8) [16,30,31,35,36,[START_REF] Hudson | Using roaming behaviours of dogs to estimate contact rates: The predicted effect on rabies spread[END_REF][START_REF] Hudson | Modelling targeted rabies vaccination strategies for a domestic dog population with heterogeneous roaming patterns[END_REF][START_REF] Brookes | Rabies-induced behavioural changes are key to rabies persistence in dog populations: Investigation using a network-based model[END_REF] and metapopulation (n = 5) [25,28,32,37,[START_REF] Beyer | Metapopulation dynamics of rabies and the efficacy of vaccination[END_REF] models. Other model types such as network models or branching processes are also represented [29,[START_REF] Ozella | High-resolution contact networks of free-ranging domestic dogs Canis familiaris and implications for transmission of infection[END_REF][START_REF] Mollentze | A bayesian approach for inferring the dynamics of partially observed endemic infectious diseases from space-time-genetic data[END_REF][START_REF] Bourhy | Revealing the Micro-scale Signature of Endemic Zoonotic Disease Transmission in an African Urban Setting[END_REF][START_REF] Cori | A graph-based evidence synthesis approach to detecting outbreak clusters: An application to dog rabies[END_REF] (S3 and S4 Tables). The development of new dog rabies models builds upon the literature since 15 models out of the 37 identified were adapted from previously published dog rabies or wildlife rabies models (S3 and S4 Tables). This is the case notably for compartmental models which correspond to the simplest models of rabies dynamics. Metapopulation, agent-based, and other model types are more complex, in that these approaches often integrate spatial dynamics of dog rabies [25,30,32,[35][36][37][START_REF] Ozella | High-resolution contact networks of free-ranging domestic dogs Canis familiaris and implications for transmission of infection[END_REF][START_REF] Hudson | Using roaming behaviours of dogs to estimate contact rates: The predicted effect on rabies spread[END_REF][START_REF] Hudson | Modelling targeted rabies vaccination strategies for a domestic dog population with heterogeneous roaming patterns[END_REF][START_REF] Talbi | Phylodynamics and Humanmediated dispersal of a zoonotic virus[END_REF][START_REF] Mollentze | A bayesian approach for inferring the dynamics of partially observed endemic infectious diseases from space-time-genetic data[END_REF][START_REF] Cori | A graph-based evidence synthesis approach to detecting outbreak clusters: An application to dog rabies[END_REF].

Population structure can be integrated in any modelling framework under the form of contact heterogeneity, age-structured populations, roaming behavior, or individual heterogeneity. In compartmental models, population structure is integrated either as a set of strata (stray dogs, owned free-roaming dogs, owned confined dogs) interacting together [33], or by specifying a structured next-generation matrix from which R is generally derived [34]. Such models are also referred to as multi-host models and may integrate other hosts: humans [32,[START_REF] Beyene | Impact of One-Health framework on vaccination cost-effectiveness: A case study of rabies in Ethiopia[END_REF][START_REF] Taib | Model simulation for the spread of rabies in Sarawak, Malaysia[END_REF][START_REF] Zinsstag | Transmission dynamics and economics of rabies control in dogs and humans in an African city[END_REF][START_REF] Zhang | Analysis of rabies in China: transmission dynamics and control[END_REF][START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF][START_REF] Zhang | Spatial spread of rabies in China[END_REF], cattle [START_REF] Beyene | Impact of One-Health framework on vaccination cost-effectiveness: A case study of rabies in Ethiopia[END_REF], wildlife [27,[START_REF] Huang | Modeling the Transmission Dynamics of Rabies for Dog, Chinese Ferret Badger and Human Interactions in Zhejiang Province, China[END_REF]. In agent-based and network models, population structure is defined at the individual level using spatial kernels [16,25,30,31,36,[START_REF] Hudson | Using roaming behaviours of dogs to estimate contact rates: The predicted effect on rabies spread[END_REF], individual contact rates [30,35,[START_REF] Brookes | Rabies-induced behavioural changes are key to rabies persistence in dog populations: Investigation using a network-based model[END_REF], vaccination status [30,36], life span, infectious period [16,31,[START_REF] Brookes | Rabies-induced behavioural changes are key to rabies persistence in dog populations: Investigation using a network-based model[END_REF], etc.

Sensitivity analyses

Sensitivity analyses are commonly used to assess the robustness of inference to both data representativity and model specifications, and to identify the most influential parameters on specific model outputs. In our text corpus, no sensitivity analyses were found to be carried out in phylodynamic studies which can be attributed to the relatively small number of sequences analyzed in those studies. In contrast, sensitivity analyses were commonly performed in mathematical models, either to unravel the key parameters influencing rabies dynamics or to verify the robustness of the results to model assumptions. Dog ecology parameters such as birth rate and carrying capacities are often reported as key parameters on rabies dynamics predictions although they are not estimated using local data. Transmission rates are also determinant in model predictions (S3 Table ). In spatially explicit studies, mobility parameters also have a strong impact on model inferences. Finally, the impact of under-reporting was tested only in interdisciplinary studies, two of which reported a strong impact of the reporting rate on model inference [20,[START_REF] Cori | A graph-based evidence synthesis approach to detecting outbreak clusters: An application to dog rabies[END_REF] whereas the other two were robust to a change in this parameter [START_REF] Bourhy | Revealing the Micro-scale Signature of Endemic Zoonotic Disease Transmission in an African Urban Setting[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF] (S4 Table ).

Insights into dog rabies dynamics and its drivers from phylodynamic and modelling studies

Phylogeographic analyses have aimed to unravel the spatial dynamics of dog rabies at the global and regional scales and showed that dog RABV lineages cluster spatially at the global scale, except for one lineage, referred to as the cosmopolitan lineage, which is largely PLOS NEGLECTED TROPICAL DISEASES distributed across the world [START_REF] Bourhy | The origin and phylogeography of dog rabies virus[END_REF]. At the regional and country scales, there is co-circulation of dog-related lineages, notably in China [START_REF] Meng | Evolutionary dynamics of rabies viruses highlights the importance of China rabies transmission in Asia[END_REF][START_REF] Yu | The spatial and temporal dynamics of rabies in China[END_REF][START_REF] Yao | The Spatiotemporal Expansion of Human Rabies and Its Probable Explanation in Mainland China, 2004-2013[END_REF][START_REF] Zhang | Cross-border spread, lineage displacement and evolutionary rate estimation of rabies virus in Yunnan Province, China[END_REF][START_REF] Wang | Phylodynamic and transmission pattern of rabies virus in China and its neighboring countries[END_REF], in the Middle East [START_REF] Horton | Complex Epidemiology of a Zoonotic Disease in a Culturally Diverse Region: Phylogeography of Rabies Virus in the Middle East[END_REF][START_REF] Dellicour | Using phylogeographic approaches to analyse the dispersal history, velocity and direction of viral lineages-Application to rabies virus spread in Iran[END_REF], as well as in Western and Central Africa [START_REF] Talbi | Evolutionary history and dynamics of dog rabies virus in western and central Africa[END_REF]. However, each lineage exhibits a strong geographical structure. In the case of country-specific lineages, various studies have suggested that transboundary movements are not a major force of rabies dispersal [19,[START_REF] Lemey | Bayesian phylogeography finds its roots[END_REF][START_REF] Talbi | Evolutionary history and dynamics of dog rabies virus in western and central Africa[END_REF][START_REF] Mollentze | Dog rabies in southern Africa: Regional surveillance and phylogeographical analyses are an important component of control and elimination strategies[END_REF][START_REF] Guo | National Borders Effectively Halt the Spread of Rabies: The Current Rabies Epidemic in China Is Dislocated from Cases in Neighboring Countries[END_REF][START_REF] Dellicour | Using Viral Gene Sequences to Compare and Explain the Heterogeneous Spatial Dynamics of Virus Epidemics[END_REF]. All study categories unraveled the role of human-mediated movements in rabies spread. Overall, phylogeographic analyses provided evidence for the effect of anthropogenic factors: major roads are associated with rabies dispersal in North Africa [START_REF] Talbi | Phylodynamics and Humanmediated dispersal of a zoonotic virus[END_REF], and RABV lineages tended to preferentially circulate within populated areas in North Africa [START_REF] Dellicour | Using Viral Gene Sequences to Compare and Explain the Heterogeneous Spatial Dynamics of Virus Epidemics[END_REF] and the Middle East [START_REF] Dellicour | Using phylogeographic approaches to analyse the dispersal history, velocity and direction of viral lineages-Application to rabies virus spread in Iran[END_REF]. Other factors are associated with rabies spread in Yunnan (China, Tables 1 andS5). These results may reflect the intimate link between rabies dynamics, host ecology and dog-human interactions. Mathematical models highlighted the short length of canine rabies transmission chains [31,[START_REF] Mollentze | A bayesian approach for inferring the dynamics of partially observed endemic infectious diseases from space-time-genetic data[END_REF][START_REF] Cori | A graph-based evidence synthesis approach to detecting outbreak clusters: An application to dog rabies[END_REF] and unraveled the importance of long-range human movements in disease spread [25,32]. Finally, interdisciplinary approaches highlighted the crucial role of long-distance transmission events likely due to humans in rabies dynamics in North Africa [START_REF] Talbi | Phylodynamics and Humanmediated dispersal of a zoonotic virus[END_REF] and also showed that main roads act as barriers to dog rabies dispersal in an urban setting in Africa [35].

Phylodynamic studies showed that introduction through infected dog movement is the major force of rabies spread towards disease-free areas, as Indonesia [16][17][18] and the Philippines [19,20] have recently experienced, and also represents a driver of rabies spread in endemic areas where frequent reintroductions counteract local rabies elimination after vaccination campaigns [START_REF] Bourhy | Revealing the Micro-scale Signature of Endemic Zoonotic Disease Transmission in an African Urban Setting[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]. In these settings, phylodynamic analysis constitutes a powerful tool to confirm introduction events [19,[START_REF] Hayman | Evolutionary history of rabies in Ghana[END_REF][START_REF] Mollentze | Dog rabies in southern Africa: Regional surveillance and phylogeographical analyses are an important component of control and elimination strategies[END_REF][START_REF] Talbi | Phylodynamics and Humanmediated dispersal of a zoonotic virus[END_REF][START_REF] Bourhy | Revealing the Micro-scale Signature of Endemic Zoonotic Disease Transmission in an African Urban Setting[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]. Multiple mathematical models have also shown that frequent reintroductions drive rabies persistence in endemic areas [31,37,[START_REF] Mollentze | A bayesian approach for inferring the dynamics of partially observed endemic infectious diseases from space-time-genetic data[END_REF][START_REF] Cori | A graph-based evidence synthesis approach to detecting outbreak clusters: An application to dog rabies[END_REF].

Population structure constitutes another driving force of rabies maintenance as explored in simulation studies integrating dog ecology data in Australian [30,[START_REF] Hudson | Using roaming behaviours of dogs to estimate contact rates: The predicted effect on rabies spread[END_REF][START_REF] Hudson | Modelling targeted rabies vaccination strategies for a domestic dog population with heterogeneous roaming patterns[END_REF][START_REF] Brookes | Rabies-induced behavioural changes are key to rabies persistence in dog populations: Investigation using a network-based model[END_REF], Japanese [36], Tanzania [28,[START_REF] Beyer | Metapopulation dynamics of rabies and the efficacy of vaccination[END_REF] and Chadian [35] settings. Rabies-induced behavioral changes were shown to contribute to rabies persistence in small dog populations [START_REF] Brookes | Rabies-induced behavioural changes are key to rabies persistence in dog populations: Investigation using a network-based model[END_REF] as well as differential roaming behavior, contact rates between dog strata and the structure of contact networks [30,[34][35][36][START_REF] Brookes | Rabies-induced behavioural changes are key to rabies persistence in dog populations: Investigation using a network-based model[END_REF].

The contribution of wildlife to canine rabies spread and maintenance is rarely addressed in phylodynamic studies because viruses isolated from wildlife specimens often correspond to dog-related lineages [19,[START_REF] Hayman | Evolutionary history of rabies in Ghana[END_REF][START_REF] Yao | The Spatiotemporal Expansion of Human Rabies and Its Probable Explanation in Mainland China, 2004-2013[END_REF][START_REF] Zhang | Cross-border spread, lineage displacement and evolutionary rate estimation of rabies virus in Yunnan Province, China[END_REF][START_REF] Wang | Phylodynamic and transmission pattern of rabies virus in China and its neighboring countries[END_REF] or because of insufficient sampling efforts when it comes to wildlife [START_REF] Yu | The spatial and temporal dynamics of rabies in China[END_REF] (S1 Table ). Nevertheless, specific RABV lineages were shown to circulate both in wildlife and domestic dogs in the Middle East and Tanzania with complex interspecies transmissions [START_REF] Horton | Complex Epidemiology of a Zoonotic Disease in a Culturally Diverse Region: Phylogeography of Rabies Virus in the Middle East[END_REF][START_REF] Troupin | Large-Scale Phylogenomic Analysis Reveals the Complex Evolutionary History of Rabies Virus in Multiple Carnivore Hosts[END_REF][START_REF] Brunker | Landscape attributes governing local transmission of an endemic zoonosis: Rabies virus in domestic dogs[END_REF][START_REF] Dellicour | Using phylogeographic approaches to analyse the dispersal history, velocity and direction of viral lineages-Application to rabies virus spread in Iran[END_REF]. A phylodynamic study at the global scale showed that host shifts from dogs to wildlife with adaptation to the new host were common in RABV history [START_REF] Troupin | Large-Scale Phylogenomic Analysis Reveals the Complex Evolutionary History of Rabies Virus in Multiple Carnivore Hosts[END_REF], which may explain why different lineages circulate in dogs and wild foxes in Brazil [START_REF] Carnieli | Phylogeographic dispersion and diversification of rabies virus lineages associated with dogs and crab-eating foxes (Cerdocyon thous) in Brazil[END_REF], in dogs and ferret badgers in Asia [START_REF] Troupin | Large-Scale Phylogenomic Analysis Reveals the Complex Evolutionary History of Rabies Virus in Multiple Carnivore Hosts[END_REF] and in dogs and mongooses in South Africa [START_REF] Troupin | Large-Scale Phylogenomic Analysis Reveals the Complex Evolutionary History of Rabies Virus in Multiple Carnivore Hosts[END_REF] with rare interspecies transmission events. By incorporating direct interspecies transmission, mathematical modeling studies showed that dog population contributes to sustained rabies circulation in wildlife instead of the other way around [27,[START_REF] Huang | Modeling the Transmission Dynamics of Rabies for Dog, Chinese Ferret Badger and Human Interactions in Zhejiang Province, China[END_REF]. Similarly, the proximity to wildlife was shown to not impact rabies spread in dogs in the model of Beyer et al. [28].

Finally, mathematical models and phylodynamics provide convenient estimates of a range of parameters on rabies dispersal dynamics (lineage dispersal velocities, diffusion coefficients; Table 1), rabies evolutionary processes and dog ecology. For example, the evolutionary rate was homogeneously estimated to be between 1 x 10 -4 and 5 x 10 -4 substitutions per site per year across RABV genes and lineages, except for the Asian lineage which is estimated to evolve faster (Fig 3A). The time to the most recent common ancestor (TMRCA) is also frequently PLOS NEGLECTED TROPICAL DISEASES estimated in phylodynamic studies (S2 Table ) which is generally more recent than suggested by historical records. R, the expected number of secondary infections, is often estimated by fitting case data to mathematical models (Fig 3B) or by computing its value based on the choice of parameters value (S6 Table ). Its estimate ranges from 0.80 to 3.36 according to the setting but it is generally estimated to be between 1 and 2, corresponding to a low-grade transmission with frequent stochastic extinctions. Other parameters such as the dog-to-dog transmission rate, the introduction rate or the dog carrying capacity are also frequently estimated (S6 Table ).

Effective control strategies

Interdisciplinary and modelling studies generally assessed the impact of past or potential control strategies to eliminate dog rabies. The specifications of the explored control strategies depended on the economic situation of the country in which the study was supposed to be performed, as well as the model type. Dog vaccination was the most studied control measure (n = 28) [16,23,24,[26][27][28][30][31][32][33][34][35][36][37][START_REF] Beyene | Impact of One-Health framework on vaccination cost-effectiveness: A case study of rabies in Ethiopia[END_REF][START_REF] Taib | Model simulation for the spread of rabies in Sarawak, Malaysia[END_REF][START_REF] Huang | Modeling the Transmission Dynamics of Rabies for Dog, Chinese Ferret Badger and Human Interactions in Zhejiang Province, China[END_REF][START_REF] Hudson | Modelling targeted rabies vaccination strategies for a domestic dog population with heterogeneous roaming patterns[END_REF][START_REF] Brookes | Rabies-induced behavioural changes are key to rabies persistence in dog populations: Investigation using a network-based model[END_REF][START_REF] Carroll | The use of immunocontraception to improve rabies eradication in urban dog populations[END_REF][START_REF] Ortega | Fuzzy dynamical systems in epidemic modeling[END_REF][START_REF] Hampson | Synchronous cycles of domestic dog rabies in sub-Saharan Africa and the impact of control efforts[END_REF][START_REF] Zinsstag | Transmission dynamics and economics of rabies control in dogs and humans in an African city[END_REF][START_REF] Zhang | Analysis of rabies in China: transmission dynamics and control[END_REF][START_REF] Beyer | Metapopulation dynamics of rabies and the efficacy of vaccination[END_REF][START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF], whereas culling (n = 7) [30,33,[START_REF] Hudson | Using roaming behaviours of dogs to estimate contact rates: The predicted effect on rabies spread[END_REF][START_REF] Carroll | The use of immunocontraception to improve rabies eradication in urban dog populations[END_REF][START_REF] Zinsstag | Transmission dynamics and economics of rabies control in dogs and humans in an African city[END_REF][START_REF] Zhang | Analysis of rabies in China: transmission dynamics and control[END_REF][START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF], dog confinement or movement ban (n = 4) [30,31,36,[START_REF] Hudson | Using roaming behaviours of dogs to estimate contact rates: The predicted effect on rabies spread[END_REF], control of dog birth rate (n = 4) [START_REF] Taib | Model simulation for the spread of rabies in Sarawak, Malaysia[END_REF][START_REF] Carroll | The use of immunocontraception to improve rabies eradication in urban dog populations[END_REF][START_REF] Zhang | Analysis of rabies in China: transmission dynamics and control[END_REF][START_REF] Zhang | Spatial spread of rabies in China[END_REF] and community behavior (n = 1) [31] were rarely modelled.

Culling was shown to be effective in two compartmental model studies [START_REF] Carroll | The use of immunocontraception to improve rabies eradication in urban dog populations[END_REF][START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF] while Abbreviations: HPD, Highest Posterior Density; SEA-1, South-East Asia 1; SEA-2, South-East Asia 2; SEA-3, South-East Asia 3.

The sampling window and the spatial scale of the studies are highly variable. Thus, it is not possible to directly compare the velocity and diffusion coefficients amongst the different study settings. a Depending on the study, estimates of RABV lineage velocity or diffusivity were obtained by estimating different dispersal statistics. Talbi et al. [72] reconstructed for each branch of the phylogenetic tree the expected number of migrations between two locations using a discrete phylogeographic model. The authors multiplied these estimates by the great-circle distance between the two locations, and thus, obtained the expected distance travelled within the time elapsed on each branch. Carnieli et al. [START_REF] Carnieli | Phylogeographic dispersion and diversification of rabies virus lineages associated with dogs and crab-eating foxes (Cerdocyon thous) in Brazil[END_REF], Bourhy et al. [74], Brunker et al. [68], Tian et al. [START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF], and Dellicour et al. [START_REF] Wang | Phylodynamic and transmission pattern of rabies virus in China and its neighboring countries[END_REF] estimated the mean branch velocity using continuous phylogeographic reconstructions. Finally, Dellicour et al. [START_REF] Ma | Re-emerging of rabies in Shaanxi province, China, from 2009 to 2015[END_REF] estimated the temporal evolution of the wavefront velocity that corresponds to the distance between the reconstructed epidemic origin and the maximal epidemic wavefront. While the mean branch velocity (v) and diffusion coefficient (D) are estimates of the dispersal velocity and of the diffusion coefficient averaged over all tree branches, respectively, their weighted average counterparts involve a weighting by branch time resulting in lower-variance estimates [START_REF] Wang | Phylodynamic and transmission pattern of rabies virus in China and its neighboring countries[END_REF].

b Depending on the study, the impact of environmental factors on dispersal of viral lineages were investigated using different approaches. Talbi et al. [72] simulated random or conditional dispersal of RABV in northern Africa along phylogenetic trees reconstructed by phylogeographic inference and compared simulated dispersal patterns with the observed spread. Brunker et al. [START_REF] Dellicour | Using Viral Gene Sequences to Compare and Explain the Heterogeneous Spatial Dynamics of Virus Epidemics[END_REF] parametrized a generalized linear model (GLM) in a discrete phylogeographic framework with resistance distances derived from landscape data between clusters of rabies cases. Dellicour et al. [67] and Tian et al. [START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF] assessed which environmental factors are associated with RABV velocity using continuous phylogeographic inference and post hoc statistical analyses. Dellicour et al. [70] and Tian et al. [77] also identified factors associated with the direction of spread using phylogeographic reconstructions and subsequent post hoc analyses. c 95% Highest Posterior Density (HPD) intervals are not specified in the original publications.

https://doi.org/10.1371/journal.pntd.0009449.t001

PLOS NEGLECTED TROPICAL DISEASES vaccination was generally found to be the most effective strategy. Vaccination coverage strongly depends on the setting: 90% or complete dog vaccination coverages are recommended in rabies-free areas with high surveillance and control capacities whereas lower coverages associated with complementary strategies are recommended in endemic areas (Table 2). Nevertheless, the efficacy of vaccination strategies is mitigated by new introductions due to neighboring transmission or long-distance movements mediated by humans [25,29,31,37,[START_REF] Bourhy | Revealing the Micro-scale Signature of Endemic Zoonotic Disease Transmission in an African Urban Setting[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF][START_REF] Knobel | Dog Rabies and Its Control[END_REF], notably in low vaccinated populations [32]. In this case, reactive vaccination strategies [16] or dog movement bans [25] constitute alternative effective measures. However, Ferguson et al. [31] evaluated the impact of new introductions in vaccinated areas, and concluded that vaccination coverages were robust to rabies introduction in their specific setting. Similarly, Beyer et al. [START_REF] Beyer | Metapopulation dynamics of rabies and the efficacy of vaccination[END_REF] suggested that the spatial structure of dog population had more impact than rabies introduction on the efficacy of vaccination campaigns. In terms of vaccination coverage, successful vaccination campaigns should target homogenous coverage since hidden pockets of rabies transmission might jeopardize control efforts [16,23,29,31]. In terms of campaign frequency, the efficacy of pluriannual compared to annual vaccination campaigns is difficult to evaluate as it results from many factors including the number of vaccination pulses, the time interval between each pulse, dog birth rate and the introduction rate of infectious animals [23,28,[START_REF] Carroll | The use of immunocontraception to improve rabies eradication in urban dog populations[END_REF].

Recent studies [28,[34][35][36][START_REF] Hudson | Using roaming behaviours of dogs to estimate contact rates: The predicted effect on rabies spread[END_REF][START_REF] Hudson | Modelling targeted rabies vaccination strategies for a domestic dog population with heterogeneous roaming patterns[END_REF] proposed targeting at-risk dog populations, such as explorers and roaming dogs, to improve the efficacy of vaccination campaigns (Table 2). However, the sensitivity analysis of Laager et al. [37] showed that population structure did not impact the efficacy of vaccination strategies. There are conflicting results concerning stray dog vaccination which was either less efficient than owned dog vaccination [START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF] or dependent on population composition [34].

Several studies also suggested an impact of dog birth rate reduction on the incidence of rabies [23,26,[START_REF] Taib | Model simulation for the spread of rabies in Sarawak, Malaysia[END_REF][START_REF] Huang | Modeling the Transmission Dynamics of Rabies for Dog, Chinese Ferret Badger and Human Interactions in Zhejiang Province, China[END_REF][START_REF] Carroll | The use of immunocontraception to improve rabies eradication in urban dog populations[END_REF][START_REF] Zhang | Analysis of rabies in China: transmission dynamics and control[END_REF]. However, the cost and feasibility of dog population management strategies such as sterilization render this unfeasible in many settings [START_REF] Taylor | The role of dog population management in rabies elimination-A review of current approaches and future opportunities[END_REF]. Dog confinement, which is generally spontaneously put in place by local communities during rabies outbreaks, may improve elimination prospects but, when implemented, the level of confinement is not sufficient to reach elimination [25,30,31]. Concerning the rabies burden in humans, some studies recalled the importance of public awareness (Table 2) and proper PEP coverage to reduce the number of human cases, even though it does not impact rabies circulation in dogs [26,35,36,[START_REF] Huang | Modeling the Transmission Dynamics of Rabies for Dog, Chinese Ferret Badger and Human Interactions in Zhejiang Province, China[END_REF]. All these findings confirmed and justified the strategic plan that provides a phased, all-inclusive, intersectoral approach to eliminate human deaths from rabies recently launched by United Against Rabies, in a collaboration between four partners: WHO, FAO, OIE and GARC [13].

Discussion

Insights on rabies epidemiology and control

In this review, we assessed the respective contributions of mathematical modelling and phylodynamics to the understanding of rabies spread and control in dog populations. Contrary to phylodynamic studies, mathematical modelling approaches were multi-faceted and mainly addressed the efficacy of control strategies and, less frequently, the drivers of rabies spread. They revealed the crucial role of frequent introductions and the potential role of dog population structure in disease dispersal and maintenance, as well as the overwhelming efficacy of dog vaccination campaigns over other control strategies. Certain studies also estimated key parameters of rabies dynamics and dog ecology, such as dog birth rate or dog carrying capacity. On the other hand, phylodynamic studies mostly focused on the description of viral dynamics at the global, regional, and local scales, and recently tested which environmental factors are impacting RABV spread. These approaches consistently unraveled the occurrence of long-distance movements suspected to be human-mediated and confirmed the role of humans Kitala et al., 2002 [23] N'Djame ´na, Chad Zinsstag et al., 2009 [48] Even coverage Bali, Indonesia Townsend et al., 2013 [16] Serengeti and Ngorongoro districts, Tanzania Fitzpatrick et al., 2012 [27] �50% dog vaccination coverage � 50% fertility control coverage Carroll et al., 2010 [45] Sarawak state, Malaysia Taib et al., 2019 [40] Even dog vaccination coverage Region IV, Philippines Ferguson et al., 2015 [31] Targeted dog vaccination campaigns

PLOS NEGLECTED TROPICAL DISEASES

Frequent dog vaccination campaigns targeting the reduction in metapopulation risk Serengeti district, Tanzania Beyer et al., 2012 [28] Stray dog vaccination coverage based on dog population composition Leung et al., 2017 [34] Vaccination based on social and roaming behaviors Public awareness Locally reactive interventions Reporting of 60% of cases by the surveillance system N'Djame ´na, Chad Laager et al., 2018 [35] Dog population management

Dog vaccination Public awareness

China Zhang et al., 2012 [26] Massive dog vaccination campaigns in urban areas Dog movement bans Central African Republic Colombi et al., 2020 [25] Dog vaccination China Zhang et al., 2011 [49] The efficacy of control strategies on dog rabies dynamics has been addressed in only a subset of the currently available mathematical modelling studies. Studies presented in this table compared several control strategies or different dog vaccination coverages on rabies elimination prospects. The optimal control strategy inherently depends on the epidemiological context (endemic or introduction in previously rabies-free areas), the setting (local surveillance and vaccination capacities), the assumptions of the dog rabies model and the control strategies tested by the researchers. Here, we report the strategies recommended by the authors which include quantitative and qualitative criteria such as the estimated impact of public awareness on rabid dog detection and management. Three studies [35,[START_REF] Taib | Model simulation for the spread of rabies in Sarawak, Malaysia[END_REF][START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF] are not grounded in a specific geographical area. Using simulated scenarios, they test the impact of control strategies according to the time to detection [35], dog population structure [START_REF] Taib | Model simulation for the spread of rabies in Sarawak, Malaysia[END_REF] and the use of immunocontraceptives [START_REF] Hou | Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China[END_REF].

https://doi.org/10.1371/journal.pntd.0009449.t002

PLOS NEGLECTED TROPICAL DISEASES

in rabies dispersal dynamics in Africa and the Middle East. A third kind of studies either combined phylodynamics and mathematical modelling or presented new models integrating epidemiological and genetic data. In the former approach, hypotheses on rabies spread were generated and tested in the same epidemiological context, and thus, confirmed the impact of introductions and human movements in a low-grade transmission process characterized by small clusters and frequent stochastic extinctions. The latter approaches aimed at reconstructing local transmission chains or clusters, opening new horizons on data integration and the study of rabies (Fig 4). Unfortunately, a large number of endemic countries is still not, or poorly studied. Data collection and/or model formulation are still needed in Russia, and most of Africa, and South-East Asia.

The limitations of our review should be acknowledged. In preliminary analyses, we noticed a high variability in record selection according to the combination of search terms, and certainly due to the ambiguous use of specific terms such as phylodynamics in the literature. Since the studies selected in this review are mainly in line with previous reviews [START_REF] Brunker | Genomic sequencing, evolution and molecular epidemiology of rabies virus[END_REF][START_REF] Rattanavipapong | The impact of transmission dynamics of rabies control: Systematic review[END_REF][START_REF] Fisher | The spread and evolution of rabies virus: Conquering new frontiers[END_REF], we argue that we retrieved a large part of the available studies on rabies dynamics and control.

Open questions in rabies epidemiology and control

In this review, we summarized the findings of mathematical modelling and phylodynamics on the factors that impact rabies spread. Nevertheless, the full picture of rabies epidemiology remains unclear. First, the role of dog roaming behavior, and dog contact networks in dog rabies spread should be further investigated. In this review, we identified seven studies [33][34][35][START_REF] Ozella | High-resolution contact networks of free-ranging domestic dogs Canis familiaris and implications for transmission of infection[END_REF][START_REF] Hudson | Using roaming behaviours of dogs to estimate contact rates: The predicted effect on rabies spread[END_REF][START_REF] Hudson | Modelling targeted rabies vaccination strategies for a domestic dog population with heterogeneous roaming patterns[END_REF][START_REF] Brookes | Rabies-induced behavioural changes are key to rabies persistence in dog populations: Investigation using a network-based model[END_REF], all situated in Australia and Africa, showing that highly connected dogs or free roaming dogs participate in a large part in the spread of the disease. By specifically targeting this type of dogs, vaccination campaigns could be more effective according to Leung et al., 2017 [34], Laager et al., 2018 [35], and Hudson et al., 2019 [43]. Yet only one study combined contact data with epidemiological data [35]. The ecological and behavioral drivers of rabies circulation in domestic dogs are still not fully understood. If stray dogs do constitute a major driver of rabies dispersal, this could have direct implications on the field concerning stray dog population management for example.

Additionally, the role of wildlife and other host species remains unclear [START_REF] Rupprecht | Priorities in applied research to ensure programmatic success in the global elimination of canine rabies[END_REF]. Even though the circulation of dog rabies seems predominant in dog populations, there are too few studies addressing the dynamics of RABV in wildlife and dogs. Furthermore, the interactions between dogs and other carnivore species are expected to change from location to location. Indeed, the interactions between dog populations and wild carnivores depend on the abundance of wild populations and the frequency of contacts between the dog reservoir and wildlife [27,[START_REF] Huang | Modeling the Transmission Dynamics of Rabies for Dog, Chinese Ferret Badger and Human Interactions in Zhejiang Province, China[END_REF]. Better understanding the role of wildlife could also have direct implications on local policies such as increasing public awareness, notably in rural areas or strengthening wildlife surveillance systems for rabies.

At a broader scale, the spatial dynamics of rabies are still poorly understood. Urban areas were first thought to be hubs of rabies transmission but recent studies have shown that rabies could be eliminated temporarily at the city-level through mass dog vaccination campaigns [37,[START_REF] Bourhy | Revealing the Micro-scale Signature of Endemic Zoonotic Disease Transmission in an African Urban Setting[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]. These case studies suggest that urban areas are not hubs of rabies transmission but part of the complex spatial heterogeneity of dog ecology and dog movement. By exploring the dynamics of dog rabies circulation in urban, peri urban and rural areas, rabies research could see an improved understanding of rabies ecology. This could have direct implications on the design of vaccination campaigns, by prioritizing vaccination campaigns in hubs of rabies transmission, followed by locations with intermediate and low transmission.

Finally, there is extensive evidence of the efficacy of dog vaccination to control the spread of rabies in both human and dog populations. We showed in this review that higher coverages are recommended in rabies-free areas than in endemic areas, however, the practicalities of vaccination campaigns are rarely addressed. As a neglected tropical disease, rabies control programs are designed and deployed in resource-limited contexts. Thus, high, and even intermediate vaccination coverages cannot be achieved at once over a large area. The periodicity, the spatial prioritization, the targeted populations, and the association with other control strategies (dog population management, dog movement ban. . .) are interesting modalities that could be tested in models and could substantially improve resource allocation.

Future directions of mathematical modelling and phylodynamics for rabies research

There is an evident lack of extensive and adequate databases possibly due to restricted data collection, data accessibility and/or data analysis capacity in resource-limited settings [START_REF]Aiming for elimination of dog-mediated human rabies cases by 2030[END_REF][START_REF] Hampson | Lessons for rabies control and elimination programmes: a decade of One Health experience from Bali, Indonesia[END_REF]. This constitutes the main weakness of mathematical modelling and phylodynamic studies that we identified in this review (Table 3). Epidemiological and ecological (census data, population structure, contact networks) data are needed to account for local specificities in terms of modeling interactions between rabies virus (RABV), dog reservoir, domestic animals, wildlife reservoir and human populations. Similarly, there is a need for longer RABV genetic sequences and more thorough sampling to discriminate fine-scale migration events and better characterize the interactions between RABV lineages [START_REF] Brunker | Elucidating the phylodynamics of endemic rabies virus in eastern Africa using whole-genome sequencing[END_REF][START_REF] Brunker | Genomic sequencing, evolution and molecular epidemiology of rabies virus[END_REF][START_REF] Brunker | Rapid in-country sequencing of whole virus genomes to inform rabies elimination programmes[END_REF]. Improving operational data collection is nevertheless challenging. Genomic surveillance relies on laboratory infrastructures, supply chains and expertise, all of which are costly and generally lacking in low-and middle-income countries. New portable sequencing technologies combined with bioinformatics workflows could accelerate capacity building through portability and affordability [START_REF] Brunker | Rapid in-country sequencing of whole virus genomes to inform rabies elimination programmes[END_REF][START_REF] Gigante | Portable Rabies Virus Sequencing in Canine Rabies Endemic Countries Using the Oxford Nanopore MinION[END_REF]. In parallel, potential sampling bias effects should not be overlooked [START_REF] Lemey | Bayesian phylogeography finds its roots[END_REF][START_REF] Ishikawa | A Fast Likelihood Method to Reconstruct and Visualize Ancestral Scenarios[END_REF] since they may hide a part of disease dynamics such as silent spread in deprived rural areas. Additionally, many endemic countries with high human incidence (Russia, Malaysia, Cambodia, Burma, Niger, Mozambique, etc.) [8] remain largely unstudied using quantitative approaches. This represents an opportunity for data collection, rabies dynamics characterization and control strategy optimization. Besides filling knowledge gaps, improving the availability of epidemiological, ecological, and genetic data offers an opportunity to strengthen countries' veterinary surveillance capacities [15] and enhance the impact assessment of control strategies, two pillars of the 2030 strategic elimination plan.

Other data types such as social sciences data could help identify knowledge gaps and refine control measures to be tested further using mathematical models. For example, there is little quantitative evidence of the impact of community response on the efficacy of control measures [START_REF] Rupprecht | Priorities in applied research to ensure programmatic success in the global elimination of canine rabies[END_REF], although it is key to human rabies prevention [START_REF] Hasanov | Assessing the impact of public education on a preventable zoonotic disease: Rabies[END_REF][START_REF] Bardosh | Global aspirations, local realities: The role of social science research in controlling neglected tropical diseases[END_REF] and it is expected to change over rabies outbreaks and affect rabies dynamics. By bridging the two disciplines, alternative control strategies that are both effective and adapted to community preferences could be designed [99] (Fig 4). Finally, novel methodologies combining genetic, epidemiological, and environmental data in a comprehensive analysis framework are promising tools for the rabies field. Indeed, the interdisciplinary studies identified in this review exploited the complementarity of genetic and epidemiological information to efficiently generate and test hypotheses on the mechanisms of rabies dynamics [20,[START_REF] Talbi | Phylodynamics and Humanmediated dispersal of a zoonotic virus[END_REF][START_REF] Mollentze | A bayesian approach for inferring the dynamics of partially observed endemic infectious diseases from space-time-genetic data[END_REF][START_REF] Cori | A graph-based evidence synthesis approach to detecting outbreak clusters: An application to dog rabies[END_REF][START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF], and the limitations of control strategies [START_REF] Bourhy | Revealing the Micro-scale Signature of Endemic Zoonotic Disease Transmission in an African Urban Setting[END_REF][START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF]. These new avenues represent a significant improvement on past studies and a promising opportunity for canine rabies research in the frame of a One Health concept that aims to achieve better public health outcomes through cross-sector collaboration.

Conclusions

In this review, we highlighted the need for more epidemiological, ecological, and genetic data to better characterize rabies dynamics and to get practical information on the drivers of disease transmission. We think that the development of new methodologies integrating genetic and epidemiological data, or the combined use of mathematical models and phylodynamics, constitutes a promising approach that could ultimately contribute to the improvement of the efficacy of control measures including vaccination campaigns and help optimizing the allocation of resources in a context of limited funding.

Initially submitted September 2, 2021; accepted for publication March 1, 2022. Several studies have characterized the effectiveness of vaccines against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections. However, estimates of their impact on transmissibility remain limited. Here, we evaluated the impact of isolation and vaccination (7 days after the second dose) on SARS-CoV-2 transmission within Israeli households. From December 2020 to April 2021, confirmed cases were identified among health-care workers of the Sheba Medical Centre and their family members. Recruited households were followed up with repeated PCR for at least 10 days after case confirmation. Data were analyzed using a data augmentation Bayesian framework. A total of 210 households with 215 index cases were enrolled; 269 out of 667 (40%) susceptible household contacts developed a SARS-CoV-2 infection. Of those, 170 (63%) developed symptoms. Compared with unvaccinated and unisolated adult/teenager (aged >12 years) contacts, vaccination reduced the risk of infection among unisolated adult/teenager contacts (relative risk (RR) = 0.21, 95% credible interval (CrI): 0.08, 0.44), and isolation reduced the risk of infection among unvaccinated adult/teenager (RR = 0.12, 95% CrI: 0.06, 0.21) and child contacts (RR = 0.17, 95% CrI: 0.08, 0.32). Infectivity was reduced in vaccinated cases (RR = 0.25, 95% CrI: 0.06, 0.77). Within households, vaccination reduces both the risk of infection and of transmission if infected. When contacts were unvaccinated, isolation also led to important reductions in the risk of transmission. COVID-19; household; infectious disease transmission; physical distancing; SARS-CoV-2; vaccination; vaccine effectiveness Abbreviations: CrI, credible interval; COVID-19, coronavirus disease 2019; HCW, health-care workers; PCR, polymerase chain reaction; SAR, secondary attack rate; SARS-CoV-2, severe acute respiratory syndrome coronavirus 2.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a highly transmissible virus that was first detected in Wuhan China in December 2019 (1,2). It is the cause of coronavirus disease 2019 , which has spread through the world, leading to a pandemic that had infected at least 250 million people and caused more than 5 million deaths worldwide by November 10, 2021 (3). The advent of novel coronavirus disease 2019 (COVID-19) vaccines has been an important breakthrough in the management of the pandemic. To determine how vaccination may modify epidemic dynamics, it is essential to estimate its effectiveness with respect to infection, transmission, and disease severity.

Multiple studies have shown that COVID-19 vaccines are effective at reducing both the risk of infection (4)(5)(6)(7)(8) and the risk of developing severe symptoms (4,(8)(9)(10) in the general population.

Documenting vaccine impact on transmission is more challenging, stemming from the difficulty of thoroughly documenting chains of transmission and accounting for the ways different types of contacts may lead to different risks of transmission (11). Households represent the perfect environment to evaluate factors affecting transmission such as vaccination because the probability of SARS-CoV-2 transmission among household members is high, ranging between 14%

Vaccination and SARS-CoV-2 Household Transmission 1225 and 32% (12)(13)(14). Beyond the evaluation of vaccine effectiveness, understanding how vaccines affect household transmission is also important to determine how recommendations should evolve with vaccines. For example, should isolation precautions be maintained in partially vaccinated households (15)? A number of studies have shown that vaccines provide indirect protection against household transmission (16)(17)(18)(19)(20). However, none of these studies evaluated how isolation affected the outcome, and for some of the studies (16)(17)(18)(19), the passive nature of surveillance may have led to underestimating household transmission rates.

During the first months of 2021, Israel underwent its third pandemic wave due to the rise of the Alpha variant that quickly accounted for 90% of infections (21). Concomitantly, vaccination was extended to all adults older than age 16 years, making Israel one of the first countries to reach high vaccination coverage in their population, with 60% of the total population being vaccinated by March 22, 2021 (3). During this period, we followed SARS-CoV-2 transmission in the households of 12,518 health-care workers (HCWs) of the Sheba Medical Center, the largest medical center in Israel. Here, we describe dynamics of transmission in these households and evaluate the impact vaccination and isolation measures had on these dynamics.

METHODS

Study design and study population

All HCWs, regardless of their vaccination status, were required to use an electronic questionnaire to report daily any COVID-19 related symptom they, or a member of their household, had. SARS-CoV-2 polymerase chain reaction testing (PCR) was readily available, and HCWs were encouraged to be tested for any mild symptom or suspected exposures. All HCWs were instructed to notify the infection prevention and control unit if one of their household members was SARS-CoV-2 positive. All SARS-CoV-2detected HCWs as well as those with a positive SARS-CoV-2 household member were immediately contacted as part of the epidemiologic investigation for contact tracing and were provided with instructions regarding isolation precautions. All unvaccinated household members (i.e., those that did not receive the 2 vaccine doses at least 7 days before the detection of the COVID-19 patient) were required to perform 2 PCR tests in the 10 days after the diagnosis of the positive COVID-19 patient. Vaccinated household members were encouraged to perform 2 PCR tests during the 10 days after detection. Household members were not required to test a second time if they had a positive test (Web Table 1 in Web Appendix 1, available at https://doi.org/10.1093/ aje/kwac042). Unvaccinated HCW contacts were isolated at home, whereas vaccinated HCWs were instructed to perform a PCR test every day they reported to the hospital for work.

Between December 31, 2020, andApril 26, 2021, the HCWs who were SARS-CoV-2-positive or reported a positive household member were contacted at least 10 days after detection and were offered enrollment in the study. Those who agreed, and gave their consent, answered a telephone interview.

Data and sample collection

Data collected during the phone interview included the age and gender of the HCW's household members, their vaccination status, information about prior their symptoms (i.e.,fever,cough,myalgia,headache,congestion,diarrhea,vomiting,anosmia,or ageusia), the number of rooms and bathrooms in the household, and the degree to which isolation precautions were adhered to (Web Appendix 2). At the time of the study, only individuals 16 years old or older were eligible for vaccination.

The household member who had the first positive PCR test was defined as the index case. When multiple household members had a positive PCR test on the same day, they were defined as co-index cases. We defined complete isolation as complete separation in sleeping and eating between household contacts and index case(s) (i.e., they did not spend any time in the same room) and whether a separate bathroom was provided for the index case(s). Partial isolation was defined if one of the above was violated, but masks were continuously used, and eating was consistently separate.

For HCWs, nasopharyngeal swabs were collected by trained personnel, and reverse-transcriptase quantitative PCR analysis was performed using the Allplex 2019-nCov RT-qPCR assay (Seegene Inc., Seoul, South Korea) and expressed by cycle threshold (Ct). Other household members reported the results of their COVID-19 test(s) performed by their health-care providers.

Clinical outcome

Confirmed SARS-CoV-2 infections were defined by a positive PCR test (i.e., with a Ct value lower than 40). Symptomatic cases were defined as confirmed cases with the presence of at least 1 symptom from among the following: fever, cough, myalgia, headache, congestion, diarrhea, vomiting, anosmia, or ageusia. Contacts who reported at least 1 of the above-mentioned symptoms but were not confirmed because they performed no PCR test (n = 6) or a single test at inclusion (n = 2) were also considered as symptomatic cases. Asymptomatic cases were defined as confirmed cases who did not report any symptom over the follow-up period of the household.

Statistical analysis

We evaluated transmission in households using 2 metrics: the secondary attack rate (SAR), defined as the proportion of susceptible household contacts that are infected after the index case is detected (22), and the person-to-person probability of transmission, defined as the per-capita probability that an infected individual transmits to a susceptible household contact. The first metric includes tertiary (i.e., household contacts infected by a household member that is not the index case) and community cases (i.e., household contacts infected in the community) contrary to the second metric. In both cases, we assumed that individuals who reported past infection of SARS-CoV-2 confirmed by PCR over the year preceding the detection of the household index case (n = 20) were protected from infection and therefore, did not count as susceptible household contacts. Baseline characteristics of the index cases and household contacts were described according to their vaccination status. All individuals older than 12 years were considered as adults/teenagers. We calculated the SAR for different categories of household contacts: unisolated and unvaccinated adults/teenagers, unisolated and vaccinated adults/ teenagers, isolated and unvaccinated adults/teenagers, vaccinated and isolated adults/teenagers, unisolated children, and isolated children. Here, isolation corresponds to complete or partial isolation between household contacts and the index case. We also defined the SAR of vaccinated and unvaccinated index cases as the proportion of infected household contacts in households with vaccinated or unvaccinated index cases, respectively. In a sensitivity analysis, the SAR calculation was restricted to households in which a single index case was identified (Web Table 2 in Web Appendix 3). We also report the 95% confidence interval of the SAR.

We developed a statistical model to evaluate the effect of age, isolation precautions, BNT162b2 vaccination, and household size on SARS-CoV-2 transmission dynamics in households (Web Appendix 4). The model uses the sequence of symptom onset dates and positive molecular test dates to estimate the person-to-person risk of transmission within the household while accounting for the community hazard of infection (i.e., household contacts infected outside the household) and the possibility of tertiary transmissions (i.e., household contacts infected by a member of the household that is not the index case) (23). The person-to-person risk of transmission is decomposed into the baseline personto-person risk of infection depending on household size, the relative infectivity of the infector depending on their vaccination status (reference group: unvaccinated cases), and the relative susceptibility of the infectee depending on their age, isolation behavior, and vaccination status. The relative susceptibility is estimated separately for unisolated children, isolated children, isolated and unvaccinated adults/teenagers, unisolated and vaccinated adults/teenagers, and adults/teenagers that are both isolated and vaccinated, considering the group of adults/teenagers that are unisolated and unvaccinated as the reference group. None of the children were vaccinated at the time of the study. This formulation accommodates the potential confounding effects between the 3 variables characterizing household contacts (i.e., being vaccinated, being isolated, or being a child). We assumed that individuals whose isolation behavior was missing (n = 6) did not comply with isolation precautions.

Model parameters were estimated using Bayesian Markov chain Monte Carlo sampling with data augmentation (23) 1232 Layan et al. the data that isolation also benefited vaccinated individuals, although credible intervals were larger, and further investigations are required to confirm this finding.

Our study has several limitations. First, household studies such as ours may be affected by multiple sources of bias. On the one hand, we may overestimate the SAR if we are more likely to detect households with multiple cases. On the other hand, we might underestimate it if some asymptomatic, or paucisymptomatic, cases are missed during follow-up. Second, we estimated an important reduction of infectivity in vaccinated cases with 2 doses compared with unvaccinated cases as previously shown (18)(19)(20)34). However, this is associated with important uncertainty due to the small number of cases (15 vaccinated index cases and 21 vaccinated secondary cases). Thus, more data are needed to reduce the size of credible intervals. Third, we assumed that vaccination was effective from 7 days after the second dose (or 15 days after the first dose in our sensitivity analysis; see Web Table 11 in Web Appendix 8). In practice, the effect of the vaccine is likely to be progressive, which might push down estimates of effectiveness since individuals with early partial protection would be considered to be unvaccinated. However, excluding households with the early-vaccinated index cases did not affect our estimates (Web Figure 4 and Web Table 12 in Web Appendix 8). The limited number of households does not make it possible to dissociate early vs. full protection conferred by the vaccine nor to investigate the infectivity of children relative to adults/teenagers. Fourth, testing instructions were different for vaccinated and unvaccinated household contacts, as well as HCWs and non-HCWs. Most vaccinated contacts were HCWs at the Sheba Medical Center who complied with testing instructions to go back to work, leading to high testing rates in vaccinated individuals, with 67% having at least 2 PCR tests and 70% having 1 positive PCR or at least 2 PCR tests in the 10 days following case detection (Web Table 1 in Web Appendix 1). Among unvaccinated contacts, 49% had at least 2 PCR tests and 79% had 1 positive PCR or at least 2 PCR tests in the 10 days following case detection. This higher testing rate is notably due to the high proportion of single positive tests (30%). These differential testing behaviors and positivity rates between vaccinated, unvaccinated, HCW, and non-HCW contacts make it difficult to anticipate the directionality of a potential bias. When restricting our evaluation to households where all negative contacts were tested at least once or twice, estimates remained relatively similar to the baseline values. In the analysis with at least 2 tests for all negative contacts, we observed a slight reduction in the point estimate for vaccine effectiveness against infection that remained difficult to interpret given the very broad credible intervals (17%-91%). Fifth, the measurement of isolation precautions may be subject to recall bias and/or overreporting, as they represent a socially desirable behavior. The timing and evolution of isolation precautions were not measured, and thus not integrated in our model. Nevertheless, our estimate of isolation effectiveness is consistent with a 10-day period of quarantine in modeling studies (35). Finally, we estimate vaccine effectiveness against infection and transmission in a context where the Alpha variant was dominant. These estimates are very likely to be different for the Delta variant (36) that was first reported in October 2020 and rapidly became dominant worldwide (37).

To conclude, vaccination with 2 doses substantially reduces the risk of transmission and the risk of infection in households. Isolation from the index case while sleeping and eating provides a high level of protection to unvaccinated household members, whether they are adults/teenagers or children. Household contacts of COVID-19 patients should ideally isolate, or at least refrain from significant contact, with household cases. This may also be the case for vaccinated household members, although larger studies are required to confirm this finding.

In the article "Impact of BNT162b2 Vaccination and Isolation on SARS-CoV-2 Transmission in Israeli Households: An Observational Study" by Layan et al. (1), there was an error in the code of the Markov chain Monte Carlo inference model that led to minor errors in the estimates of transmission parameters. In our analysis, inference is performed in continuous time. However, in our code, the probability of infection of detected cases was expressed in discrete time, 1exp -λ t infection , instead of continuous time, λ t infection . We have now corrected this error.

Table 1 shows a comparison of the uncorrected and corrected median estimates and 95% credible intervals reported at the end of the abstract and in the last 3 paragraphs of the results.

Overall, the correction of the inference model code had only a very minor impact on estimates. It slightly modified the posterior probabilities that isolated and vaccinated adult/teenager contacts are less susceptible than are unisolated and vaccinated adult/teenager contacts in the sensitivity analyses. We reported a posterior probability of 88% with a Bayes factor (BF) of 7 with 1 polymerase chain reaction (PCR) test and a posterior probability of 89% with a BF of 8 with 2 PCR tests, whereas the correct estimates are 90% probability and a BF equal to 9 with 1 PCR test and a posterior probability of 91% and a BF of 10 with 2 PCR tests.

Finally, we reported in the discussion that the reduction in the risk of infection in vaccinated adults/teenagers compared to that in unvaccinated adults/teenagers was 79% instead of 80% and that the vaccine effectiveness against transmission was 75% (95% credible interval: 23, 94) instead of 76% (95% credible interval : 31, 94). We also referred to the broad credible interval of vaccine effectiveness against infection that was 17%-91% instead of 24%-91%.

The code published on GitHub has been corrected. The Web Material detailing all parameters values have been corrected as well.

The authors regret these errors.

Figure 1 :

 1 Figure 1: Transmission cycle of pathogens. (A) The three minimal steps of the transmission process. First, the pathogen infects an individual, then multiplies within the individual, and finally is shed into the environment (from Choisy 2010). (B) Transmission cycle of West Nile virus (WNV). WNV disease is a vector-borne disease affecting bird populations. Human and horse populations can be infected through mosquito bites but they are dead-end hosts (from the CDC). (C) Transmission cycle of rabies virus (RABV). Although domestic dogs are the main reservoir of RABV worldwide, other terrestrial carnivores and bat populations contribute to its circulation. Infections in humans are due to spillover infections from the animal reservoirs. Similar to WNV, human is a dead-end host of RABV and cannot naturally transmit the virus (adapted from Fisher et al. 2018).

  immune escape • Adaptation to herd immunity by fast evolution • High genetic diversity (quasispecies) with low or even non-overlapping antigenic repertoires • Variable gene expression • Host tissues colonized by the pathogen Environmental determinants Factors affecting survival and persistence of pathogens in the environment • Temperature, humidity, ventilation, airflow etc. Factors affecting geographic occurrence and seasonal dynamics • Climate impacts vector geographic location for vectorbone diseases • Seasonal changes in climatic variables impact seasonal dynamics of vectorborne and waterborne diseases Host determinants Factors affecting host infectivity at the individual level • Biological characteristics that modulate the immune system responsiveness (age, sex, underlying pathological condition) • Pre-existing immunity from past infection or vaccination that diminishes pathogen shedding in breakthrough infections Factors affecting host susceptibility to infection at the individual level • Host genetics (e.g., receptor glycosylation) • Biological characteristics that modulate the immune system responsiveness (age, sex, underlying pathological condition) • Pre-existing immunity from past infection or vaccination Factors affecting transmission at the population level • Herd immunity • Host behavior, social structure, and age-related mixing patterns

Figure 2 :

 2 Figure 2: Pathogen, host, and environmental determinants of pathogen transmission. Pathogen, host, and environmental factors influence the success of the transmission process by affecting the host susceptibility, host infectivity, and pathogen persistence in the environment (adapted from Leung 2021; Mistry et al. 2021; Ariën et al. 2007).

Figure 4 :

 4 Figure 4: Flow diagram of the Susceptible-Infectious-Recovered (SIR) model. The host population is divided into three compartments: susceptible (S), infectious (I), and recovered (R) individuals. The total number of individuals is N. Susceptible individuals acquire infection upon contact with infectious individuals that transmit with force of infection β . Infectious individuals recover from the disease at rate γ and are protected from reinfection.

Figure 5 :

 5 Figure 5: Phylodynamic models. (A) Rooted molecular phylogenies are estimated from alignments of pathogen genetic sequences using a nucleotide substitution model. Branch length corresponds to the genetic distance between an ancestor and its descendant, indicating their phylogenetic proximity. (B) By adding a molecular clock model to the inference framework, one can calibrate genetic divergence on calendar time, and thereby, date clade emergence and introduction events. (C) Demographic models stemming from population genetics describe pathogen population dynamics either backwards-in-time as depicted here for the coalescent model, or forwardsin-time for the birth-death model. These models allow the reconstruction of pathogen population growth and can be used to estimate the transmission potential of pathogens. (D) Discrete phylogeography enables to incorporate spatial heterogeneity and is particularly adapted for the study of human diseases. (E) Continuous phylogeography treats geospatial coordinates as continuous variables and models transmission without having to arbitrarily discretize space. It is particularly insightful when applied to pathogen circulation in animal populations (adapted from Pybus and Rambaut 2009 and Dellicour et al. 2021a).

  tific collaboration, and increases confidence in new findings. Phylodynamics comes from a place where open science really participated in the advancements of science. Public repositories of genetic sequences like NCBI GenBank where researchers publish their newly generated data have been used all over the world for a while now. Originally founded for influenza research, the GISAID Initiative, a public-private partnership, promotes the sharing of influenza virus and SARS-CoV-2 genomes along with their clinical and epidemiological data. Nextstrain is a third example. This open-source project that provides access and tools to analyze pathogen genomes has become a major actor of phylodynamic research for outbreak response (Hadfield et al., 2018). In epidemiological modeling, open access is less advanced but new tools like the Our World In Data global database on COVID-19 vaccination have recently emerged during the SARS-CoV-2 pandemic (Ritchie et al., 2020) paving the way to global epidemiological data sharing.

  ' theorem is the foundation of Bayesian statistics. When a statistical model with parameters θ is fitted to observed data x, Bayes' theorem stipulates that the joint posterior probability density of the model parameters given the data p(θ |x) is a weighted combination of the data likelihood p(x|θ ) (joint probability of the observed data as a function of model parameters) and the joint prior probability density of model parameters p(θ ) that represents prior beliefs on the values that model parameters can take on.

Figure 7 :

 7 Figure 7: Applications of epidemiological and phylodynamic modeling. (A) Epidemiological and phylodynamic modeling allow to estimate key transmission parameters, link data across scales, explain observed patterns by unravelling the drivers of spread, predict future trends, and help design control measures (adapted from Lloyd-Smith et al. 2009). (B) Modelling is a powerful tool for public health by improving scientific understanding and advice policies. One can design a model to address policy questions. The model structure then relies on the current scientific understanding of the transmission process and the available relevant data. The model may require changes during the model validation and model fit steps. Sensitivity and uncertainty analyses may provide information on additional data that could be collected (adapted from Heesterbeek et al. 2015).

  [START_REF] Quilty | Quarantine and testing strategies in contact tracing for SARS-CoV-2: a modelling study[END_REF] investigated the potential beneficial impact of testing to reduce quarantine and highlighted that decreased test and trace delays and increasing adherence would improve the effectiveness of combined testing and quarantine measures. So far, very few studies attempted to use phylodynamics to evaluate nonpharmaceutical interventions. Dellicour et al. (2018a) developed a methodology to assess the impact of hypothetical interventions using estimates of a discrete phylogeographic model. This way, they showed that preventing short-distance transmission would have drastically impeded the geographic expansion and epidemic size of the 2014

  gies used to analyze these data, epidemiological modeling for individual-level data and phylodynamic approaches for pathogen genetic sequences, notably concerning missing data and sampling bias. These objectives are addressed by focusing on two case studies of viral diseases: RABV in domestic dog populations and SARS-CoV-2 in households. RABV circulation in animal populations has been studied since the developments of epidemiological modeling to understand its spread and help design effective control strategies but it remains a neglected tropical disease for which limited resources and data are available. Dogs are the main reservoir in Africa and Asia but the drivers of RABV spread in these populations remain poorly characterized. Concerning SARS-CoV-2, it has caused a major pandemic and has led to massive lockdowns and vaccination campaigns around the world. Its high transmission potential coupled to its fast evolution necessitated rapid understanding of the drivers of spread and rapid assessment of control strategies. It has led to an unprecedented scientific production in virology, immunology, epidemiology, evolutionary biology, medical anthropology etc. Although the modes of transmission of RABV and SARS-CoV-2 differ, similar quantitative analytical tools can be applied to better understand the drivers of their spread at the individual and population levels. This thesis is divided into five chapters that address specific questions related to the disease (rabies or COVID-19), methodological choice (phylodynamics or epidemiological modeling), and setting (large spatial scale or individual-level).

Figure 8 :

 8 Figure 8: PRISMA-ScR Flow Diagram showing the number of identified and selected records along the multi-stage selection process. Scopus accounted for most of the records as it retrieved 71% (n = 46) of PubMed records and 79% (n = 74) of Web of Science records.

Figure 9 :

 9 Figure 9: General characteristics of the selected dog rabies studies. (A) Classification of the included publications with the total number of studies, the publication time span, and the number of publications per continent of study. Asia and Africa account for up to 78% of the included studies. (B) Number of publications per year and per methodological category. Mathematical models were the first studies to be published followed by phylodynamic and interdisciplinary studies. (C) Number of publications per country of study. Each publication was attributed to one or multiple countries based on the origin of the RABV genetic sequences, rabid case data or dog ecology data.For phylodynamic studies, countries were not considered if their genetic data were included only in regular phylogenetic tree reconstructions. Similarly, two studies which described rabies dynamics at the global scale(Bourhy et al., 2008; Troupin et al., 2016) were not considered in this figure. In our collected records, China accounts for most Asian studies. Spain appears on the map because Ceuta and Melilla, which are Spanish enclaves in North Africa, are represented in two data sets of RABV genetic sequences(Dellicour et al., 2017; Talbi et al., 2010). (D) Number of studies per topic and methodological category. The World Bank, https://datacatalog.worldbank.org/dataset/world-bank-official-boundaries,CC-BY4.0.

  simulated random or conditional dispersal of RABV in northern Africa along phylogenetic trees reconstructed by phylogeographic inference and compared simulated dispersal patterns with the observed spread. Brunker et al. (2018b) parameterized a generalized linear model (GLM) in a discrete phylogeographic framework with resistance distances derived from landscape data between clusters of rabies cases. Dellicour et al. (2017) and Tian et al. (2018) assessed which environmental factors are associated with RABV velocity using continuous phylogeographic inference and post hoc statistical analyses. Dellicour et al. (2019) and Tian et al. (2018) also identified factors associated with the direction of spread using phylogeographic reconstructions and subsequent post hoc analyses. c 95% Highest Posterior Density (HPD) intervals are not specified in the original publications.

Figure 10 :

 10 Figure 10: Estimates of the mean evolutionary rate of RABV and the reproduction ratio of canine rabies in the included studies. (A) Bayesian credibility intervals (mean and 95% Highest Posterior Density, HPD) of the mean evolutionary rate of canine RABV per genetic sequence and RABV lineage. a The estimate corresponds to the upper bound of the 95% HPD. b The dot corresponds to the median and the interval to the 95% HPD interval. c The 95% HPD was not specified in the original publication. (B) Estimates of the reproduction ratio of dog rabies per control strategy or geographical location. The dot corresponds to the mean and the interval to the 95% confidence interval unless stated otherwise. a The interval corresponds to the standard error. b The authors estimated the effective reproduction ratio along time. Here, the value range of the median monthly point estimate is depicted.

1

  µl of 50 µM of random hexamers (Invitrogen), then placed on ice. The complementary step was performed with the addition of 10 µl of 2X First-Strand Reaction Mix and 2 µl of Superscript III Reverse transcriptase / RNaseOUT Enzyme Mix for a final volume of 22 µl. The mix was incubated at 25°C for 10 min then at 50°C for 50 min. Finally, inactivation of the enzymes was performed after incubation at 85°C for 5 min. Afterward, double-stranded DNA (dsDNA) was synthesized in a reaction mix containing 20 µl of fresh cDNA, 10x Second-Strand Synthesis Reaction Buffer (New England Biolabs), 3 µl of 10 mM dNTP mix (Invitrogen), 1 µl (10 U) of Escherichia coli DNA ligase (New England Biolabs), 4 µl (40 U) of E. coli DNA polymerase I (New England Biolabs), 1 µl (5 U) of E. coli RNase H (New England Biolabs), and 43 µl of nuclease-free water, after incubation at 16°C for 2 h. The total volume (

Figure 12 :

 12 Figure 12: Investigating the endemic signature of RABV circulation in Cambodia. (A) Comparison between patristic distances (in years) computed on the Maximum clade credibility (MCC) at the inter-countries level (excluding Cambodia; in gray), at the intra-country level (excluding Cambodia; in orange), and within the main Cambodian clade (*; in purple). (B) MCC tree obtained from the preliminary discrete phylogeographic inference based on the N gene sequences and considering only two different discrete locations: "Cambodia" and "other countries". Tip nodes and phylogeny branches are colored according to their sampling location and inferred ancestral location, respectively. (*) refers to the main Cambodian clade inferred by the discrete phylogeographic analysis, whose introduction in Cambodia is estimated to be around 1971 (95% HPD = [1963-1979]). (C) Zoom on one particular part of the MCC tree corresponding to the terminal branches outside the main Cambodian clade. The country of origin of sampled sequences are displayed below the tip nodes. (D) Map of log10-transformed human population density in Cambodia. (E) Sampling map of all N gene sequences used for the discrete phylogeographic as well as in the subsequent analyses. Comparison between patristic distances computed on the Maximum clade credibility (MCC) at the inter-countries level (excluding Cambodia; in gray), at the intra-country level (excluding Cambodia; in orange), and within the main Cambodian clade (*; in purple).

Figure 13 :

 13 Figure 13: Dispersal and genetic diversity history of RABV lineages in Cambodia, as inferred by a spatiallyexplicit phylogeographic analysis jointly performed with a skygrid reconstruction. The analyses were either based on the full genomes (panels A and C) or on the N genes (panels B and D). (A-B) For both continuous analyses, we mapped the maximum clade credibility (MCC) tree whose nodes are colored from purple (the time of the most recent common ancestor, TMRCA) to yellow (most recent sampling time). MCC trees are superimposed on 80% highest posterior density (HPD) polygons reflecting phylogeographic uncertainty and colored according to the same time scale. (C-D) Skygrid reconstructions of the recent evolution of the effective size of the viral population (Ne) based on the full genomes and N genes data sets, respectively. The solid lines correspond to the median estimates and the surrounding polygons colored according to the time scale of the corresponding continuous phylogeographic inference correspond to the 95% HPD interval.

Figure 14 :

 14 Figure14: Comparison of RABV lineage dispersal velocity among different data sets. Specifically, we compare the weighted lineage dispersal velocity estimated for the following data sets: RABV in Cambodia (for both the full genomes and N genes data sets), northern Africa(Talbi et al., 2010), Tanzania(Brunker et al., 2018b), Iran(Dellicour et al., 2019), and Yunnan province in China[START_REF] Tian | Transmission dynamics of re-emerging rabies in domestic dogs of rural China[END_REF]. (A) Evolution of the weighted lineage dispersal velocity when increasing the maximal geographic distance used as the cut-off value to select the lineage dispersal events for the estimation. Solid curves and shaded polygons represent the median and 80% highest posterior density (HPD) interval estimates, respectively. (B-D) Weighted lineage dispersal velocity estimates for different maximal geographic distance cut-off values(50, 100, and 200 km, respectively).

Figure 15 :

 15 Figure15: Environmental variables tested for their impact on the dispersal dynamic of RABV lineages in Cambodia. Elevation is reported in meters, mean annual temperature is reported in Celsius degrees, and annual precipitation is reported in meters per year.

2. 1 .

 1 Study design and study populationAll HCWs, regardless of their vaccination status, were required to use an electronic questionnaire to report daily any COVID-19 related symptom they, or a member of their household, had. SARS-CoV-2 PCR testing was readily available, and HCWs were encouraged to be tested for any mild symptom or suspected exposures. All HCWs were instructed to notify the infection prevention and control unit if one of their household members was SARS-CoV-2 positive. All SARS-CoV-2-detected HCWs as well as those with a positive SARS-CoV-2 household member were immediately contacted as part of the epidemiologic investigation for contact tracing and were provided with instructions regarding isolation precautions. All unvaccinated household members (i.e., those that did not receive the 2 vaccine doses at least 7 days before the detection of the COVID-19 patient) were required to perform 2 PCR tests in the 10 days after the diagnosis of the positive COVID-19 patient. Vaccinated household members were encouraged to perform 2 PCR tests during the 10 days after detection. Household members were not required to test a second time if they had a positive test (Table

Figure 16 :

 16 Figure 16: Flow chart of the households included in our analysis, Ramat Gan, Israel, 2020-2021. HCW, health-care worker; PCR, polymerase chain reaction; SARS-CoV-2, severe acute respiratory syndrome coronavirus 2.

Figure 17 :

 17 Figure17: Estimates of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission parameters within households, Ramat Gan, Israel, 2020-2021. (A) Estimated relative susceptibility of isolated and unvaccinated adults/teenagers, unisolated but vaccinated adults/teenagers, isolated and vaccinated adults/teenagers, unisolated children, and isolated children. The reference group is the group of adults/teenagers that were unisolated and unvaccinated. (B) Estimated relative infectivity of vaccinated cases compared with unvaccinated cases. The posterior median and its associated 95% Bayesian credible interval are reported.

Figure 18 :

 18 Figure18: Person-to-person probability of transmission within households according to the characteristics of the case and of the contact, Ramat Gan, Israel, 2020-2021. Estimated person-to-person probability of transmission within households of size 4, decomposed by the age, isolation behavior, and vaccination status of the contact as well as the vaccination status of the case. The posterior median and its associated 95% Bayesian credible interval are reported.

Chapter 3 .Figure 19 :

 319 Figure19: Impact of model assumptions on the estimation of the relative susceptibility and relative infectivity parameters, Ramat Gan, Israel, 2020-2021. (A) Estimates of the relative susceptibility of household contacts for the baseline and sensitivity analysis scenarios. (B) Estimates of the relative infectivity of vaccinated cases compared with unvaccinated ones for the baseline and sensitivity analysis scenarios. In the baseline scenario (black circle), we assumed that vaccination was effective from 7 days after the second dose, the relative infectivity of asymptomatic cases compared with symptomatic cases was equal to 60%, and the log-standard deviation of the relative infectivity and relative susceptibility prior distributions was equal to 1. Sensitivity analysis scenarios: yellow square, vaccination is effective ≥ 15 days after the dose; orange triangle, 1 polymerase chain reaction (PCR) test for all negative contacts; red star, 2 PCR tests for all negative contacts; pink diamond, 100% infectivity of asymptomatic cases; blue inverted triangle, relative parameter prior with log-standard deviation = 0.7; blue pentagon, relative parameter prior with log-standard deviation = 2. The posterior median and its associated 95% Bayesian credible interval are reported.

Figure 20 :

 20 Figure 20: Rabies virus (RABV) epidemic simulation framework. We simulate realistic epidemics by emulating the scenario of RABV spread in dog populations in Morocco. (A) Metapopulation model of rabies spread in dogs. In each geographical location j, the dog population is divided into three compartments: susceptible, exposed but yet not infectious, and infectious individuals. Individuals are born at rate b and die from natural causes at rate γ. The rate of infection corresponds to the per-capita force of infection λ j,t that aggregates the force of infection from infectors in location j and all the other locations. Individuals become infectious at rate ε. We identify all infected individuals and simulate their infector, incubation period, infectious period and date of death. (B) Connectivity between the seven arbitrary Moroccan regions estimated by the radiation model and estimated dog population size per region. Curvature indicates flux direction. (C) Example for one simulation of the prevalence (first row) and cumulative number (second row) of rabid cases per month and location. (D) Graphical illustration of the potential impact of sampling bias on the reconstruction of the phylogenetic relationships between viral samples over an epidemic, assuming no intra-host evolution.

  analyzed this data set to characterize SARS-CoV-2 spread across 44 location states by incorporating individual travel histories of sampled individuals to help correct for sampling bias and unsampled locations. By using the carefully obtained results of[START_REF] Lemey | Accommodating individual travel history and unsampled diversity in Bayesian phylogeographic inference of SARS-CoV-2[END_REF] as a reference, we can evaluate how the four algorithms are impacted by sampling bias.The data set comprises 282 SARS-CoV-2 genomic sequences sampled in the five continents from December 24th, 2019 to March 4th, 2020. We assumed an HKY nucleotide substitution model with a proportion of invariant sites, an among-site rate heterogeneity modeled by a discretized gamma distribution, and a strict molecular clock. For the CTMC, we assumed an exponential growth model for the viral demographics. MASCOT and BASTA assume a constant size model for the viral demes demographics.

Figure 21 :

 21 Figure 21: Estimation of genetic and phylogenetic parameters under spatially-biased sampling conditions. (A) Comparison of the simulated transmission chain and the estimated maximum clade credibility (MCC) tree topologies. For the estimated and simulated topologies, we computed the total divergence time between every pair of sampled tips. We compared the two using linear regression. (B) Pearson's determination coefficient of the pairwise divergence time between the simulated transmission chain and the MCC tree. (C) Estimation of the evolutionary rate. Each dot corresponds to the median estimate of the evolutionary rate in one simulation (n = 50 per sampling protocol and sample size).

Figure 22 :

 22 Figure 22: Impact and mitigation of spatial bias on the estimation of the total migration counts.(A-E) Impact of the increasing levels of spatial bias on the correlation, the calibration, the mean relative 95% highest posterior density (HPD) width, the mean relative bias, and the WIS between the simulated and the estimated total migration counts. (F-J) Mitigation of the impact of spatial bias on the correlation, the calibration, the mean relative 95% HPD width, the mean relative bias, and the WIS between the simulated and estimated total migration counts by using alternative sampling strategies. In the left and right columns, samples are drawn from biobanks with an underlying bias of 10 and 20, respectively. Overall, the algorithms correctly estimate the total migration counts when the correlation and the calibration are high (close to 1 and 100, respectively) and when the mean relative 95% HPD width, the mean relative bias, and the WIS are close to zero. Finally, the mean relative bias and the mean relative 95% HPD width are not defined when the true value is null. We removed 612 out of 3,600 and 380 out of 3,600 simulated migration events in the small and large samples, respectively, due to null true values.

Figure 23 :

 23 Figure 23: Impact and mitigation of spatial bias on the estimation of the lineage introduction dates.(A-D) Impact of the increasing levels of spatial bias on the correlation, the calibration, the mean relative 95% highest posterior density (HPD) width, and the mean relative bias between the simulated and the estimated introduction dates. Uniform samples are representative of the simulated spatiotemporal dynamics of the virus. Samples 2.5, 5, 10, 20 and 50 samples biased towards Regions 3 and 4. Samples 2.5 and 5 correspond to low levels of bias, samples 10 and 20 to intermediate levels of bias and sample 50 to high levels of bias. E-H: Mitigation of the impact of spatial bias on the correlation, the calibration, the mean relative 95% HPD width, and the mean relative bias between the simulated and estimated introduction dates by using alternative sampling strategies. In the left and right columns, samples are drawn from biobanks with an underlying bias of 10 and 20, respectively.

Figure 24 :

 24 Figure 24: Impact and mitigation of spatial bias on the estimation of the root location. (A) Posterior probability of estimating the true root state for increasing levels of biais. (B-C): Mitigation of the effects of spatial biais using alternative sampling strategies under a surveillance bias of 10 and 20, respectively. Each dot corresponds to the median root state posterior probability in one simulation (n = 50 per sampling protocol and sample size).

Figure 25 :

 25 Figure 25: Maximum clade credibility (MCC) trees and median total migration counts estimated on the rabies data set. (A-C) MCC trees and median number of total migration counts estimated on the rabies data set by CTMC, BASTA, and MASCOT, respectively. Branch width is proportional to the maximal ancestral location probability predicted by the algorithms, and branches are colored by the maximal ancestral location. Posterior support of the Negros Oriental, Catanduanes, Mindanao, and Luzon island lineages are reported. Pie charts displayed at root nodes represent the posterior probability distribution of the root location. Median estimates of the total migration counts are reported as heatmaps. Gray tiles correspond to transitions associated with a migration rate that is not statistically supported, i.e., with a Bayes factor lower than 3.

  : clades A, A.1, B.1, and B.4. Whereas clades A.1, B.1, and B.4 are predicted with high posterior support by all algorithms, clade A is predicted with a satisfying posterior support only by CTMC (Fig.D21). In general, CTMC and MASCOT-WHO predictions are closer to the original predictions than the other algorithms, in terms of tree topology (Fig.D21.A) and of total migration counts (Fig.26). As previously shown, BASTA and MASCOT lead to more uncertain ancestral migration histories with the extreme case of BASTA for which the posterior evolutionary rate and the structured coalescent density are bimodal. We report two maximum clade credibility (MCC) trees for BASTA, corresponding to the two modes of the evolutionary rate and structured coalescent density (Fig.D21.B-C and Fig.D22). The first mode of BASTA infers a tree topology and a migration history that are similar to CTMC and CTMC-TRAVEL. For example, the predicted location of the MRCA of the B.4 lineage is China for CTMC-TRAVEL, CTMC, and the 1st mode of BASTA, whereas it is located in Oceania by MASCOT and the 2nd mode of BASTA (Table

Figure 26 :

 26 Figure 26: Posterior distributions of the total migration counts estimated on the SARS-CoV-2 data. Source locations are displayed by rows and destination locations by columns.For CTMC, BASTA and MASCOT, posterior distributions of the total migration counts with a Bayes factor (BF) < 3 are not depicted but marked as non-significant (NS). We identify bimodal marginal posterior distributions with a (*) and we report for each posterior distribution the median and 95% HPD. We normalize the width of the violin plots so that the cumulative density is equal to one.

Figure 27 :

 27 Figure 27: Impact of contact patterns on the estimation of within household transmission and children infectivity and susceptibility in severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections. (A-C) Posterior median estimates of the transmission rate in heterosexual couples, child relative susceptibility, and child relative infectivity for the correct (heterogeneous mixing) inference model in dark blue (n=100), and the incorrect (homogeneous) inference model in light orange (n=100). The black horizontal line corresponds to the true value used in the simulations. (D-F) Relative bias between the posterior median estimate and the true value for the transmission rate in heterosexual couples, child relative susceptibility, and child relative infectivity. Positive values indicate overestimation and negative values underestimation. Relative bias is expressed in percentage. (G-I) 95% coverage of the transmission rate in heterosexual couples, child relative susceptibility, and child relative infectivity.

Figure 28 :

 28 Figure 28: Impact of contact patterns on the estimation of within household transmission, child infectivity, and child susceptibility in influenza virus infections. (A-C) Posterior median estimates of the transmission rate in heterosexual couples, child relative susceptibility, and child relative infectivity for the correct (heterogeneous mixing) inference model in dark blue (n=100), and the incorrect (homogeneous) inference model in light orange (n=100). The black horizontal line corresponds to the true value used in the simulations. (D-F) Relative bias between the posterior median estimate and the true value for the transmission rate in heterosexual couples, child relative susceptibility, and child relative infectivity. Positive values indicate overestimation and negative values underestimation. Relative bias is expressed in percentage. (G-I) 95% coverage of the transmission rate in heterosexual couples, child relative susceptibility, and child relative infectivity.

  At the time of the study presented in Chapter 3, vaccine effectiveness against infection was already well quantified but evidence about vaccine effectiveness against transmission in breakthrough infections remained limited. Regev-Yochay et al. (2021) showed that individuals with breakthrough infections display lower viral loads compared to infected individuals with no prior vaccination. Shah et al. (2021) quantified the indirect effect of vaccination on the risk of infection in individuals who live with a vaccinated individual. Finally, Harris et al. (2021) estimated a reduction of the odds of SARS-CoV-2 infection in household contacts when the index case is vaccinated. In Chapter 3, I estimate that vaccine is effective against transmission, but a high uncertainty around the point estimate remains. Prunas et al. (2022) estimated

  Abbrevations: ACCTRAN, Accelerated Transformation; BSSVS, Bayesian Stochastic Search Variable Selection; DELTRAN, Delayed Transformation; DTA, Discrete Trait Analysis; GLM, Generalized Linear Model; tMRCA, time to the Most Recent Common Ancestor; WHO World Health Organization.

  Abbreviations: MCMC, Markov Chain Monte Carlo; R, reproduction ratio; Rc, constrained reproduction number.

  study, estimates of RABV velocity were obtained with different methodologies. b 95% HPD intervals are not specified in the original papers c 95% HPD upper value d Median with the 95% HPD interval Abbreviations: SEA-1, South-East Asia 1; SEA-2, South-East Asia 2; SEA-3, South-East Asia 3.

  Abbreviations: CI, Confidence Interval; CL, Confidence Limit; R, reproduction ratio; PEP, Post-Exposure Prophylaxis.

  . 1 1 u e L y a P y a e R -a i d o b m a C 6

  0 . 2 1 g n e o B a r P -a i d o b m a C 1 o d K -y e h C g n u e o d S -y e r P g n u e o h C -m a h C g K -a i d o b m a C 4

  . 2 1 u e L h e h h c a r P h c a s h K -a i d o b m a C 2 lupus-familiaris 1988 Ethiopia NA NA KX148202 Dog-Canis-familiaris 1995 Gabon NA NA KT119785 Canis-lupus-familiaris 1996-03-28 Gabon-Libreville NA NA KT119777 Canis-lupus-familiaris 1989-06-19 Gabon-PortGentil NA NA KR906774 Canis-lupus-familiari s 2011-09-22 Tanzania-Serengeti NA NA KR534230 Canis-lupus-familiar is 2010 Tanzania-Serengeti NA NA DQ900547 Canis-lupus-familia ris 1996-11 Tanzania-Serengeti NA NA DQ900550 Canis-lupus-familia ris 1997-04 Tanzania-Serenget i NA NA DQ900568 Crocuta-crocuta 2004-10 Tanzania-Ngorong oro NA NA AB284510 Canis-lupus-famili aris 1999-10-12 Zambia NA NA MT454633 Proteles-cristata 2015 SouthAfrica NA NA MT454640 Otocyon-megalot is 2016 SouthAfrica NA NA KY553263 Civettictis-civetta 2000 SouthAfrica NA NA A NA NA KT119780 Canis-lupus-fam iliaris 1992-05-02 CentralAfricanR epublic-Bangui NA NA KX148210 Human-Homo-s apiens 1998 Madagascar NA NA JF973781 Bos-taurus 1978 Montenegro NA NA FJ228496 Mongoose 2006 PuertoRico NA NA JQ513537 Mongoose 1997 PuertoRico NA NA JQ513529 Felis-catus 1997 PuertoRico NA NA JQ513535 Mongoose 1997 PuertoRico NA NA FJ228497 Mongoose 2006 PuertoRico NA NA A

  N u r e P 5 0 0 2 s n e i p a s -o m o H 0 0 5 8 2 2 J F A N A N u r e P 4 0 0 2 e a d i n a C 1 0 5 8 2 2 J F A N A N a b u C 1 0 0 2 e s o o g n o M 9 2 5 4 5 8 Y A A N A N a b u C 2 0 0 2 e s o o g n o M 1 3 5 4 5 8 Y A A N A N a b u C 1 0 0 2 e s o o g n o M 4 3 5 4 5 8 Y A A N A N a b u C 0 0 0 2 e s o o g n o M 4 0 5 4 5 8 Y A A N A N a b u C 1 0 0 2 e s o o g n o M 5 1 5 4 5 8 Y A A N A N a b u C 1 0 0 2 e s o o g n o M 5 2 5 4 5 8 Y A A N A N a b u C 0 0 0 2 e s o o g n o M 4

  explored the impact of similar infectivity levels between symptomatic and asymptomatic cases (π asymp = 1.0) on the estimation of the relative susceptibility and relative infectivity parameters.

Figure C2 :

 C2 Figure C2: Prior and posterior distributions of model parameters in the baseline analysis.

Figure D13 :

 D13 Figure D13: Median estimates of the transition-transversion ratio for all sampling conditions and the four algorithms. Median estimate of the transition-transversion ratio κ for the systematic bias (A), surveillance bias 10 (B), and surveillance bias 20 (C) sampling conditions. The true value of the parameter is represented as the horizontal black line.

Figure D16 :

 D16 Figure D16: Impact and mitigation of spatial bias on the estimation of the lineage migration counts. (A-E) Impact of the increasing levels of spatial bias on the correlation, the calibration, the mean relative 95% HPD width, the mean relative bias, and the WIS between the simulated and the estimated lineage migration counts. (F-J) Mitigation of the impact of spatial bias on the correlation, the calibration, the mean relative 95% HPD width, the mean relative bias, and the WIS between the simulated and estimated lineage migration counts by using alternative sampling strategies. The mean relative bias and the mean relative 95% HPD width are not defined when the true value is null. We removed 3,126 out of 13,200 and 1,410 out of 9,588 simulated migration events in the small and large samples, respectively, due to null true values.

Figure D18 : 5 .

 D185 Figure D18: Impact and mitigation of spatial bias on the estimation of the introduction dates.(A-D) Impact of the increasing levels of spatial bias on correlation, calibration, mean relative 95% HPD width, and average relative error between the simulated and estimated introduction dates. (E-H) Mitigation of the impact of spatial bias on correlation, calibration, mean relative 95% HPD width, and average relative error between the simulated and estimated introduction dates by using alternative sampling strategies.

2 Figure E1 :

 2E1 Figure E1: Example of prior and posterior distributions of model parameters for the SARS-CoV-2 infection scenario. Prior and posterior distributions of model parameters for the SARS-CoV-2 infection scenario.The examples depicted here correspond to one simulation inferred by the model that accounts for heterogeneous contact patterns ("correct"), and the model that assumes homogeneous mixing within households ("incorrect"). From left to right, the panels depict the hazard of infection in the community α, the infection rate in an heterosexual couple

Figure E2 :

 E2 Figure E2: Example of prior and posterior distributions of model parameters for the influenza virus infection scenario. Prior and posterior distributions of model parameters for the influenza virus infection scenario.The examples depicted here correspond to one simulation inferred by the model that accounts for heterogeneous contact patterns ("correct"), and the model that assumes homogeneous mixing within households ("incorrect"). From left to right, the panels depict the hazard of infection in the community α, the infection rate in an heterosexual couple β 4/2 κ child,child µ sus,child µ in f ,child , the relative susceptibility of adults µ sus,adult , and the relative infectivity of adults µ in f ,adult .

  La rage se transmet à bas bruit chez le chien mais est maintenue grâce à une forte hétérogénéité spatiale et sa dynamique est souvent impactée par l'homme. La modélisation épidémiologique a montré que la vaccination est la stratégie de contrôle la plus efficace mais il n'y a pas de consensus clair sur la fréquence des campagnes de vaccination. De nombreux défis restent à relever. En effet, le rôle des populations animales sauvages, de la structure sociale de la population de chiens domestiques et de leurs interactions avec l'homme restent peu caractérisés. Des études de terrain sont nécessaires pour recueillir ce type de données et informer les modèles épidémiologiques et phylodynamiques. Par ailleurs, la situation épidémiologique est inconnue dans la majorité des pays endémiques d'Asie et d'Afrique.

1

  Mathematical Modelling of Infectious Diseases Unit, Institut Pasteur, UMR2000, CNRS, Paris, France, 2 Sorbonne Universite ´, Paris, France, 3 Spatial Epidemiology Lab (SpELL), Universite ´Libre de Bruxelles, Bruxelles, Belgium, 4 Department of Microbiology, Immunology and Transplantation, Rega Institute, KU Leuven, Leuven, Belgium, 5 Lyssavirus Epidemiology and Neuropathology Unit, Institut Pasteur, Paris, France, 6 WHO Collaborating Centre for Reference and Research on Rabies, Institut Pasteur, Paris, France ‡ These authors are joint senior contribution on this work. * maylis.layan@pasteur.fr

Fig 1 .

 1 Fig 1. PRISMA-ScR Flow Diagram showing the number of identified and selected records along the multi-stage selection process. Scopus accounted for most of the records as it retrieved 71% (n = 46) of PubMed records and 79% (n = 74) of Web of Science records. https://doi.org/10.1371/journal.pntd.0009449.g001

Fig 2 .

 2 Fig 2. General characteristics of the selected dog rabies studies. (A) Classification of the included publications with the total number of studies, the publication time span, and the number of publications per continent of study. Asia and Africa account for up to 78% of the included studies. (B) Number of publications per year and per methodological category. Mathematical models were the first studies to be published followed by phylodynamic and interdisciplinary studies. (C) Number of publications per country of study. Each publication was attributed to one or multiple countries based on the origin of the RABV genetic sequences, rabid case data or dog ecology data.For phylodynamic studies, countries were not considered if their genetic data were included only in regular phylogenetic tree reconstructions. Similarly, two studies which described rabies dynamics at the global scale[START_REF] Bourhy | The origin and phylogeography of dog rabies virus[END_REF][START_REF] Troupin | Large-Scale Phylogenomic Analysis Reveals the Complex Evolutionary History of Rabies Virus in Multiple Carnivore Hosts[END_REF] were not considered in this figure. In our collected records, China accounts for most Asian studies. Spain appears on the map because Ceuta and Melilla, which are Spanish enclaves in North Africa, are represented in two datasets of RABV genetic sequences[START_REF] Dellicour | Using Viral Gene Sequences to Compare and Explain the Heterogeneous Spatial Dynamics of Virus Epidemics[END_REF][START_REF] Talbi | Phylodynamics and Humanmediated dispersal of a zoonotic virus[END_REF]. (D) Number of studies per topic and methodological category. The World Bank, https://datacatalog.worldbank.org/dataset/world-bank-official-boundaries, CC-BY 4.0.

Fig 3 .

 3 Fig 3. Estimates of the mean evolutionary rate of RABV and the reproduction ratio of canine rabies in the included studies. (A) Bayesian credibility intervals (mean and 95% Highest Posterior Density, HPD) of the mean evolutionary rate of canine RABV per genetic sequence and RABV lineage. a The estimate corresponds to the upper bound of the 95% HPD. b The dot corresponds to the median and the interval to the 95% HPD interval. cThe 95% HPD was not specified in the original publication. (B) Estimates of the reproduction ratio of dog rabies per control strategy or geographical location. The dot corresponds to the mean and the interval to the 95% confidence interval unless stated otherwise. a The interval corresponds to the standard error. b The authors estimated the effective reproduction ratio along time. Here, the value range of the median monthly point estimate is depicted. https://doi.org/10.1371/journal.pntd.0009449.g003

Fig 4 .

 4 Fig 4. Visual summary of the uses of epidemiological data, environmental data and RABV genetic sequences for the study of rabies dynamics and control.Epidemiological data, environmental data, RABV genetic sequences and social sciences data are highlighted in cyan, yellow, pink, and brown, respectively. The section corresponding to models combining epidemiological data and RABV genetic sequences only is colored in grey since no study that meets this criterion has been identified using our search strategy. Models and their contributions to the understanding of rabies spread and control are detailed in the colored tags. Models using multiple types of data are colored with the intersection color of the corresponding data types. In our text corpus, few studies combined epidemiological, ecological, and genetic data in a unified framework. https://doi.org/10.1371/journal.pntd.0009449.g004

Figure 1 .

 1 Figure 1. Flow chart of the households included in our analysis, Ramat Gan, Israel, 2020-2021. HCW, health-care worker; PCR, polymerase chain reaction; SARS-CoV-2, severe acute respiratory syndrome coronavirus 2.

  2.4. Development of dedicated statistical methods to analyze these dataEpidemiological and genetic data represent the tip of the iceberg, hence parameters of interest (e.g., reproduction number, proportion of asymptomatic cases) are rarely directly measurable. Models are needed to describe how the underlying transmission process results in the observed data, and statistical methods are needed to fit models to empirical data and estimate model parameters.

	2.4.1. Bayesian statistics

Bayesian statistics are popular in epidemiology because they provide a flexible inference framework that can adapt to complex situations. Contrary to classical statistics, Bayesian statistics treat model parameters as random variables which explicitly captures parameter uncertainty in estimations. The most probable range of values of model parameters is estimated by updating existing information on value ranges with observed evidence. Simply put, in Bayesian statistics we combine what we know with

  3.1.2. Quantifying transmission risk factors at the population-level3.1.2.1. Dynamics related to the hostHost mobility and contact patterns influence disease spread at the population-level and may drive disease emergence in new host species or in new geographic areas. Phylodynamics can be used to point the shaping role of host mobility. For instance, molecular dating suggests that Zika was first introduced

  Second, I reconstruct possible transmission chains from empirical data at the country level to characterize RABV endemicity in Cambodia (Chapter 2), and at the household level to evaluate COVID-19 vaccine effectiveness (Chapter 3). In Chapter 2, I analyze a novel RABV genome data set that covers the whole country by using phylogeographic approaches to assess the role of intra-country transmission versus external introductions from neighboring countries, compare circulation in Cambodia to other settings, and investigate the landscape features associated with RABV spread. In Chapter 3, I estimate the secondary attack rates of SARS-CoV-2 stratified by age, vaccination, and isolation status in Israeli households. I further apply an epidemiological model to quantify the transmission probability, as well as vaccine effectiveness against transmission and infection.

Table 1 :

 1 Estimated parameters in phylodynamic models. The sampling window and the spatial scale of the studies are highly variable. Thus, it is not possible to directly compare the velocity and diffusion coefficients amongst the different study settings.

			Reference			Bourhy et	al. 2016				Brunker	et al.	2018b	Tian et al.	2018
		Factors impeding	viral spread b		-					Elevation	Rivers	-
		Factors facilitat-	ing viral spread b		-					Dog presence	Forest coverage	(but with a ten-	dency to spread	towards areas	associated with rel-	atively low forest	coverage)
	Diffusion	coefficient	(km 2 .year -1 ,	95% HPD)	-					-	D = 1733 (1082	-2928)
	Velocity a	(km.year -1 ,	95% HPD)	v = 0.9 (0.65 -	1.2)				v = 4.46 (3.22 -	5.88)	Coefficient of	variation M =	3.10	v = 57.5 (39.2 -	85.1)	v weighted = 23.4	(2.4 -32.6)
			,
	Migration rate	(migration.year -1	95% HPD)	-					-
		RABV se-	quence		N	P	M	G	intergenic G-L	Whole-genome	N	G
			Viral lineages			Africa 1	Africa 2				Africa 1b	SEA-1	SEA-2
		Sampling	window		1986-2012					2004-2013	2008-2015
			Location		Bangui,	Central	African	Republic			Serengeti	district,	Tanzania	Yunnan	province,	China

Table 1

 1

	continued from previous page

Table 2 :

 2 Recommended control strategies in mathematical modeling studies. The efficacy of control strategies on dog rabies dynamics has been addressed in only a subset of the currently available mathematical modeling studies. Studies presented in this table compared several control strategies or different dog vaccination coverages on rabies elimination prospects.

Table 3 :

 3 Strengths and weaknesses of phylodynamics and mathematical modeling studies identified in this review for the study of rabies.

		Strengths	Weaknesses
	Phylodynamics		• Small data sets and short genetic sequences
		• Homogeneous methodology which facilitates the	• Studies generally remain descriptive in terms of
		comparison of rabies dynamics in different areas	environmental factors contributing to rabies spread
		• Recent advances in phylogeographic models	• Large room to apply other models (such as models implemented in BEAST 2)
			• The potential impact of reporting biases is barely
			addressed
	Mathematical	• Diversity of models that explore multiple aspects	• Mostly simulation studies, models are rarely fitted
	modeling	of rabies spread	to dog rabies data
			• Mostly deterministic models with strong assump-
		• Assessment of rabies control strategies efficacy	tions (homogeneous mixing of dogs, absence of dog population structure, absence of individual hetero-
			geneity)

Table 4 :

 4 Characteristics of the Index Cases According to Age.

		Adult/teenager index cases a	Child index cases		All index cases
	Characteristic			(N = 191)		(N = 24)		(N = 215)
		No. %	Median	No.	%	Median	No. %	Median	Median
				(IQR)			(IQR)		(IQR)	(IQR)
	Male sex	76 40		14	58		90 42
	Age, years b	36 (14)		6 (4)		32 (16)
	Symptom status
	Symptomatic	172 90		10	42		182 85
	Asymptomatic	19 10		14	58		33 15
	Vaccination
	Vaccinated	15	8		N/A N/A		15	7
	Days from 2 nd dose to detection			44 (13 -59)			N/A		44 (13 -59) 44 (13 -59)
	Abbreviations: IQR, interquartile range; N/A, not applicable.

a Individuals aged >12 years were considered adults/teenagers. b Values are expressed as mean (standard deviation).

Table 5 :

 5 Characteristics of the Household Contacts According to Age.

		Adult/teenager household contacts a	Child household contacts	All household contacts
	Characteristic			(N = 494)		(N = 193)	(N = 687)
		No. %	Median	No.	%	Median	No. %	Median
				(IQR)			(IQR)	(IQR)
	Male sex	242 49		109	56		351 51
	Age, years b	36 (17) c		6 (4)		27 (20)
	Infection and symptom status
	Past infection	16	3		4	2		20	3
	Not infected	304 62		94	49		398 58
	Symptomatic	127 26		41	21		168 24
	Asymptomatic	46	9		53	27		99 14
	Symptomatic (missing onset)	1	0		1	1		2	0
	Vaccination
	Vaccinated	125 25		N/A N/A		125 18
	Days from 2 nd dose to exposure			23 (14 -36)			N/A	23 (14 -36)
	Isolation
	Partial	115 23		32	17		147 21
	Complete	227 46		58	30		285 41
	Missing	5	1		1	1		6	1

Abbreviation: IQR, interquartile range; N/A, not applicable. a Individuals aged >12 years were considered adults/teenagers. b Values are expressed as mean (standard deviation). c Missing age for 5 adult/teenager contacts.

Table 6 :

 6 Observed Secondary Attack Rates According to the Type of Contact.

	Type	No. of infected contacts No. of susceptible contacts		SAR
				% 95% CI
	Contacts a
	Unisolated and unvaccinated adult/teenager	80	105	76	67, 84
	Isolated and unvaccinated adult/teenager	71	245	29	23, 35
	Unisolated but vaccinated adult/teenager	11	40	28	15, 44
	Isolated and vaccinated adult/teenager	9	83	11	5, 20
	Unisolated child	66	101	65	55,75
	Isolated child	29	87	33	24, 44
	Index b
	Vaccinated	8	42	19	9, 34
	Unvaccinated	261	622	42	38, 46

  • Kendall's tau correlation: a rank-correlation measure that is less sensitive to outliers compared to

	Pearson's correlation coefficient
	τ =	(no. concordant true/simulated value pairs)(no. discordant true/simulated value pairs) n
		2

Table 7 :

 7 Summary of the simulation study.

		CTMC	BASTA	MASCOT	MASCOT-GLM
	Model type	Continuous-time	Approximation of the	Approximation of the	Approximation of the
		Markov chain	structured coalescent	structured coalescent	structured coalescent
			with equal deme sizes	with equal deme sizes	with	time-varying
					deme sizes

Table 8 :

 8 Parameter values used in the simulations.

	Parameter	SARS-CoV-2 Influenza virus
	Force of infection in the community α	0.001	0.001
	Transmission rate in heterosexual couples β	0.46	0.99
	Relative susceptibility of children µ s,child	0.5	2
	Relative infectivity of children µ i,child	0.8	1

Table A1 :

 A1 General characteristics of the included studies. Studies 1 to 22 correspond to phylodynamic studies, studies 23 to 52 correspond to mathematical modeling studies, and studies 53 to 59 correspond to interdisciplinary studies.

			Table A1 continued from previous page
		Dynamics after incur-sion	NO	Indonesia		1997 -2010	Domestic animals	Dibia et al. 2015
		Dynamics in an en-
		demic area; Identifica-tion of factors associ-	NO	China		1989 -2012	Domestic animals, hu-mans, wildlife	Yao et al. 2015
		ated with spread
		Global dynamics of dogs and wildlife lineages; Host shifting	NO	World		1950 -2015	Domestic animals, hu-mans, wildlife	Troupin et al. 2016
		Role of lineage incur-sions; Causes of lineage displacement	NO	Yunnan		1963 -2013	Domestic animals, hu-mans, wildlife	Zhang et al. 2017
		Dynamics after incur-sion	NO	Shaanxi province, China		2009 -2012	Humans		Ma et al. 2017
		Dynamics in an en-
		demic area; Identifica-tion of factors associ-	NO	North Africa	2001 -2008	Domestic wildlife	animals,	Dellicour et al. 2017
		ated with velocity
		Identification of factors associated with velocity	NO	Tanzania		2004 -2013	Domestic wildlife	animals,	Brunker et al. 2018b
		Dynamics in an en-demic area	NO	China		1983 -2016	Domestic animals, hu-mans, wildlife	Wang et al. 2019
		Dynamics in an en-
	#	Study context locity and direction demic area; Identifica-tion of factors associ-ated with dispersal ve-	New method-ology YES	Study area Iran	Temporal scale 2008 -2015	Additional species Wildlife	host	Reference Dellicour et al. 2019
	1	Global dynamics	NO	World Memhis Shelby County, &	1969 -2004	Domestic wildlife	animals,	Bourhy et al. 2008
		Dynamics in an en-		USA;	Her-
	2	demic area; Mainte-nance of viral epidemic cycles Critical dog vaccination coverage	YES NO	West Africa mosillo, Mex-ico; Central Java, Indone-	1986 -2007	-		Lemey et al. 2009a
	3 4	Dynamics in an en-demic area Dynamics in an en-demic area	NO NO	West Africa sia; Kuala Lumpur, China Malaysia	1986 -2007 1931 -2009	--		Talbi et al. 2009 2011 Meng et al.
	5	Dynamics in an en-demic area	NO	Ghana		1979 -2009	Domestic animals, hu-mans, wildlife	Hayman et al. 2011
	6	Dynamics in an en-demic area	NO	Brazil		1985 -2006	-		Carnieli et al. 2011
	7	Dynamics in an en-demic area; Contribu-tion of wildlife	NO	China		2003 -2008	Domestic wildlife	animals,	Yu et al. 2012
	8	Incursion in a rabies-free area	NO	KwaZulu Na-tal Province, South Africa	1980 -2011	Humans		Mollentze et al. 2013
	9	Role of lineage incur-sions	NO	China		2003 -2010	Domestic animals, hu-mans, wildlife	Guo et al. 2013
	10	Lineage dynamics in dogs and wildlife	NO	Brazil		2002 -2005	Domestic animals, hu-mans, wildlife	Carnieli et al. 2013
	11	Dynamics in an en-demic area	NO	Philippines		2004 -2010	Domestic wildlife	animals,	Tohma et al. 2014
	12	Role of lineage in-cursions; Inference of clade reservoirs	NO	Middle East	1972 -2014	Wildlife		Horton et al. 2015
		Dynamics in an en-
	13	demic area; Identifica-tion of factors associ-	NO	Tanzania		2003 -2012	-		Brunker et al. 2015
		ated with spread

Table A4 :

 A4 Description of the interdisciplinary studies combining phylodynamics and mathematical modeling or integrating epidemiological and genetic data. The first part of the table describes the genetic data and phylodynamic approach of the interdisciplinary studies, while the second part of the table describes the epidemiological data and the epidemiological model.

	Phylodynamics category	Model scription	de-	Software	Genetic se-quences	Sequence length (pb)	Data source	Parameters in-ferred	Reference
								Markov jumps,
								migration
	Bayesian discrete phylo-geography	Asymmetric DTA + BSSVS	BEAST 1	N, P, inter-genic G-L (n = 250)	3080	Passive	rates, reward-associated associated dis-tances, spread-	Talbi et al. 2010
								landscape fea-
								tures, tMRCA
	Bayesian phy-lodynamics	Exponential growth coales-cent	BEAST 1	intergenic G-L (n = 176)	760	Passive	tMRCA	Mollentze et al. 2014
	Bayesian discrete phylo-geography	Symmetric DTA + BSSVS	BEAST 1	G, P (n = 39)	2463	Passive	Migration rates, tMRCA	Tohma et al. 2016
								Nucleotide
	Bayesian con-tinuous phylo-geography	Relaxed ran-prior) dom walk (lognormal	BEAST 1	N, P, M, G, 88) intergenic G-L (n =	5061	Passive	substitution tions, tMRCA, rate, number of introduc-	Bourhy et al. 2016
								velocity
	Bayesian phy-lodynamics	Birth-Death		BEAST 2	N (n = 29)	1350	Passive	Re	Zinsstag et al. 2017
					N, P, M, G,
	-	-		-	intergenic G-L (n =	5061	Passive	-	Cori et al. 2018
					151)
								tMRCA, veloc-
	Bayesian discrete phylo-geography	DTA a and GLM on the effec-tive population sizes	BEAST 1	N (n = 543) 1350	Passive	ity, diffusion landscape coefficients, velocity-associated	Tian et al. 2018
								features
	Bayesian con-tinuous phylo-geography	Relaxed ran-prior) dom walk (lognormal		G (n = 491) 1575

  Table A4 continued from previous page

Table A6 :

 A6 Detailed list of the estimated parameters in phylodynamic models.

			Reference
		Factors pre-	venting spread
		Factors facili-	tating spread
				,
	Diffusion	coefficient	(km 2 .year -1	95% HPD)
			,
	Velocity a	(km.year -1	95% HPD)
	Migration rate	(migrations.	, 95% year -1	HPD)
				,
	sub-	rate	.year -1
	Nucleotide	stitution	(subs.site -1	95% HPD)
			Sequence
			Viral lineages	Global

Table A7 :

 A7 Detailed list of the estimated parameters in mathematical models.

				Reference					Coleman and	Dye 1996			Coleman and	Dye 1996			Coleman and	Dye 1996
	Dog ecology param-	eters -Carrying ca-	pacity K (dogs.km -2 ,	95% CI) -Birth rate b	, 95% CI) (year -1			-				-			-
	Vaccination	coverage (95%	upper CL or	95% CI)	Critical vac-	cination cov-	erage: 57.1%	(71%)	Critical vac-	cination cov-	erage: 49.5%	(64.5%)	Critical vac-	cination cov-	erage: 44.1%	(62.8%)	Critical vac-	cination cov-	erage: 38.5%	(55.2%)
			Rabies-related pa-	rameters (95% CI)					-				-			-	-
			rates
			Transmission	(95% CI)					-				-			-	-
				Reproduction ratio					R = 2.334 (1.778 -2.89,	S.E.)			R = 1.981 (1.563 -	2.399, 95% S.E.)			R = 1.789 (1.338 -2.24,	95% S.E.)	R = 1.627 (1.325 -	2.091, 95% S.E.)
				Location				Memphis and	Shelby County,	USA		Hermosillo,	Mexico			Central Java,	Indonesia	Kuala Lumpur,	Malaysia
			Study cate-	gory				Mathematical	modeling			Mathematical	modeling			Mathematical	modeling	Mathematical	modeling

Table B5 :

 B5 Maximum likelihood tree of worldwide representatives and Cambodian RABV N genes. Tips are colored by continent, except Cambodian sequences that are colored in dark grey, and by RABV clade that is determined for each tip with the online RABV genotyping tool RABV-GLUE (http://rabv-glue.cvr.gla. ac.uk/#/home). Accession number and epidemiological and phylogenetic information for the 776 rabies virus samples analyzed in Chapter 2.

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	type clade N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian	N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian	N gene Asian N gene Asian N gene Asian N gene Asian N gene N gene Asian N gene Asian N gene Asian Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian Genome Arctic N gene N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian Asian N gene N gene Asian N gene Asian N gene Asian N gene N gene N gene Asian N gene Asian Asian N gene Asian Asian Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian	N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian	N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian	N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian	N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian	N gene Asian N gene Asian N gene Asian N gene Asian	N gene Asian N gene Asian N gene Asian N gene Asian	N gene Asian N gene Asian N gene Asian N gene Asian	N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian	N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian	N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene N gene N gene Asian N gene Asian N gene Asian Asian N gene Asian N gene Asian Asian N gene Asian N gene Asian	N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian	N gene Asian N gene Asian N gene Asian N gene Asian N gene N gene Asian N gene Asian Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian N gene Asian
	1.0 KM366203 0 02/01/2006 KM366222 27/06/2011 KM366239 07/01/1999 KM366258 20/03/2006 KM366276 KM366204 01/09/2004 KM366223 24/02/2010 KM366240 13/12/2001 14/09/2006 KM366293 22/02/2007 KM366294 25/12/2006 KM366313 17/02/2004 KM366331 17/06/2009 KM366332 20/10/1998 KM366350 30/07/2004 KX148226 KM366295 KM366205 17/07/2010 KM366244 22/12/2000 KM366241 27/01/1999 KM366259 25/10/2004 KM366278 24/05/2001 07/08/1999 KM366296 KM366206 04/05/2004 KM366224 02/08/2000 KM366260 05/06/2002 KM366279 KM366242 Continent Clade KM366207 19/09/2007 KM366225 18/10/2011 20/09/2001 KM366243 KM366208 18/05/2004 KM366226 24/03/2001 26/03/2007 KM366261 11/10/2005 KM366262 10/02/2009 22/12/2008 KM366280 12/01/2008 01/10/2007 KM366297 25/06/2004 KM366298 16/03/2002 KM366314 09/05/2009 KM366315 20/04/2006 KM366316 16/04/2005 KM366317 20/01/2003 KM366333 21/12/2009 KM366334 08/06/1999 KM366335 16/08/2000 KM366336 19/04/2010 2002 Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Asia KM366221 KM366202 30/10/2008 08/08/2011 KM366238 23/02/2009 KM366257 08/10/2006 KM366275 06/09/2000 KM366312 14/11/2005 KM366330 19/01/1998 KM366349 16/12/2004 Figure B2: ID date KM366220 04/11/2011 KM366237 11/03/2008 KM366256 18/02/2002 KM366274 08/04/2008 KM366292 01/05/2006 KM366311 18/04/2007 KM366329 28/08/1998 KM366348 23/10/2006 Southeast Asia Southeast Asia Southeast Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia KM366245 KM366209 16/05/2002 KM366227 26/07/2010 24/04/2000 KM366263 23/12/2011 KM366281 17/07/2008 KM366299 26/01/2009 KM366318 28/06/2010 KM366337 05/09/2009 Southeast Asia Southeast Asia KM366246 KM366210 06/08/2000 KM366277 13/12/2002 29/11/2006 KM366264 04/11/2001 KM366282 30/08/2000 KM366300 09/06/2002 KM366319 14/10/2008 KM366338 16/01/2010 Southeast Asia Southeast Asia KM366247 KM366211 03/09/2010 KM366228 04/07/2008 11/04/2002 KM366265 08/02/2000 KM366283 22/06/2009 KM366301 19/08/2009 KM366320 11/05/2007 KM366339 04/02/2004 Southeast Asia Southeast Asia KM366248 27/04/2006 KM366284 26/07/2011 KM366302 28/01/2004 KM366321 25/10/2001 Southeast KM366212 14/06/2008 KM366229 20/05/2011 KM366266 30/12/2010 KM366340 22/04/2004 Asia KM366249 04/07/2005 KM366285 02/07/1998 KM366303 12/11/2007 KM366322 04/08/2011 Southeast Asia Southeast KM366230 KM366213 12/03/1998 02/08/2011 KM366250 16/05/2003 KM366267 21/08/2010 KM366286 14/11/2011 KM366304 07/05/2001 KM366323 28/10/2006 KM366341 27/05/2004 Southeast Asia Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia KM366268 KM366214 16/06/2003 KM366231 21/08/2008 KM366251 15/05/1998 07/09/2005 KM366287 12/09/1998 KM366305 08/05/2002 KM366324 15/09/2003 KM366342 27/07/2004 Southeast Asia Southeast Asia Southeast Asia KM366269 KM366215 10/02/2002 KM366232 02/12/2003 KM366252 18/09/1998 22/01/1999 KM366288 16/02/2009 KM366306 26/10/1998 KM366325 KM366270 KM366216 20/05/2010 KM366233 30/08/2002 KM366253 28/05/2007 10/11/2003 KM366289 08/02/2007 KM366307 15/07/1998 16/01/2001 KM366343 09/06/2004 KM366344 11/04/2004 Southeast Asia Southeast Asia Southeast Asia Southeast Asia KM366271 Continent Asian Cambodia Southeast Asia Asia Middle East Europe North Africa Sub-Saharan Africa North America Caribbean Central America South America Arctic Cosmopolitan Africa-2 Africa-3 Indian-sub Clade KM366217 25/03/2009 KM366218 07/11/2003 KM366219 16/07/2004 KM366234 01/04/1999 KM366235 06/02/2009 KM366236 17/07/2008 KM366254 16/07/2009 KM366255 26/09/2011 25/09/2001 KM366272 29/12/2003 KM366273 31/08/2004 KM366290 26/12/2001 KM366291 22/12/2003 KM366308 28/07/2003 KM366309 25/01/1999 KM366310 29/05/2008 KM366326 29/03/2000 KM366327 06/09/1999 KM366328 29/01/1999 KM366345 11/06/2004 KM366346 24/03/2005 KM366347 22/06/2005 Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Southeast Asia Middle East continent country province district municipality village Cambodia Takeo Baty Lumpong TRAPAING KRALANH 11.318 104.765 Cambodia Battambang Battambang O Cha ANGDONG CHENH 13.104 103.174 Cambodia Siem Reap Puok Doung Keo KOUK PH-NAO 13.473 103.756 Cambodia Prey Veng Pearaing Kampong Popil KHSAM TBONG 11.643 105.159 Cambodia Kg Chh-nang Toek Phus Kraing Ske PRA SHET 12.22 104.464 Cambodia Kandal Ponhieleu Chhvang TA AUK 11.688 104.789 Cambodia Prey Veng Mesang Svay Chrum PO TA-MOM 11.375 105.562 Cambodia Udoor Meanchey Anloung Veng Anloung Veng TUOL KANDAL 14.229 104.104 Cambodia Kampong Speu Bosed Por Muoy Real TA NUON 11.138 104.55 Cambodia Kg Chh-nang Boribou Po Peal KRA CHY 12.407 104.447 Cambodia Kandal Khsach Kandal Prek Ampil PREK DAUN-HEM 11.649 104.962 Cambodia Kampong Chhnang Kampong Tralach Lonvaek ANLONG TNOUT 11.891 104.712 Cambodia Phnom Penh Meanchey Chbar Am-pov Ii NA 11.537 104.939 Cambodia Takeo Prey Kam-bass Prek Pdov SAYVAR 11.162 104.88 Cambodia Kg Speu Kong Pisey Sdok TRAPAING-LEUK 11.216 104.616 Cambodia Koh Kong Botumsakor Angdong Toek ANGDONG TOEK 11.191 103.478 Cambodia Kampong Speu Samroung Tong Vorsar CHAMBOK 11.472 104.566 Cambodia Kg Speu Phnom Sruoch Treng Tray-oeng PHUM 3 11.273 104.213 Table B5 continued from previous page Cambodia Kg Cham Choeung Prey Sdoeung Chey KDOY 12.195 105.107 Cambodia Kratie Chhong Prak Tamann PREAK DACH 12.277 106.027 Cambodia Kg Thom Baray Chrolorng HANTHVEA 12.267 105.126 Cambodia Kg Cham Kang Meas Sour Kong PREK KRUOS 11.982 105.18 Cambodia Takeo Baty Cham Bak TANOP 11.091 104.436 Cambodia Takeo Tram Kak Trapaing Kragnog KDOUCH 11.236 104.794 Cambodia Prey Veng Ba Phnom Cheu Kach CHEU KACH 11.256 105.406 Cambodia Phnom Penh Mean Chey Niroude TA NGOV 11.556 104.851 Cambodia Svay Rieng Svay Chrum Tasok BOENG ANDENG 11.528 104.939 Cambodia Phnom Penh Mean Chey Chbar Em-pao I NA 11.087 105.683 Cambodia Phnom Penh Reussey Keo Chroy Changva 2 11.576 104.936 Cambodia Phnom Penh Dangkor Cham Chao PHUM 4 11.539 104.824 Cambodia Banteay Meanchey Poipet Poipet PALELAY 13.649 102.57 Cambodia Kg Speu Thpong Rong Roeurng THMEY DONG TUNG 11.72 104.524 Cambodia Kampong Cham Prey Chhor Lvea LVEA 11.999 105.019 Cambodia Kandal Shang Treuy Sla PORLEU 11.352 105.021 Cambodia Kandal Ksach Kan-dal Prek Takov PREK LOVEAR 11.603 104.956 Cambodia Takeo Prey Kab-bas Prey Phdao CHHUM ROM 11.142 104.874 Cambodia Kandal Ang Snuol Makak CHONG BOENG 11.644 104.714 Table B5 continued from previous page Cambodia Koh Kong Kapong Sila Kampong Sila KRAING AT 11.103 103.922 Cambodia Kg Cham Srey San-thor Reussey Srok REUSSEY SROK 11.927 105.207 Cambodia Phnom Penh Chamcar Morn Olimpic NA 11.568 104.933 Cambodia Kampong Chhnang Samaki Mean Chey Svay PHSAR TRACH 11.815 104.674 Cambodia Kandal Leuk Dek Prek Talorp KAMPONG CHAM-LONG 11.256 105.278 Cambodia Kampong Thom Kampong Svay Achar Leak ACHAR LEAK 12.725 104.893 Cambodia Takeo Samrorng Rovieng THMEY 11.196 104.788 Cambodia Kampong Speu Kang Pisey Angpopeal SAMRONG REASMEI 11.354 104.72 Cambodia Koh Kong Sre Ambil Sre Ambil SRE AM-BIL 11.122 103.748 Cambodia Kampong Thom Santuk Kampong Thmar KAMPONG THMAR 12.499 105.127 Cambodia Kandal Sa Ang Kraing Yov SAMRONG 11.299 104.957 Cambodia Siem Reap Siem Reap Svay Dan-gkom KRUOS 13.371 103.84 Cambodia Kandal Muk Kam-poul Rokar Ko-rng 1 PEAM 11.85 105 Cambodia Kandal Angnaul Kambol AMPIL 11.543 104.757 Cambodia Phnom Penh Tuol Kork Psar Daum Kor NA 11.553 104.906 Cambodia Prey Veng Baphnom Cheu Chach TREA 11.26 105.424 Cambodia Phnom Penh Mean Chey Boeng Tompun SANSAM-KOSAL 11.531 104.911 Cambodia Kandal Sa Arng Prek Ombil ANLONG TASEK LEU 11.184 105.021 Table B5 continued from previous page Cambodia Kratie Ang Snuol Snuol SNUOL 12.097 106.46 Cambodia Prey Veng Mesang Chhi Puch TRORK 11.309 105.548 Cambodia Kg Cham Srey San-thor Prek Rum-deng SVAY TANUN KOR 11.9 105.257 Cambodia Phnom Penh Chamkar Mon Boeng Kengkang1 WILDAID ORGANI-ZATION 11.553 104.929 Cambodia Kampot Angkor Chey Tani REUSSEI 10.772 104.684 Cambodia Kratie Chhloung Han Chey HAN CHEY 3 12.255 105.941 Cambodia Kandal Kandal Stoeng Spean Thmor MEUN TRA 11.459 104.872 Cambodia Takeo Bati Dong YUTHKA 11.234 104.908 Cambodia Prey Veng Mesang Chi Phoch SAMRONG VEAL 11.36 105.559 Cambodia Phnom Penh Mean Chey Steung Mean Chey NA 11.527 104.892 Cambodia Rattanakiri Ban Long Ta Veng TA VENG 13.738 107.019 Cambodia Phnom Penh Dangkor Chomchao NA 11.527 104.846 Cambodia Phnom Penh Mean Chey Prek Pra OU AN-DAUNG1 11.492 104.952 Cambodia Kampot Banteay Meas Samrong Loeu TRAM SAR SAR 10.728 104.597 Cambodia Kampot Angkor Chey Tany PRAL 10.783 104.665 Cambodia Siem Reap Angloung Veng Trapaing Prey PRAMBEY RUOY 14.226 103.942 Cambodia Kg Chh-nang Samaki Meanchey Svay PORITHI-KRAI 11.833 104.718 Cambodia Kapot Angkor Chey Tany BREAL 10.783 104.665 Table B5 continued from previous page Cambodia Prey Veng Baphnom Beong Preah ANG-KROUNG 11.323 105.453 Cambodia Prey Veng Baphnom Choeung-phnom RONG-DAMREY 11.257 105.386 Cambodia Kapot Chhouk Krang Svay DAMNAK TRAB KHANG-CHOEURNG 10.862 104.478 Cambodia Kampong Speu Samrong Trapaing Kang TRAPAING KHSANG 11.485 104.643 Cambodia Takeo Samrorng Boeng Tranh Tboung BOENG TRANH 11.088 104.749 Cambodia Pursat Sampov Meas Phteas Prey PEAL NHEK 2 12.536 103.921 Cambodia Kandal Khsach Kandal Svaychrom BARACHA-NARAM 11.578 104.959 Cambodia Kampong Cham Kang Meas Kchao VAR RIN 11.903 105.135 Cambodia Kapot Cambodia Kampong Cham Cambodia Kg Speu Cambodia Kampong Cham Cambodia Kg Thom Cambodia Phnom Penh Cambodia Kampong Cham Cambodia Banteay Meanchey Cambodia Kg Thom Cambodia Banteay Meanchey Cambodia Phnom Penh Cambodia Kampong Speu Cambodia Kg Speu Cambodia Kandal Cambodia Banteay Meanchey Cambodia Preah Vi-hear Cambodia Kampong Speu Cambodia Kg Chh-nang Cambodia Svay Rieng Cambodia Svay Rieng Cambodia Kandal Cambodia Prey Veng Cambodia Kampong Speu Cambodia Kandal Cambodia Prey Veng Cambodia Kampong Cham Cambodia Kg Cham Cambodia Kapot Cambodia Kg Thom Cambodia Kg Cham Cambodia Banteay Meanchey Cambodia Takeo Cambodia Kg Chh-nang Cambodia Takeo Cambodia Kg Thom Cambodia Svay Rieng Cambodia Kg Thom Cambodia Takeo Cambodia Kandal Cambodia Kg Speu Cambodia Kampong Thom Cambodia Kampot Cambodia Kampong Cham Cambodia Takeo Cambodia Phnom Penh Cambodia Kandal Cambodia Phnom Penh Cambodia Kg Som Cambodia Kandal Cambodia Kapot Cambodia Kampot Cambodia Kandal Cambodia Kapot Cambodia Kg Speu Cambodia Kandal Cambodia Phnom Penh Cambodia Phnom Penh Cambodia Phnom Penh Cambodia Phnom Penh Cambodia Phnom Penh Cambodia Phnom Penh Cambodia Phnom Penh Cambodia Phnom Penh Cambodia Phnom Penh Cambodia Phnom Penh Cambodia Phnom Penh Cambodia Phnom Penh Afghanistan NA Cambodia Battambang Rukhakiri Prek Chik KAM RENG 13.045 102.507 Dangtung Torteung TOCH 10.712 104.526 Srey San-thor Prek Damboque TAKOY 11.897 105.167 Borseth Svay Rompea TRAM SAR SAR 11.195 104.566 Ta Bong Kahmom Kor KBAL O 11.957 105.719 Baray Sralao TUOL AMPIL 12.325 105.107 Meanchey Chbar Am-pov2 NA 11.533 104.939 Bateay Bateay SVAY POK 11.995 104.954 Thmor Puok Thmor Puok THMOR PUOK 13.939 103.058 Table B5 continued from previous page Baray Svay Phloeung SVAY PHLOE-UNG 12.228 105.157 Pranet Preah Toek Chor TOEK CHOR 13.603 103.401 7Makara Mithpheap NA 11.559 104.899 Cbar Morn Cbar Morn BEK CHAN 11.485 104.491 Boset Po Angkrong PREY TAPHEM 11.138 104.662 Kien Svay Kbal Koh PREK THOM 11.507 105.026 Serey Sophorn Toeuk Thla KAMPONG SVAY 13.592 102.976 Khcham San Khcham San TORK SRALAO 14.214 104.936 Borseth Svayrompear SLAPLENG 11.212 104.585 Rolea Pha Air Rolea Pha Air PREY KHMER 12.165 104.665 Svay Chrum Krorl Kour THLORK 11.137 105.632 Svay Thom Svay Thom KRANG-LEAV 11.002 105.599 Angsnoul Prey Pouch PREY POUCH 11.466 104.718 Sdech Rom Chak CHUNG RUK 11.163 105.367 Kangpisey Roka Kaoh ROKA KAOH 11.43 104.692 Kien Svay Phum Thom RETEING 11.495 105.046 Pmesang Chiphuch KROSAING 11.313 105.513 Kung Meas Rokaar CHROY KRA BAO 11.865 105.128 Siem Reap Sala Kam-roeuk SLOR KRAM 13.341 103.865 Table B5 continued from previous page Dang Tong Angkor Meas SNOR TOCH 10.761 104.399 Baray Andoung Po CHIVIPHEAP 12.292 105.152 Kang Meas Roka A SVAY SRANEAH 1 11.855 105.113 Poi Pet Nimit NIMIT 13.615 102.739 Prey Kab-bas Prey Phdao PREY KHNHEY 11.159 104.873 Kampong Tralach Long Vek PHSAR TRACH 11.846 104.728 Samrounrng Khvav ANGKONH 11.159 104.708 Baray So Young SO YOUNG 12.237 105.126 Chan Trea Prey Angkunh CHREY THOM 11.035 106.012 Siem Reap Sala Kam-roeurn TAVEAN 13.355 103.878 Sarong Samrong KRAING ROAUT 11.128 104.798 Koh Thom Prek Thmey PREK THMEY 11.125 105.06 Thpong Monorum THNAL 11.723 104.544 Santok Kampong Thnor KAMPONG THMOR 12.499 105.127 Kampong Trach Damnak Kantoude DAMNAK KAN-TOUDE 10.577 104.466 Bathay Taingkraing PRASATH 11.868 104.933 Prey Kam-bas Prey Phdov PREY PH-DOV 11.137 104.872 Mean Chey Cbar Am-pao Ii NA 11.537 104.939 Table B5 continued from previous page Saang Troy Slar N1L 11.352 105.021 Roussey Keo NA NA 11.626 104.908 Stoeng Hav Tomnub Rolok PHUM 2 10.738 103.632 Kien Svay Kampong Svay KAMPONG SVAY 11.418 105.055 Angkor Chey Bra Phnom DAMNAK KRASIANG 10.841 104.655 Chhuok Chhuok Angsnoule Samrong Leu PREY PCHITH Angkor Chey Phnom Kong SKOUR TUNG Thpong Veal Pon PREY MICH Ang Snuol Damnak Ampil TRAPAING TRACH Chamkar Mon Tuol Tom-poung 2 1 Daun Penh Sras Chak NA Russeykeo Chroy Changva 2 Reussey Keo Chroy Changva DOEUM KOR Russeykeo Chroy Changva 4 Mean Chey Boeng Tompun THNOAT CHRUM Russey Keo Prek Leap PREK LEAP Chamkar Mon Tuolsvayprey1 5 Mean Chey Nirot RUSSEY SROS Russeykeo Toekthla Russey Keo Chroy Changva NA Dangkor Samrong Krorm NA Table B5 continued from previous page NA 2 TRAPAING THNONG NA KRASAING 10.834 104.443 11.558 104.707 10.753 104.663 11.788 104.609 11.53 104.685 11.564 104.924 11.56 104.923 11.576 104.936 11.587 104.927 11.591 104.94 11.518 104.909 11.636 104.925 11.559 104.926 11.53 104.949 11.547 104.888 11.576 104.936 11.569 104.812 NA NA latitude longitude host Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog Dog 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Table C3 :

 C3 Comparison of the observed and expected distributions of the number of infected individuals for households of size 2 to 5. The mean and the 95% credible interval are reported.

	Household size Distribution	Number of infected individuals per household
			1	2	3	4	5
	2	Observed	22	10
	2	Expected	20.5 (15-26) 11.5 (6-17)
	3	Observed	21	9	12
	3	Expected	19.2 (14-25) 13.4 (8-19) 9.4 (5-14)
	4	Observed	25	9	8	7
	4	Expected	21 (14-27)	15.3 (9-22) 8.8 (4-14) 3.9 (1-7)
	5	Observed	19	9	10	2	6
	5	Expected	12.8 (7-19)	13.2 (8-19) 9.6 (4-15) 6.5 (2-11) 4 (1-8)

Table C5 :

 C5 Estimates of the person-to-person transmission probability from vaccinated adult/teenager cases and unvaccinated cases to the different categories of contacts within a household of size 4. Probabilities are reported in percentage with their 95% credible interval.

	Contact	Vaccinated adult/teenager case Unvaccinated case
	Unisolated and unvaccinated adults/teenagers	22.2 (6.2-51.6)	65.5 (53.1-76.3)
	Isolated and unvaccinated adults/teenagers	2.9 (0.7-9.2)	12.2 (6.3-18.4)
	Isolated and vaccinated adults/teenagers	1.6 (0.3-6.2)	7 (2.5-13.9)
	Unisolated and vaccinated adults/teenagers	4.7 (1-15.4)	19.1 (7.9-33.5)
	Unisolated children	11.3 (2.8-30.2)	39.7 (28.9-50.4)
	Isolated children	3.9 (0.8-12.1)	15.6 (7.5-26)

  Median estimates of the transition-transversion ratio for all sampling conditions and the four algorithms. Median estimate of the transition-transversion ratio κ for the systematic bias (A), surveillance bias 10 (B), and surveillance bias 20 (C) sampling conditions. The true value of the parameter is represented as the horizontal black line.

	A A	2.4
		2.4
		2.2
		2.2
	500 sequences 150 sequences 500 sequences 150 sequences 500 sequences Figure D6: 500 sequences uniform 2.5 5 10 20 50 1.6 1.8 2.0 1.6 1.8 2.0 2.2 2.4 Transition-transversion ratio 150 sequences 500 sequences uni. surv. region region+year 1.6 1.8 2.0 2.2 2.4 1.6 1.8 2.0 2.2 2.4 Transition-transversion ratio B uni. surv. region region+year 1.6 1.8 2.0 2.2 2.4 1.6 1.8 2.0 2.2 2.4 C CTMC BASTA MASCOT MASCOT-GLM uniform 2.5 5 10 20 50 1.6 1.8 2.0 1.6 1.8 2.0 2.2 2.4 Transition-transversion ratio 150 sequences 500 sequences uni. surv. region region+year 1.6 1.8 2.0 2.2 2.4 1.6 1.8 2.0 2.2 2.4 Transition-transversion ratio B uni. surv. region region+year 1.6 1.8 2.0 2.2 2.4 1.6 1.8 2.0 2.2 2.4 C CTMC BASTA MASCOT MASCOT-GLM

Table D2 :

 D2 Values of simulation parameters.

	Notation	Parameter description	Value	Source
	b b b	Dog birth rate per day	1/365	Assumption
	d	Dog death rate per day	1/365	Assumption
	β β β	Rabies transmission rate	3.2	Assumption
	H i H i H i	Human population size per region	7 demes	WorldPop n.d.
			Region 1: 4,917,672
			Region 2: 2,208,003
			Region 3: 11,913,790
			Region 4: 5,773,588
			Region 5: 3,431,383
			Region 6: 5,023,878
			Region 7: 672,319
			3 demes
			Region 1: 10,557,059
			Region 2: 17,687,379
			Region 3: 5,696,197
	r d r d r d	Dog:human ratio	0.1	Assumption
	C s C s C s	Scaling factor	1.00e-08	Assumption
				Radiation model (Si-
	ν i→ j ν i→ j ν i→ j	Contact matrix	-	mini et al., 2012; Gold-
				ing et al., 2015)
	γ γ γ	Infectious period	Discretized gamma distribution from 1 to 15 days Γ(3, 1.1)	Hampson et al. 2009
	ε ε ε	Incubation period	Γ(2, 11.055)	Hampson et al. 2009
	µ µ µ	Mutation rate	2.44e-4 subs.site -1 .yr -1	Troupin et al. 2016
	κ κ κ	Transition/transversion ratio	2	Assumption
	π A π A π A	Base A frequency in the reference genome	0.2852	Marston et al. 2013
	π C π C π C	Base C frequency	0.2198	Marston et al. 2013
	π G π G π G	Base G frequency	0.2313	Marston et al. 2013
	π T π T π T	Base T frequency	0.2638	Marston et al. 2013

  4.2. MéthodesAfin de mieux comprendre la dynamique de transmission de la rage en Asie du Sud-Est, 199 génomes de RABV isolés chez des chiens ont été séquencés et analysés conjointement à tous les gènes N de RABV d'Asie du Sud-Est disponibles sur GenBank. Les dynamiques spatiales entre deux localisations, le Cambodge d'une part et les autres pays d'Asie du Sud-Est d'autre part, sont reconstruites par phylogéographie discrète. Les dynamiques spatiales au sein du Cambodge sont quant à elles décrites par une analyse en phylogéographie continue des génomes et des gènes N isolés au Cambodge. Ces dynamiques sont comparées aux estimations par phylogéographie continue des dynamiques d'autres pays. Enfin, les facteurs du paysage associés à la vélocité des lignées virales ou à la localisation des lignées virales sont identifiés par phylodynamique du paysage. Les lignées circulant au Cambodge appartiennent essentiellement au même clade qui circule majoritairement au Cambodge et plus minoritairement au Vietnam. La transmission au sein du Cambodge n'est donc probablement pas maintenue par des introductions depuis les pays voisins ce qui corrobore l'hypothèse d'endémicité stricte de la rage au Cambodge. Au sein du pays, la région de Phnom Penh est la zone de transmission la plus active. Même les ancêtres directs des échantillons prélevés aux fron-La principale limite de cette étude concerne les biais d'échantillonnage. En effet, l'effort de séquençage déployé au Cambodge n'a pas d'équivalent dans les autres pays d'Asie du Sud-Est et la couverture spatiotemporelle n'est très certainement pas représentative des dynamiques de la rage dans toute l'Asie du Sud-Est y compris le Cambodge. Ces biais conduiraient à la sous-estimation des mouvements entre le Cambodge et les autres pays d'Asie du Sud-Est. Par ailleurs, le Nord-Est du Cambodge n'est quasiment pas échantillonné, une région où les ethnies ont une relation différente au chien et circulent beaucoup au Laos et au Vietnam. Comme ces ethnies ont peu de relation avec le reste du Cambodge, il est probable que les lignées virales qui y circulent aient une dynamique différente ce qui ne change pas nos conclusions sur le reste du Cambodge.Dans le cadre des maladies respiratoires telles que la grippe et la COVID-19, les études de ménages sont idéales pour identifier les facteurs individuels qui influencent le processus de transmission et pour quantifier leur impact. Les modèles mathématiques de transmission intra-ménagère qui sont utilisés pour évaluer le rôle des enfants font l'hypothèse que l'ensemble des membres des ménages, parents et enfants, ont le même niveau de contact. Or, cette hypothèse n'est pas vérifiée par les données empiriques.Le modèle d'inférence qui prend en compte l'hétérogénéité de contacts entre les membres d'un même ménage estime correctement la susceptibilité relative et l'infectivité relative des enfants dans le scenario COVID-19 avec un biais relatif inférieur à 5%. Lorsque les contacts hétérogènes ne sont pas pris en compte, les deux paramètres sont estimés de 20% environ. Nous obtenu les mêmes résultats concernant la susceptibilité relative des enfants dans le scenario grippe. Cette sous-estimation compense le niveau de contact plus faible que les enfants ont avec les autres membres du ménage par rapport au couple mère-père.

	7. Étude n°5: Contacts hétérogènes et transmission intra-
	ménagère
	7.1. Contexte
	Ici, nous explorons dans une étude de simulation comment les contacts hétérogènes dans les ménages
	peuvent conduire à une estimation biaisée de la susceptibilité et l'infectivité des enfants par rapport aux
	4.3. Résultats adultes.
	7.2. Méthodes
	7.4. Limites de l'étude
	Le nombre de scenarii testés dans cette étude est relativement limité car nous n'avons exploré que deux
	scenarios de susceptibilité et d'infectivité relative des enfants. Par ailleurs, nous avons choisi la valeur

tières du Cambodge sont prédits dans la région de Phnom Penh ce qui signifie qu'il y a des événements de transmission à longue distance. Ces événements à longue distance peuvent être plus rapides que les événements de transmission à courte distance car médiés par l'homme ; c'est pourquoi les dynamiques spatiales entre pays doivent être comparées à la même échelle spatiale. La comparaison avec d'autres pays très affectés par la rage montre que la transmission à petite échelle est similaire donc probablement médiée par le mouvement des chiens. Enfin, aucun facteur du paysage n'est associé avec la vélocité des lignées virales ce qui est en faveur de l'hypothèse d'endémicité stricte. 4.4. Limites de l'étude 4.5. Conclusion L'ensemble des techniques de phylogéographie nous a permis de mieux caractériser la transmission de la rage en Asie du Sud-Est et plus spécifiquement au Cambodge. Elle est marquée par peu de migrations avec ses voisins, évoluant quasiment en vase clos. Toutefois, les réimportations ne sont pas improbables Nous avons simulé des épidémies dans une base de données synthétique de 1,000 ménages dont la composition est dérivée d'une étude multicentrique européenne sur la transmission du variant historique du SARS-CoV-2 dans les ménages. Les taux de contact entre les membres des ménages sont tirés d'une étude belge qui montre que le couple mère-père a le plus de contacts, suivi du couple mère-enfant, puis enfant-enfant, et enfant le couple père-enfant. Nous avons testé deux scenarii : un scenario type COVID-19 où les enfants sont deux fois moins susceptibles et 20% moins infectieux que les adultes, et un scenario type grippe où les enfants sont deux fois plus susceptibles que les adultes. La susceptibilité et l'infectivité relatives des enfants par rapport aux adultes sont estimées par inférence Bayésienne et augmentation de données, soit en faisant l'hypothèse d'homogénéité des contacts, soit en précisant les niveaux réels d'hétérogénéité de contacts.

7.3. Résultats des paramètres dans les simulations de manière à obtenir un taux d'attaque secondaire de 37% ce qui correspond à la fourchette haute des taux d'attaque secondaires estimés dans les ménages pour les infections au SARS-CoV-2 et aux virus influenza. Pour ces deux types d'infection, les taux d'attaque secondaires observés varient de quelques pourcents à 45%.

Table 1 . Estimated parameters in phylodynamic models.

 1

	Location	Sampling	Viral	RABV	Migration rate	Velocity a		Diffusion	Factors facilitating viral	Factors impeding	Reference
		window	lineages	sequence	(migrations.	(km.year -1 ,	coefficient	spread b	viral spread b
					year -1 , 95%	95% HPD)	(km 2 .year -1 ,
					HPD)			95% HPD)
	Bangui,	1986-2012 Africa 1	N	-	v = 0.9 (0.65-	-	-	-	Bourhy
	Central		Africa 2	P		1.2)					et al., 2016
	African			M							[74]
	Republic			G
				intergenic
				G-L
	Serengeti	2004-2013 Africa	Whole-	-	v = 4.46		-	Dog presence	Elevation Rivers	Brunker
	district,		1b	genome		(3.22-5.88)				et al., 2018
	Tanzania					Coefficient of				[69]
						variation
						M = 3.10
	Yunnan	2008-2015 SEA-1	N	-	v = 57.5		D = 1733	Forest coverage (but with	-	Tian et al.,
	province,		SEA-2	G		(39.2-85.1)	(1082-2928)	a tendency to spread		2018 [77]
	China		SEA-3			v weighted =	D weighted =	towards areas associated
						23.4 (2.4-	1064 (116-	with relatively low forest
						32.6)		1638)	coverage)
	North and	2002-2005 -	N	-	v overall =		-	-	-	Carnieli
	Northeast					12.88 c					et al., 2013
	regions,					v dogs = 30.5 c				[61]
	Brazil					v cerdocyon thous = 9.0 c
	Algeria	2001-2008 Africa 1 N	-	v great circle	-	Major roads	-	Talbi et al.,
				P		distances = 26				2010 [72]
				intergenic		(18-34)
				G-L		v road distances
						= 33 (23-43)
	Algeria	2001-2008 Africa 1 N	-	v wavefront	15 D = 2874	Grasslands	Elevation	Dellicour
				P		c		(1900-5420)	Urban areas		et al., 2017
				intergenic				D weighted =			[68]
				G-L				1305 (1086-
								1574)
	Morocco	2004-2008 Africa 1 N	-	v great circle	-	Major roads	-	Talbi et al.,
				P		distances = 42				2010 [72]
				intergenic		(26-58)
				G-L		v road distances
						= 51 (34-72)
	Morocco	2004-2008 Africa 1 N	-	v wavefront	22 D = 2874	Grasslands	Elevation	Dellicour
				P		c		(1900-5420)	Urban areas		et al., 2017
				intergenic				D weighted =			[68]
				G-L				1305 (1086-
								1574)
	Iran	2008-2015 -	Whole-	-	v = 55.5		D = 2676	(Tendency to spread	(Tendency to avoid	Dellicour
				genome		(38.9-142.4)	(1935-5066)	towards and preferentially	circulating in	et al., 2019
						v weighted =	D weighted =	circulate within accessible	barren vegetation	[71]
						18.1 (16.3-	1643 (1356-	areas associated with	areas and to avoid
						20.8)		2325)	relatively higher human	spreading towards
									population density)	grasslands)
											(Continued )

Table 1 .

 1 (Continued)

	Location	Sampling	Viral	RABV	Migration rate	Velocity a	Diffusion	Factors facilitating viral	Factors impeding	Reference
		window	lineages	sequence	(migrations.	(km.year -1 ,	coefficient	spread b	viral spread b
					year -1 , 95%	95% HPD)	(km 2 .year -1 ,
					HPD)		95% HPD)
	China	1983-2016 Arctic-	N	5.81e-3 (3.92e-	-	-	-	-	Wang
			like 2		3-7.77e-3)					et al., 2019
			Central							[70]
			Asian 1
			SEA-1
			SEA-2
			SEA-3
			SEA-5

Table 2 . Recommended control strategies in mathematical modelling studies. Epidemiological context Recommended control strategy Specificities of the recommended control strategie Location Reference

 2

	Introduction in previously	Reactive dog vaccination Followed by a 2-year monitoring period		Townsend et al.,
	rabies-free areas				2013 [29]
			Until all targeted dogs are vaccinated	Northern Peninsula Area and	Du ¨rr et al., 2015
				Elcho Island, Australia	[30]
		90% dog vaccination		Northern Australia and New South	Sparkes et al., 2016
		coverage		Wales, Australia	[33]
				Kubin, Saibai and Warraber	Brookes et al., 2019
				divisions, Australia	[44]
		Targeted dog vaccination	Vaccination of free-roaming dogs	Northern Peninsula Area,	Hudson et al., 2019
		campaigns		Australia	[43]
		Integrated approach	Mandatory dog vaccination	Ibaraki and Hokkaido prefectures,	Kadowaki et al.,
			Dog owner awareness	Japan	2018 [36]
			Dog registration,
			Capture of free-roaming dogs
			Quarantine of imported animals
	Endemic areas	90% dog vaccination		Lemuna-bilbilo and bishoftu	Beyene et al., 2019
		coverage		districts, Ethiopia	[39]
		75% dog vaccination	Stray dog management	Guangdong, China	Hou et al., 2012
		coverage			[51]
		70% dog vaccination	Annual vaccination (or biannual vaccination with a	Machakos district, Kenya
		coverage	60% coverage)

Table 3 . Strengths and weaknesses of phylodynamics and mathematical modelling studies identified in this review for the study of rabies.

 3 Integration of the waning of vaccine-induced immunity • Mostly simulation studies, models are rarely fitted to dog rabies data • Mostly deterministic models with strong assumptions (homogeneous mixing of dogs, absence of dog population structure, absence of individual heterogeneity) • No direct comparison of rabies dynamics due to the diversity of models https://doi.org/10.1371/journal.pntd.0009449.t003

		Strengths	Weaknesses
	Phylodynamics	• Homogeneous methodology which facilitates the	• Small datasets and short genetic sequences
		comparison of rabies dynamics in different areas	• Studies generally remain desriptive in terms of environmental factors contributing
		• Recent advances in phylogeographical models	to rabies spread
			• Large room to apply other models (such as models implemented in BEAST 2)
			• The potential impact of reporting biases is barely addressed
	Mathematical	• Diversity of models that explore multiple aspects of
	modelling	rabies spread
		• Assessment of rabies control strategies efficacy
		•

PLOS Neglected Tropical Diseases | https://doi.org/10.1371/journal.pntd.0009449May 27, 2021

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Acknowledgments

Acknowledgments

We would like to thank Dr Nathanae ¨l Hoze ´for his informed advice related to scoping reviews and data visualization.

PLOS NEGLECTED TROPICAL DISEASES

Mathematical modelling and phylodynamics to study dog rabies ACKNOWLEDGMENTS Author affiliations: Mathematical Modelling of Infectious Diseases Unit, Institut Pasteur, Université de Paris Cité, UMR2000, Centre national de la recherche scientifique (CNRS), Paris, France (Maylis Layan, Alessio Andronico, Nathanaël Hozé, Simon Cauchemez); Collège Doctoral, Sorbonne Université, Paris, France (Maylis Layan); Infectious Disease Unit, Sheba Medical Centre, Ramat-Gan, Israel (Mayan Gilboa); Sackler School of Medicine, Tel Aviv University, Tel Aviv, Israel (Mayan Gilboa, Tal Gonen, Miki Goldenfeld, Lilac Meltzer, Gili Regev-Yochay); and Infection Prevention and Control Unit, Sheba Medical Center, Ramat-Gan, Israel (Tal Gonen, Miki Goldenfeld, Lilac Meltzer, Gili Regev-Yochay). M.L. and M.G. contributed equally to the work as first authors. S.C. and G.R.-Y. contributed equally as senior authors. This work was supported by Sheba Medical Center, Ramat-Gan, Israel. S.C. acknowledges financial support from the Investissement d'Avenir program, the Laboratoire d'Excellence Integrative Biology of Emerging Infectious Diseases program (grant ANR-10-LABX-62-IBEID), the National Research Agency (ANR) through the ANR-Flash call for COVID-19 (grant ANR-20-COVI-0018), the EMERGEN project (ANRS0151), Haute Autorité de Santé (HAS), the INCEPTION project (grant PIA/ANR-16-CONV-0005), the European Union's Horizon 2020 research and innovation program (grants RECOVER 101003589 and VEO 874735), AXA, and Groupama.

Data and code are available online at https://github.com/ mlayan/VaccineEffectivenessSheba.

We acknowledge the Infection Prevention and Control Unit team for their devoted work, the extensive epidemiologic investigations and contact tracing from which the data was derived. We thank the Sheba management for their support of this study.

Appendix C Supplementary information on SARS-CoV-2 transmission in Israeli households 2. Rabies epidemiological situation and methodologies implemented to study rabies dispersal and control at the continent level

The situation of North America is not detailed since the study of Coleman and Dye (1996) only estimated the critical vaccination coverage and R from an epidemic in the Tennessee in the 1940s and an epidemic in Mexico in the 1980s.

Africa

Current situation

Endemic

Models

• Large variety with development of multi-host, metapopulation and network models (Laager et al., 2019;[START_REF] Wilson-Aggarwal | High-resolution contact networks of free-ranging domestic dogs Canis familiaris and implications for transmission of infection[END_REF]Zinsstag et al., 2009;Kitala et al., 2002;Beyene et al., 2019;Colombi et al., 2020;Beyer et al., 2011;Fitzpatrick et al., 2012;Townsend et al., 2013a;Hampson et al., 2007;[START_REF] Beyer | The implications of metapopulation dynamics on the design of vaccination campaigns[END_REF]Laager et al., 2018).

• Parsimony, Bayesian discrete and continuous phylogeography (Lemey et al., 2009a;Mollentze et al., 2013;Brunker et al., 2015;Talbi et al., 2009;Hayman et al., 2011;Brunker et al., 2018b;Dellicour et al., 2017).

• Interdisciplinary studies (Mollentze et al., 2014;Cori et al., 2018;Talbi et al., 2010;Bourhy et al., 2016;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF].

Data

Bite incidence in humans, dog, and human rabies incidence, contact tracing, dog mobility data, dog census, RABV genetic sequences from dogs, wildlife, and humans.

Modelling aims

• Better understanding of the spatial and temporal dynamics of rabies spread (Zinsstag et al., 2009;Hampson et al., 2007;Brunker et al., 2015;Talbi et al., 2009;Hayman et al., 2011;Talbi et al., 2010;Bourhy et al., 2016).

• Identification of environmental factors impacting RABV spread and the main patterns of dispersal (Colombi et al., 2020;Mollentze et al., 2013;Brunker et al., 2015;Brunker et al., 2018b;Dellicour et al., 2017;Talbi et al., 2010).

• Role of introductions (Mollentze et al., 2013;Bourhy et al., 2016;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF], spatial heterogeneity (Laager et al., 2019;Colombi et al., 2020;Beyer et al., 2011), dog population structure [START_REF] Wilson-Aggarwal | High-resolution contact networks of free-ranging domestic dogs Canis familiaris and implications for transmission of infection[END_REF]Laager et al., 2018) and wildlife (Beyer et al., 2011;Fitzpatrick et al., 2012) in dog rabies maintenance.

• Feasible and effective control strategies (Zinsstag et al., 2009;Kitala et al., 2002;Beyene et al., 2019;Beyer et al., 2011;Fitzpatrick et al., 2012;Townsend et al., 2013a;[START_REF] Beyer | The implications of metapopulation dynamics on the design of vaccination campaigns[END_REF]Laager et al., 2018;[START_REF] Zinsstag | Vaccination of dogs in an African city interrupts rabies transmission and reduces human exposure[END_REF].

Oceania Current situation

Rabies-free.

Models

• Agent-based models [START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Hudson et al., 2019a;Hudson et al., 2019b;Brookes et al., 2019).

• Compartmental models (Sparkes et al., 2016).

Data

Dog population structure, dog roaming behavior (GPS data, questionnaires/interviews of dog owners), dog contacts, census data.

Modelling aims

Modelling dynamics following an introduction [START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Hudson et al., 2019a;Hudson et al., 2019b;Brookes et al., 2019;Sparkes et al., 2016) and assessment of the most effective control strategies [START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Hudson et al., 2019a;Brookes et al., 2019;Sparkes et al., 2016).

Main findings

Australian studies focused on rabies spread in remote rural and peri-urban locations where rabies is expected to be introduced and where surveillance systems might be weakened by the remoteness.

Rabies dynamics are expected to differ between dog categories, such as explorer dogs, roaming dogs or domestic dogs (Hudson et al., 2019b;Brookes et al., 2019;Sparkes et al., 2016), and consequently between rural and peri-urban areas (Sparkes et al., 2016).

Reactive vaccination after the detection of rabies introduction is the only beneficial strategy [START_REF] Dürr | Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment[END_REF]Hudson et al., 2019a;Brookes et al., 2019;Sparkes et al., 2016). A 90% dog vaccination coverage is recommended to break down rabies spread (Brookes et al., 2019;Sparkes et al., 2016) and targeting at-risk dogs should enhance vaccination campaigns efficacy (Hudson et al., 2019a;Sparkes et al., 2016).

Appendix B Supplementary information on dog rabies spread in Cambodia R scripts and related files needed to run all the landscape phylogeographic analyses, as well as BEAST XML files, are all available at https://github.com/sdellicour/rabv_cambodia.

Final random subsampling -Dmax = 41846453

Figure B1: Selection of the samples that were sequenced in the context of the present study. Selected samples and non-selected samples are displayed in purple and grey, respectively. See the Material and Methods section for the detailed procedure implemented to select the samples to sequence while maximising the spatio-temporal coverage of available sequences included in continuous phylogeographic inference. www.map.ox.ac.uk Table B2: Investigating the impact of several environmental factors on the dispersal location of RABV lineages in Cambodia. We report approximated Bayes factor (BF) supports for the association between environmental values and tree node locations. The results are based on 1,000 posterior trees obtained by spatially-explicit phylogeographic inference. Following [START_REF] Kass | Bayes Factors[END_REF], we consider a BF value >20 as strong support (in bold). B3: Investigating the impact of several environmental factors on the dispersal velocity of RABV lineages in Cambodia, based on the analysis of the full genomes data set. The results are based on 1,000 posterior trees obtained by spatially-explicit phylogeographic inference. R and C indicate if the considered environmental raster was considered as a resistance (R) or conductance (C) factor, and k is the rescaling parameter used to transform the initial raster (see the text for further detail). For regression coefficients and Q values we report both the median estimate and the 95% HPD interval. The Bayes factor (BF) supports are only reported when p(Q > 0) is at least 90%. Following [START_REF] Kass | Bayes Factors[END_REF], we consider a BF value >20 as strong support for a significant correlation between the environmental distances and dispersal durations. Table B4: Investigating the impact of several environmental factors on the dispersal velocity of RABV lineages in Cambodia, based on the analysis of the full N genes data set. The results are based on 1,000 posterior trees obtained by spatially-explicit phylogeographic inference. R and C indicate if the considered environmental raster was considered as a resistance (R) or conductance (C) factor, and k is the rescaling parameter used to transform the initial raster (see the text for further detail). For regression coefficients and Q values we report both the median estimate and the 95% HPD interval. The Bayes factor (BF) supports are only reported when p(Q > 0) is at least 90%, which was not the case in the context of the analyses reported in the present table.

Supplementary information on SARS-CoV-2 transmission in Israeli households

All data and codes used to perform the analyses presented in Chapter 3 are available online at https: //github.com/mlayan/VaccineEffectivenessSheba.

Differential testing instructions between vaccinated and unvaccinated household contacts

Testing instructions were different between household contacts according to their vaccination status and HCW status. Contacts who had received two vaccine doses at least seven days before detecting the COVID-19 patient were considered protected and encouraged to perform at least two PCR tests in the ten days following the detection of the patient. Contacts who did not meet this criterion were required to perform at least two PCR tests in the ten days following patient detection. If contacts tested positive, they were not required to perform a second test. Unvaccinated HCW were isolated at home whereas vaccinated HCW could come to the hospital for work provided a negative PCR test each time they reported to work.

The proportion of adult/teenager contacts who had at least two PCR tests or one positive PCR test was 79% among unvaccinated contacts and 70% among vaccinated contacts (Table C1). The positivity rate with one PCR was higher in unvaccinated contacts (30%) compared to vaccinated contacts (3%) but the proportion of contacts who performed at least two PCR tests was lower among unvaccinated contacts (49%) compared to vaccinated contacts (67%). When we stratify by HCW status, the proportion of contacts who performed at least two PCR tests is higher in HCW compared to non-HCW among vaccinated (89% in HCW versus 33% in non-HCW) and unvaccinated (76% in HCW and 45% in non-HCW) contacts. In general, HCW were more tested than the other household contacts but their share was lower in unvaccinated contacts (12%) compared to vaccinated contacts (61%).

Testing instructions and positivity rates were different between vaccinated contacts, unvaccinated contacts, HCW and non-HCW which makes it difficult to anticipate how vaccine effectiveness would be impacted. In a sensitivity analysis, we restricted our analysis to households where all negative contacts performed at least one or two PCR tests. The description of the households is detailed in Sections 8.1 and 8.2.

Table C1: Number and result of PCR tests performed by adult/teenager household contacts according to their vaccination status and HCW status. In accordance with the contact categories analyzed in our study, we report here household members corresponding to the adult/teenager category, i.e., all individuals above 12 years old. Among the 494 adult/teenager household contacts, 16 were considered not susceptible to infection over follow-up due to past infection over the preceding year, 353 were considered unvaccinated when they received testing instructions since they had not received two vaccine doses ≥7 days before the detection of the COVID-19 patient, and 125 were considered vaccinated when they received the testing instructions. 27) 0 (0) 4 ( 25) 37 ( 12) 0 (0) 37 ( 10) 14 ( 29) 2 ( 3) 16 ( 13)

One negative testno (%) 8 ( 53) 1 ( 100) 9 ( 56) 38 ( 12) 0 (0) 38 ( 11) 17 ( 35) 4 ( 5) 21 ( 17)

One positive testno (%) 0 (0) 0 (0) 0 (0) 96 ( 31) 10 ( 24) 106 ( 30) 2 ( 4) 2 ( 3) 4 ( 3)

3 ( 20) 0 (0) 3 ( 19) 140 ( 45) 32 ( 76) 172 ( 49) 16 ( 33) 68 ( 89) 84 ( 67)

Endpoint phone questionnaire to collect household data

At the end of the follow-up, sociodemographic data, household composition characteristics, SARS-CoV-2 infection-related data, and social distancing behaviors were collected over a phone interview. We present below the questions translated in English that were asked to the participants.

• Age of the participant

• Sex of the participant

• What is your SARS-CoV-2 immunization status?

• How many people do you share your household with?

• How is each of them related to you?

• What is their age, sex, and SARS-CoV-2 immunization status (unvaccinated, recovered from Covid-19, partially vaccinated)?

• Where do you live and how many rooms are there in your house?

• How many bathrooms and toilets?

• When was the first case of SARS-CoV-2 in your household diagnosed and who was it?

• When did their symptoms begin?

• In the week leading to the index case's diagnosis, did any household members share a bedroom or a bathroom with them?

• Did any household members dine with them?

• Did any household members ride in the car with them?

• During the index case's mandated isolation period, did the rest of the household members isolate from them completely?

• Did you still share a bathroom/toilet with them?

• Did you and the rest of your household members undergo PCR and rapid-antigenic testing after your exposure to the index case?

• And if so, how many tests were conducted and on which dates? What were the results?

• Were the rest of the household members symptomatic at any point during the index case's isolation period?

3. Secondary attack rates in households in which a single index case was identified

In the baseline scenario, we calculated the SAR according to the type of contact for all households regardless of the number of identified index cases. In Table C2, we restricted the calculation of the SAR to households where a single index case was identified (n = 206). There was barely an impact on the SAR. Abbreviations: CI, confidence interval; SAR, secondary attack rate.

Model of SARS-CoV-2 transmission dynamics in households 4.1. Overview

We developed a statistical model describing SARS-CoV-2 transmission within households that accounts for tertiary infections (household members infected by a household case who is not the index case), infection events in the community, household size, and varying follow up periods between households.

For an individual i in household k, data consist in a vector (a i , s i , d i , v i , m i , t end ) where a i indicates whether i is an adult/teenager above 12 years old or a child, s i is the infection status of individual i (symptomatic infection, asymptomatic infection or not infected), d i is the symptom onset date for symptomatic cases or the date of the first positive RT-qPCR test for asymptomatic cases, nu i is the vaccination status of i, m i indicates whether i isolated from the index case when applicable, and t end is the end of the follow up period of household k. For each confirmed case, we augmented their observed data with their unobserved date of infection. Infection dates were defined as continuous time to ensure the ordering of infection events within households. Time 0 corresponds to the first infection time in each household. Within household k, I k denotes the list of SARS-CoV-2 cases and S k denotes the list of susceptible individuals.

Susceptible individuals correspond to household contacts that did not report a SARS-CoV-2 infection in the year preceding the follow-up. Model parameters were estimated in a Bayesian Markov Chain Monte Carlo (MCMC) framework (Cauchemez et al., 2004).

Transmission within households

If we consider infector i and infectee j in household k of size n, the instantaneous hazard that i infects j at time t is:

where:

• β (n/4) δ models the dependency between the transmission rate and the household size n. Here, β corresponds to the transmission rate in households of size 4.

• µ sus (a j , m j , ν j ) is the relative susceptibility of recipient j according to their age, vaccination status and isolation status. We define 5 categories of contacts (isolated and unvaccinated adults/teenagers, unisolated and vaccinated adults/teenagers, isolated and vaccinated adults/teenagers, isolated children, unisolated children) that are compared to adults/teenagers who did not isolate and were unvaccinated. For the reference group, µ sus (a j , m j , ν j ) = 1.

• µ in f (ν i ) is the relative infectivity of infector i according to its vaccination status.

is the relative infectivity of infector i whether i is symptomatic or asymptomatic.

In the baseline scenario, we assumed a 40% reduction of the infectivity of asymptomatic cases compared to symptomatic cases (π asymp = 0.6) as estimated by Byambasuren et al. (2020). In the sensitivity anal-For the incubation period and the infectivity profile, we used distributions that were estimated on data from the historical lineages. Over the study period, up to 80% of the infections were caused by the alpha variant in Israel [START_REF] Benenson | BNT162b2 mRNA Covid-19 Vaccine Effectiveness among Health Care Workers[END_REF]). Yet, there is little knowledge on the mechanisms underlying the rapid spread of the alpha variant at the individual level. Modelling and phylodynamic studies support the hypothesis of its higher transmissibility compared to the historical lineages. The results concerning potentially shorter generation time and longer infectious period are less clear [START_REF] Volz | Assessing transmissibility of SARS-CoV-2 lineage B.1.1.7 in England[END_REF][START_REF] Kissler | Viral dynamics of SARS-CoV-2 variants in vaccinated and unvaccinated individuals[END_REF][START_REF] Davies | Estimated transmissibility and impact of SARS-CoV-2 lineage B.1.1.7 in England[END_REF]. Since participants were not screened for the variants, we assumed that the infectivity profile and the incubation period remained unchanged between the alpha variant and the historical lineages.

Inference framework

We used a data augmentation MCMC approach to explore the joint posterior distribution of model parameters and the augmented dates of infection.

Priors

We choose a Uniform(0,1) prior distribution for the hazard of infection within the community α and a Uniform(0,5) prior distribution for the per capita transmission rate within households β . For the dependency between the transmission rate and the household size, the prior distribution for δ was a Uniform(-3,3) distribution.

For the relative susceptibility of the different categories of contacts µ sus and the relative infectivity of vaccinated cases µ in f , a log-normal prior with log-mean=0 and log-sd=1 was used. We investigated the impact of the log-sd on parameter estimation in a sensitivity analysis (Section 8.3).

Algorithm

Parameters were updated using a Metropolis-Hastings algorithm.

Data augmentation was performed at each iteration of the MCMC chain. After the update of the parameters, the infection times of all COVID-19 cases were updated. For symptomatic cases, the incubation period was sampled from the distribution mentioned above and the infection date was obtained as the difference of the symptom onset and the incubation period. For asymptomatic cases, we chose a conservative scenario according to which asymptomatic cases could have been infected up to ten days prior to their first positive RT-qPCR test independent of the Ct value of the test.

Implementation

The data augmentation Markov Chain Monte Carlo sampling algorithm was implemented in C++. Chains were run for 100,000 iterations and one out of 10 iterations were recorded. Marginal posteriors were sampled from MCMC chains after discarding a burn-in of 10,000 steps. Convergence was inspected visually.

Model adequacy

To assess the adequation of the model to the data, we performed a simulation study. We simulated from our household transmission model 2,000 data sets with a structure identical to that of the observed data (household size, age, vaccination and isolation status of the household members, symptom status of the index case, proportion of secondary asymptomatic cases, and follow-up period) with parameters equal to samples from their joint posterior distribution. We compared the observed secondary attack rate (SAR) to the one expected under the model estimates. There was a good agreement between the observed and expected SAR for households of size 2 to 5. We also compared the observed and expected distributions of the number of infected individuals per household size. The observed values fall within the 95% credible interval of the expected values. There is a good agreement between the observed and expected distributions.

Parameter estimates

Table C4: Estimates of the relative susceptibility of household contacts and relative infectivity of cases in the baseline scenario and in the sensitivity analyses. The median and the 95% credible interval are reported. In the ≥15 days after 1st dose scenario, we assumed that vaccination is effective from 15 days after the 1st injection.

In the 1 PCR test for all contacts and 2 PCR tests for all contacts, we restricted the analysis to the households where all household members performed at least one or two PCR tests, respectively, in the 10 days following the detection of the index case. In the 100% infectivity of asymptomatic cases, we assumed that symptomatic and asymptomatic cases have the same level of infectivity. In the relative susceptibility prior with log-sd=0.7 scenario, we used a log-sd=0.7 for the prior of the relative susceptibility parameters. In the relative infectivity prior with log-sd=0.7 scenario, we used a log-sd=0.7 for the prior of the relative infectivity of vaccinated cases compared to unvaccinated cases parameter. In the baseline scenario, we assumed that vaccination was effective from 7 days after the 2nd dose, the relative infectivity of asymptomatic cases compared to symptomatic cases was equal to 60% and the log-sd of the relative infectivity and relative susceptibility prior distributions was equal to 1. The posterior median and its associated 95% Bayesian credible interval are reported. In the baseline scenario, household contacts who did not report symptoms and did not perform at least one PCR test in the ten days following the detection of the index case were considered not infected over their follow-up (n = 125). In a sensitivity analysis, we verified the robustness of our estimates to this hypothesis by removing all the households with at least one contact whose outcome was not confirmed which restricted the analysis to 141 households (Fig. C3). There were 145 index cases, including 4 co-index cases, and 429 household contacts. 410 household contacts were susceptible to SARS-CoV-2 since they did not report any SARS-CoV-2 infection in the preceding year. Among susceptible contacts, 201 (49%) developed a SARS-CoV-2 infection (Table C6). This is slightly higher than the 40% in the baseline scenario. The characteristics of the index cases and household contacts are relatively similar to the baseline scenario, except the proportion of contact that is slightly higher in the sensitivity analysis.

This is directly due to the more precise follow-up of household contacts by PCR testing.

Compared to the baseline scenario, the univariate SAR are higher in all contact categories due to the higher detection of asymptomatic cases (Table C7). The SAR in households with vaccinated index case(s) is equal to 8% in the sensitivity analysis but there are only 24 household contacts. There is low statistical power to precisely estimate the reduction of infectivity in vaccinated index cases compared to unvaccinated index cases which explains why the 95% credible interval is larger in the sensitivity analysis. Table C6: Characteristics of the index cases and household contacts according to their age for households where all contacts had at least one PCR test in the ten days following the detection of the index case. 41) 8 ( 53) 61 ( 42)

Age, years -mean (SD) 37 ( 15) 6 ( 4) 34 ( 17)

Symptom status -no. (%) Symptomatic 117 ( 90) 6 ( 40) 123 ( 85) Asymptomatic 13 ( 10) 9 ( 60 46) 72 ( 58) 213 ( 50)

Age, years -mean (SD) 36 ( 17) 6 ( 4) 27 ( 20) We further excluded households where at least one negative household contact did not perform at least 2 PCR tests in the 10 days following the detection of the index case. Here, the analysis is restricted to 130 households (Fig. C4). There were 134 index cases, including 4 co-index cases, and 388 household contacts, among whom 193 (50%) developed a SARS-CoV-2 infection (Table C8). This is slightly higher than in the 39% in the baseline scenario. The characteristics of the index cases and household contacts are relatively similar to the baseline scenario except for the median time from the 2nd dose to detection.

There are less male child index cases and less symptomatic child index cases compared to the baseline scenario. There are more asymptomatic and symptomatic contact cases compared to the baseline scenario and the vaccination coverage is lower. Compared to the baseline scenario, the univariate SAR are higher in all contact categories (Table C9). The SAR in households with vaccinated index case(s) is equal to 10% in the sensitivity analysis but there are only 21 household contacts. There is low statistical power to precisely estimate the reduction of infectivity in vaccinated index cases compared to unvaccinated index cases which explains why the 95% credible interval is larger in the sensitivity analysis. 42) 7 ( 50) 57 ( 43)

Age, years -mean (SD) 38 ( 15) 6 ( 4) 35 (17) Cluster size -median (IQR) 8.3. Prior distributions of the relative infectivity and relative susceptibility parameters

The log-sd of the relative susceptibility and relative infectivity parameters modifies the value range that is likely to be explored. In the baseline scenario, we used a log-sd=1.0 for both the relative infectivity and relative susceptibility parameters which corresponds to a relatively large 95% interval spanning from 0.14 to 7.1. With log-sd=0.7, the interval considerably shrinks around 1 and with log-sd=2 it spans from 0.02 to 50.4. In a sensitivity analysis, we tested how a different definition of effective vaccination (≥15 days after the 1st dose or ≥7 days after the 2nd dose) affects parameter estimates. There are 3 additional vaccinated index cases and 16 additional vaccinated adult/teenager contacts in the 1 dose scenario (sensitivity analysis) compared to the 2 doses scenario (baseline). The 1 dose scenario slightly increases the share of vaccinated adult/teenager index cases and vaccinated adult/teenager contacts, but it did not impact parameter estimates (see Fig. 19).

Early vaccination

To determine the impact of early vaccinated cases on our estimates, we restricted the analysis to the households where the index case was either unvaccinated or infected ≥7days after the 2nd dose (n = 165), i.e., this analysis did not contain households where the index was vaccinated but infected before the vaccine was considered effective. In this analysis, we excluded 45 households compared to the baseline scenario. The estimations are represented in Fig. C5 and the values are gathered in Table C12.

Compared to the baseline scenario, the relative susceptibility and relative infectivity parameters were not impacted.

Table C11: Vaccination status of the adult/teenager index cases and adult/teenager household contacts according to the definition of effective vaccination. Three individuals were exposed to the index case more than 15 days after they received the 1st vaccine dose but did not remember the exact date. Two index cases and three household contacts were detected or exposed about 15 days after they received the 1st vaccine dose. These individuals were considered as unvaccinated. The remaining 3 household contacts with a missing vaccination date were vaccinated less than 10 days before their exposure and thus do not verify the definition of effective vaccination.

≥15 days after the 1st dose (sensitivity analysis)

≥7 days after the 2nd dose (baseline)

Adult/teenager index cases (N = 191)

Vaccinated -no. (%) 26 ( 14) 15 (8) Days from 1st dose to detection -median (IQR) 31 (21 -67) 44 (13 -59) Missing vaccination date -no. (%) 2 ( 1) 0 (0)

Adult/teenager contacts (N = 494)

Vaccinated -no. (%) 155 ( 31) 125 ( 25)

Days from 1st dose to exposure -median (IQR) 40 (29 -55) 23 (14 -36) Missing vaccination date -no. (%) 6 ( 1) 0 (0) Simulated migration events Estimated migration events (median, 95%-HPD)

Figure D7: Impact of bias on the estimation of the total migration counts by CTMC. Median estimate of the base frequency of A for the systematic bias (A), surveillance bias 10 (B), and surveillance bias 20 (C) sampling conditions. The true value of the parameter is represented as the horizontal black line. (A-E) Impact of the increasing levels of spatial bias on the correlation, the calibration, the mean relative 95% HPD width, the mean relative bias, and the WIS between the simulated and the estimated lineage migration counts. (F-J) Mitigation of the impact of spatial bias on the correlation, the calibration, the mean relative 95% HPD width, the mean relative bias, and the WIS between the simulated and estimated lineage migration counts by using alternative sampling strategies. The mean relative bias and the mean relative 95% HPD width are not defined when the true value is null. We removed 65,399 out of 91,434 and 27,629 out of 41,916 simulated migration events in the small and large samples, respectively, due to true null values. A-E) Impact of the increasing levels of spatial bias on the correlation, the calibration, the mean relative 95% HPD width, the mean relative bias, and the WIS between the simulated and the estimated total migration counts. (F-J) Mitigation of the impact of spatial bias on the correlation, the calibration, the mean relative 95% HPD width, the mean relative bias, and the WIS between the simulated and estimated total migration counts by using alternative sampling strategies. The mean relative bias and the mean relative 95% HPD width are not defined when the true value is null. We removed 612 out of 3,600 and 380 out of 3,600 simulated migration events in the small and large samples, respectively, due to true null values. The posterior support of lineages A, A1, B1, and B4 that were identified by [START_REF] Lemey | Accommodating individual travel history and unsampled diversity in Bayesian phylogeographic inference of SARS-CoV-2[END_REF] are reported at the corresponding nodes when they gather the same sequences as in the original analysis. Lineages A1, B1, and B4 were estimated to be monophyletic with a high posterior support by all algorithms. However, BASTA, MASCOT, MASCOT-WID, and MASCOT-WHO did not infer monophyly for lineage A that is why we did not report its posterior supports on the corresponding MCC trees. Branch width is proportional to the maximal location probability of the parent node.

Lineage migration counts

Impact and mitigation of bias in

RABV spread in the Philippines

Nodes and branches are colored by location with maximal probability. The root location probability distribution is reported in the pie chart.

Table D1: Predicted lineage location on the SARS-CoV-2 data. We report the predicted locations with maximal probability of the four SARS-CoV-2 lineages estimated by all algorithms along with their posterior probability. We did not report the location of lineage A predicted by BASTA, MASCOT, MASCOT-WID, and MASCOT-WHO because these algorithms did not infer a monophyletic lineage. Location of lineage A1 and B1 is estimated in a similar fashion by all algorithms. However, lineage B4 was estimated to be located in Oceania by MASCOT and the 2nd mode of BASTA, whereas it is estimated to be located in China by CTMC-TRAVEL and CTMC. When we add case count data from Our World In Data and the WHO, the estimated lineage location is China but the posterior probability for MASCOT-WID is lower than for CTMC-TRAVEL and CTMC.

Lineage A1

Lineage A Lineage B1 Lineage B4 CTMC-TRAVEL Americas ( 1) China ( 1 Due to the bimodality of the posterior density distribution, we split in two the tree posterior distribution according to the value of the evolutionary rate. The major mode corresponds to posterior samples with an evolutionary rate higher than 11 -4 substitution.site -1 .year -1 and the minor mode to posterior samples with an evolutionary rate lower than 10 -4 substitution.site -1 .year -1 .

Transitiontransversion ratio

Lognormal (1, 1.25) Lognormal (1, 1.25) Lognormal (1, 1.25) Lognormal (1, 1.25) Base frequencies [START_REF] Ferreira | Bayesian analysis of elapsed times in continuous-time Markov chains[END_REF] Lognormal(0, 4) Lognormal(0, 4) Lognormal(0, 4)

Spatial model

Migration rate Exponential( 1) Exponential( 1) Exponential( 1) Exponential( 1)

Migration clock CTMC Rate reference [7] -Set to 1 Exponential( 1)

Deme population size (constant over time) 1/X a Exponential( 1) Exponential( 1) - Abbreviations: NA, Not applicable. Gamma(shape=0.001, scale=1000) Exponential( 1) Exponential( 1)

Analysis of the SARS-CoV-2 data set

Equal deme population sizes -Yes Yes BSSVS Sum of non-zero migration rates Poisson( 5) Poisson( 5) Poisson( 5)

Abbreviations: BSSVS, Bayesian stochastic search variable selection; HKY model, Hasegawa, Kishino, and Yano model.

Analysis of the SARS-CoV-2 data set

Transition/ transversion ratio

Lognormal (1, 1.25) Lognormal (1, 1.25) Lognormal (1, 1.25) Lognormal (1, 1.25)

Shape of the gamma rate of heterogeneity Exponential(0.5) Exponential(0.5) Exponential(0.5) Exponential(0. Dans l'Étude n°1, j'explore les contributions relatives de la modélisation épidémiologique et de la phylodynamique dans la compréhension de la transmission de la rage chez le chien et dans l'évaluation des stratégies de contrôle. Puis, je mets en pratique des approches de phylodynamique, plus précisément de phylogéographie, dans l'Étude n°2 afin de mieux caractériser la signature endémique de la rage chez le chien au Cambodge. Les limites de ces approches face au biais d'échantillonnage sont approfondies dans l'Étude n°3 par une étude de simulation. Dans l'Étude n°4, je mets également en pratique la modélisation épidémiologique mais cette fois-ci dans le contexte du SARS-CoV-2 afin d'estimer l'impact de la vaccination et des mesures de distanciation physique sur la transmission du virus dans les ménages. Enfin, j'étudie dans l'Étude n°5 comment la mauvaise spécification des contacts dans les ménages modifie l'estimation de la susceptibilité et de l'infectivité relative des enfants par rapport aux adultes.

3. Étude n°1: Revue exploratoire des études quantitatives de la transmission de la rage chez le chien

Contexte

La rage est une maladie fatale mais qui peut être prévenue par un vaccin efficace à 100% chez l'homme et chez l'animal. La rage est endémique en Afrique et en Asie dont la circulation est maintenue essentiellement par les chiens domestiques. Malgré de nombreux efforts, la situation épidémiologique des pays d'Afrique et d'Asie ne s'est pas améliorée ce qui est en partie dû à une connaissance partielle des dynamiques de la rage chez le chien. Dans cette étude, nous explorons les contributions des études quantitatives, plus précisément de la modélisation épidémiologique et de la phylodynamique dans la compréhension des dynamiques de la rage et dans l'évaluation des mesures de contrôle tout en soulignant les limites de ces méthodes et en identifiant les questions en suspens.

Méthodes

Nous avons réalisé une revue de la littérature de l'ensemble des études qui ont appliqué un modèle épidémiologique ou un modèle de phylodynamique à la transmission de la rage chez le chien. Nous avons utilisé une méthodologie rigoureuse de revue de la littérature scientifique, empruntée aux revues systématiques mais adaptée à l'étude d'articles hétérogènes dans un but d'exploration et de synthèse d'un domaine scientifique. Nous avons identifié sur les bases de données bibliographiques PubMed, Web of Science et Scopus un total de n=59 études dont n=30 études de modélisation épidémiologique, n=22 études de phylodynamique et n=7 études interdisciplinaires. Nous avons extrait systématiquement les informations suivantes : (i) l'approche de modélisation principale et ses hypothèses sous-jacentes, (ii) la source des données, (iii) les remarques sur les biais potentiels dans les données en lien avec les processus épidémiologiques et évolutifs, (iv) les résultats qualitatifs et quantitatives sur les dynamiques de la rage et (v) si réalisée, les résultats de l'étude de sensibilité.

donc la stratégie d'élimination à long-terme ne doit pas se concentrer uniquement sur l'élimination locale mais investir dans un système de surveillance pour la détection rapide de nouvelles chaînes de transmission. Par ailleurs, la situation épidémiologique générale de la rage au Cambodge n'est que partiellement connue (incidence chez l'homme et l'animal). Il en va de même des facteurs contrôlant la transmission de la rage (rôle de l'homme dans le mouvement des chiens).

Méthodes

Pour mieux comprendre l'impact des biais sur les reconstructions phylogéographiques discrètes, nous avons simulé des épidémies de rage chez le chien au Maroc avec un modèle de métapopulation et nous avons échantillonné de manière plus ou moins biaisé spatialement les séquences génétiques associées aux cas de chiens. Nous avons ensuite comparé les dynamiques estimées par les trois algorithmes de phylogéographie discrète (CTMC, BASTA, MASCOT) aux dynamiques simulées. Plusieurs stratégies d'atténuation de l'impact des biais ont été testées : augmenter le nombre de séquences utilisées, maximiser la couverture spatiale ou spatiotemporelle de l'échantillon, intégrer des données sur le nombre de cas dans MASCOT (MASCOT-GLM). Enfin, tous les algorithmes (CTMC, BASTA, MASCOT, MASCOT-GLM) ont été testés sur un jeu de données empiriques de la rage aux Philippines et un autre sur le SARS-CoV-2 dans les premiers mois de la pandémie.

Résultats

Les

Limites de l'étude

Cette étude se focalise sur des biais d'échantillonnage importants qui peuvent conduire dans les échantillons analysés à l'absence de séquences des régions les moins affectées par la rage. Notre étude cumule donc l'impact des biais dus à la non-représentativité spatiale des échantillons et dus à l'absence de représentants de certaines régions. L'ensemble des analyses a été répliqué dans un contexte où la transmission a lieu entre trois régions et donc où la majorité des échantillons a des représentants des trois régions. Les résultats obtenus sont similaires. Enfin, l'analyse des données empiriques ne nous permet pas de conclure sur l'algorithme qui reconstruit les dynamiques de manière la plus fidèle.

Conclusion

Les biais d'échantillonnage en phylogéographie sont omniprésents et concernent autant les maladies humaines qu'animales. Toutefois, leur impact peut être atténué ou pris en compte à différents niveaux : (Web Appendix 5). Data were augmented with the probable date of infection of confirmed cases. For symptomatic cases, the date of infection was reconstructed from the date of symptom onset, using the probabilistic distribution of the incubation period (24). For asymptomatic cases, we assumed that the date of infection could occur up to 10 days prior to their molecular detection based on a meta-analysis (25).

Since the study was conducted during the vaccine rollout, participants were enrolled at varying stages of their vaccination process. We assumed that vaccines reach their full effect 7 days after receiving a second dose (4,9,10). Cases were therefore considered vaccinated if their symptom onset (or if unknown, the date of their first positive PCR test) occurred ≥7 days after the second dose. Similarly, household contacts were considered vaccinated if their exposure to the index case (starting with symptom onset or, in its absence, from the date of first positive PCR of the index case) occurred ≥7 days after the second dose. In a sensitivity analysis, we investigated how parameter estimates changed under the assumption that vaccination is effective ≥15 days after the first dose. We also assessed how estimates changed when the analysis was restricted to households in which all negative contacts had performed at least 1 or 2 PCR tests in the 10 days following the detection of the index case. In the baseline scenario, we assumed that asymptomatic cases are 40% less infectious than symptomatic cases based on a meta-analysis (26), and we investigated whether assuming the same level of infectivity in asymptomatic and symptomatic cases modified our estimates. Finally, in our baseline analysis, we chose a log-normal with log-mean = 0 and log-standard deviation = 1 prior distribution for the relative infectivity and relative susceptibility parameters and explored smaller and larger values (log-standard deviation = 0.7 or 2) in a sensitivity analysis.

We compared the observed and expected distributions of the number of cases per household size to assess the goodness-of-fit of the model (Web Table 3 in Web Appendix 6). We report the posterior median and the 95% credible interval (CrI) of estimated parameters. We also report the posterior probability that isolated and vaccinated adult/ teenager contacts are less susceptible than vaccinated adult/ teenager contacts that do not isolate. To measure the strength of evidence of a reduced susceptibility in isolated contacts among vaccinated ones, we report the associated Bayes factor. Here, it directly corresponds to the posterior odds of a reduced susceptibility in isolated contacts among vaccinated ones. Additional details are available in Web Appendix 1-6.

Ethics

The study was approved by the Sheba Medical Center institutional review board committee (approval #8130-21).

RESULTS

All 12,518 HCWs employed by the Sheba Medical Center were eligible to join the study. Between December 19 and April 28, 2021, 91% of the Sheba Medical Center personnel received both doses of the BNT162b2 vaccine, and a rapid and significant decrease in newly detected cases was observed among HCWs.

From December 31, 2020, to April 26, 2021, 276 SARS-CoV-2 cases were identified among HCWs of the Sheba Medical Center and their household members (Figure 1). Of these, 212 agreed to participate, gave their consent, and were enrolled in the study with their household members. Two households were excluded due to missing vaccination 1228 Layan et al. 1) and 27 years among household contacts (Table 2). Age was missing for 5 adult/teenager contacts, and isolation behavior was missing for 6 contacts. There was a slight over-representation of females among index cases (58%), and 191 index cases (89%) were adults/teenagers, of whom 15 (8%) were vaccinated. None of the 24 child index cases were vaccinated. Among the 494 adult/teenager household contacts, 125 (25%) were vaccinated. Of these, 83 (17%) also complied with isolation precautions. Among the 369 unvaccinated adult/teenager contacts, 259 (70%) isolated during the study. None of the 193 child household contacts were vaccinated and 47% of them (n = 90) isolated during the study period (Table 2). In the following, we refer to susceptible contacts (i.e., contacts that did not report SARS-CoV-2 infection over the preceding year) as contacts. A total of 269 out of 667 (40%) household contacts developed a SARS-CoV-2 infection. Of those, 170 (63%) developed symptoms (Table 2). The SAR varied with the characteristics of the contacts. Among the 105 adult/ teenager contacts who were unisolated and unvaccinated, 80 (76%) were infected by SARS-CoV-2 (Table 3). This proportion dropped to 28% (11 out of 40) among those who were unisolated and vaccinated, 29% (71 out of 245) among those who were isolated but unvaccinated, and 11% (9 out of 83) among those who were isolated and vaccinated; 65% (66 out of 101) of child contacts who were unisolated got infected by SARS-CoV-2. This proportion declined to 33% (29 out of 87) for isolated child contacts. The proportion of asymptomatic cases varied from 26% (46 out of 174) among adult/teenager contact cases to 56% (53 out of 95) among child contact cases (Table 2).

The SAR also varied with the vaccination status of the index case regardless of the contacts' characteristics. Among the 622 household contacts whose index case was unvaccinated, 261 (42%) developed a SARS-CoV-2 infection (Table 3). This proportion dropped to 19% (8 out of 42) among household contacts whose index case was vaccinated. Finally, the SAR was relatively invariant with household size: 31%, 40%, 32%, and 32% for households of size 2, 3, 4, and 5, respectively (Web Figure 1 in Web Appendix 6).

Our statistical model makes it possible to perform a multivariate analysis of the drivers of SARS-CoV-2 transmission in households. We estimate that, relative to adult/teenager Abbreviations: CI, confidence interval; SAR, secondary attack rate. a Isolation is missing for 1 child contact and for 5 adult contacts. b The last 2 rows correspond to the SAR among the household contacts of vaccinated (n = 14 households) and unvaccinated index cases (n = 195 households). One household was excluded from this analysis because its co-index cases did not have the same vaccination status. contacts who were unisolated and unvaccinated, the relative risk of being infected was 0.21 (95% CrI: 0.08, 0.44) among adult/teenager household contacts who were vaccinated but unisolated (Figure 2A, Web Table 4 in Web Appendix 7). It was 0.12 (95% CrI: 0.06, 0.21) among household contacts who did isolate and were unvaccinated, and 0.07 (95% CrI: 0.03, 0.16) among household contacts who were both isolated and vaccinated. Isolation might reduce the risk of infection among vaccinated contacts (96% posterior prob-ability, Bayes factor = 23) with a relative risk of 0.34 (95% CrI: 0.11,1.14). Relative to adult/teenager contacts who were unisolated and unvaccinated, the relative risk of infection was 0.50 (95% CrI: 0.32, 0.77) for child contacts that did not isolate, and 0.17 (95% CrI: 0.08, 0.31) for those that did. We estimate that the risk of transmission from vaccinated cases was 0.25 (95% CrI: 0.06, 0.77) times that of unvaccinated cases (Figure 2B, Web Table 4 in Web Appendix 7). Overall, we estimate that, in a household of size 4, the person-to-person probability of SARS-CoV-2 transmission is 61% (95% CrI : 48, 72) between an unvaccinated case and an unvaccinated and unisolated adult/teenager. This probability drops to 4% (95% CrI: 1, 16) between 2 vaccinated adults/teenagers who do not follow isolation rules (Figure 3, Web Table 5 in Web Appendix 7). The person-to-person probability of transmission from an unvaccinated case to a child who does not isolate is 37% (95% CrI : 27, 48). This probability drops to 11% (95% CrI: 3, 31) if the case is vaccinated and to 14% (95% CrI: 7, 25) if the child contact is isolated.

In general, our estimates of relative susceptibility and relative infectivity were robust to model assumptions (Figure 4). When the analysis was restricted to households in which all contacts performed at least 1 or 3 PCR tests in the 10 days following the recruitment of the index case, the relative susceptibility of vaccinated adult/teenager contacts who did not isolate was slightly higher compared with the baseline scenario. It increased from 0.21 (95% CrI: 0.08, 0.44) in the baseline scenario to 0.28 (95% CrI: 0.09, 0.66) in the analysis with at least 1 PCR and 0.32 (95% CrI: 0.09, 0.83) with at least 2 PCR tests (Web Table 4 in Web Appendix 7). In the alternative scenarios, the number of individuals included was substantially lower, increasing CrIs (Web Figures 2 and3, Web Tables 6-9 in Web Appendix 8). Similarly, the relative susceptibility of vaccinated adult/teenager contacts who did isolate increased from 0.07 (95% CrI: 0.03, 0.16) in the baseline scenario to 0.12 (95% CrI: 0.04, 0.28) in the analysis with at least 1 PCR, and 0.13 (95% CrI: 0.04, 0.32) in the one with at least 2 PCR tests. Consequently, the posterior probability that isolated and vaccinated adult/teenager contacts were less susceptible than vaccinated adult/teenager contacts that did not isolate dropped from 96% to 88% with 1 PCR and 89% with 2 PCR tests. Still, the statistical support was high with a Bayes factor equal to 7 and 8, respectively. Relative infectivity and relative susceptibility were slightly sensitive to their prior distribution (Web Table 10 in Web Appendix 8). When the log-standard deviation increased, estimates were pulled towards lower values.

DISCUSSION

We evaluated the impact of BNT162b2 vaccination on case infectivity and the mitigating effect of age, isolation from the index case, and BNT162b2 vaccination on susceptibility to infection in household settings. Our approach accounts for infections in the community, potential tertiary infections within the households, the reduced infectivity of asymptomatic cases, potential misidentification of In the baseline scenario (black circle), we assumed that vaccination was effective from 7 days after the second dose, the relative infectivity of asymptomatic cases compared with symptomatic cases was equal to 60%, and the log-standard deviation of the relative infectivity and relative susceptibility prior distributions was equal to 1. Sensitivity analysis scenarios: yellow square, vaccination is effective ≥15 days after the dose; orange triangle, 1 polymerase chain reaction (PCR) test for all negative contacts; red star, 2 PCR tests for all negative contacts; pink diamond, 100% infectivity of asymptomatic cases; blue inverted triangle, relative parameter prior with log-standard deviation = 0.7; blue pentagon, relative parameter prior with log-standard deviation = 2. The posterior median and its associated 95% Bayesian credible interval are reported.

the index case(s), and varying follow-up periods between households.

In our analysis, the SAR in unvaccinated adult/teenager contacts who did not isolate was estimated at around 76%, which is substantially higher than previous estimates obtained in household settings (12-14, 18, 27, 28). In metaanalyses (12)(13)(14), the average SAR ranged between 14% and 32%; however, in some studies, it could be as high as 90% (13). Most of these studies date back to the time when historical lineages were still dominant. In contrast, our study took place when the Alpha variant represented up to 90% of infections in Israel (21). Our higher estimate could be at least partly explained by the fact that the Alpha variant is substantially more transmissible than historical lineages (21,(29)(30)(31).

In agreement with previous reports, we found that children are less susceptible to SARS-CoV-2 infections than adults/teenagers (12)(13)(14)32). We further estimated that, 7 days after their second dose, vaccinated adults/teenagers benefit from a 79% reduction in the risk of infection compared with unvaccinated adults/teenagers. We show, consistent with previous studies (21,33), that BNT162b2 vaccination is highly effective against infection by the Alpha variant. In general population studies, vaccine effectiveness for symptomatic infections ranged from 57% 14 days after the first dose (4) to 89% (4), and 97% 7 days after the second dose (9). For asymptomatic infections, vaccine effectiveness against infection was 79% 10 days after the first dose (5) and 94% 14 days after the second dose (7). Our estimate of vaccine effectiveness in household settings is lower than those obtained in the general population. This is consistent with estimates obtained in households (19,20,33) and might in part be explained by the elevated contact rates in households that may favor transmission. Additionally, studies in the general population are less suitable to detect all asymptomatic cases compared with the household setting. This might lead general population studies to overestimate vaccine effectiveness against asymptomatic infections if vaccinated contacts are less often tested than unvaccinated ones. On another note, we estimate a vaccine effectiveness against transmission of 75% (95% CrI: 23,[START_REF] Brunker | Rapid in-country sequencing of whole virus genomes to inform rabies elimination programmes[END_REF], which is in line with other studies in household settings (18)(19)(20).

To our knowledge, this is the first study estimating the effect of isolation on SARS-CoV-2 transmission in households that are partially vaccinated. We showed that isolation precautions markedly reduce the overall infection risk in both adult/teenager and child contacts even when considering partial physical distancing measures. We estimated a similar reduction of infection in adult/teenager contacts that were vaccinated but did not isolate. There was a signal in Conflict of interest: none declared. Am J Epidemiol. 2022;00(00):1-2