Of course I also would like to express my thanks to my supervisors who offered me the opportunity of this PhD and who guided me throughout this work. Thank you to Aline de Koeijer for her advices and valuable comments especially regarding the tricky task of risk assessment. I am especially thankful for her frankness and her warm welcome in the Netherlands. Merci à Agnès Leblond pour m'avoir toujours accompagnée et encouragée tout au long de ce travail. Merci aussi pour la confiance qu'elle m'a accordée et la liberté de choix qu'elle m'a laissée durant ces 3 années. I also would like to thank all the members of the EMIDA-VICE project for the constructive and valuable interactions throughout this work. They contributed to my reflection as a Ph.D. student, but I am sure that they will also influence my future work. Particular thanks must be recorded to Egil Fischer for his support, advice and availability during these 3 years. Thank you also for our many discussions from statistics to Dutch and French culture. I also want to express my thanks to Gunnar Andersson for his great help with the Bayesian approach and statistics, for his advice and his kindness. Thank you also to René Bødker for his kind welcome in Denmark. Finally, special thanks to Flavie Vial for her help during this work especially during my "discovery" of the syndromic surveillance world.

In addition, I would like to thank all the institutes who provided the data used in this work and all persons involved in data collection networks. Without this essential contribution, the majority of activities outlined in this work would never have been realized. Particular thanks to the Ministère de l'agriculture français and the Direction Générale de l'Alimentation for having provided data on mortality in horses and on trade in living animals (a thank you to Pascal Hendrikx who was a perfect facilitator), to RESPE for the supply of data on nervous and respiratory symptoms in horses, to SAGIR for having provided data on mortality in wild birds, to MARS-Agri4cast at the Institute for Environment and Sustainability, to the European Commission for the supply of temperature data, and to CIRAD with the EID-Med, and the IPPTS with the support of the Directions départementales de la protection des population, who collected and shared entomological data.

List of Figures :

List of Tables :

Table 1: Main players in the French equine industry ..

Vector-borne diseases, a major concern

The incidence of emerging infectious diseases has increased during recent decades due to changing socioeconomic, environmental, and ecological factors [START_REF] Jones | Global Trends in Emerging Infectious Diseases[END_REF]. This is especially true for vector-borne diseases (VBDs), which represent almost 29% of emerging infectious diseases in the last decade [START_REF] Jones | Global Trends in Emerging Infectious Diseases[END_REF]. The introduction and spread into Europe in the 1979 of Aedes albopictus, an efficient vector for at least 22 arboviruses [START_REF] Gratz | Critical Review of the Vector Status of Aedes Albopictus[END_REF]), of bluetongue virus (specifically BTV-8) in 2006 [START_REF] Zientara | Control of bluetongue in Europe[END_REF], and Schmallenberg virus in 2011 [START_REF] Doceul | Epidemiology, molecular virology and diagnostics of Schmallenberg virus, an emerging orthobunyavirus in Europe[END_REF] are good examples of the problem posed by VBDs. The specific emergence of VBDs is probably due in part to climate anomalies that occurred during the 1990s [START_REF] Jones | Global Trends in Emerging Infectious Diseases[END_REF], as has been shown for BTV in Europe [START_REF] Guis | Modelling the Effects of Past and Future Climate on the Risk of Bluetongue Emergence in Europe[END_REF][START_REF] Purse | Climate Change and the Recent Emergence of Bluetongue in Europe[END_REF]. Indeed, as explained by Massad and colleagues [START_REF] Massad | Modeling the Impact of Global Warming on Vector-Borne Infections[END_REF], "increased spread of insect-borne diseases is likely in a warmer world". In the context of global warming, emerging VBDs are thus a growing concern, all the more so because of their huge economic and social impact [START_REF] Marsh | The economic and social impact of emerging infectious diseases: Mitigation through detection, research, and response[END_REF]). To address this challenge, Lindgren and colleagues [START_REF] Lindgren | Monitoring EU emerging infectious disease risk due to climate change[END_REF] argue in favor of developing novel approaches for risk assessment and surveillance in order to enhance preparedness and to facilitate public-health decision making.

Equine industry, risk and specificities

Population at risk

Horses, unlike livestock, typically travel frequently over short and long distances around the world for competition, training, and/or reproduction. These movements increase the risk of the dissemination of infectious diseases [START_REF] Robin | Making Use of Equine Population Demography for Disease Control Purposes: Preliminary Observations on the Difficulties of Counting and Locating Horses in Great Britain[END_REF]. This is a concern not just for the equine industry but also for public health. Indeed, numerous equine viruses are zoonotic (e.g., rabies, brucellosis, anthraw, glanders, leptospirosis, Hendra virus). However, controlling diseases spread by equines is not only important from a sanitary point of view but also with regard to the important economic weight of the equine industry, particularly in Europe [START_REF] Liljenstolpe | Horses in Europe[END_REF]. As an example, in 2010, the European equine industry encompassed 3.7 million horses, generated 100 billion euros a year, and provided the equivalent of 400,000 full-time jobs [START_REF] Leadon | Globalisation of trade and the spread of infectious disease[END_REF]. Furthermore, the sector is growing, with an increase in the number of horse riders of 5% per annum. The introduction of exotic infectious disease may thus have huge economic consequences, as was seen with the 13-week outbreak of African horse sickness in Portugal in 1990, whose total cost was estimated around US $2 million [START_REF] Portas | African horse sickness in Portugal: a successful eradication programme[END_REF].

Population not well tracked

Despite the sanitary and economic impacts of equine diseases, effective health regulations and biosecurity systems to ensure safe equine movements are not always in place at the national and international level [START_REF] Leadon | Globalisation of trade and the spread of infectious disease[END_REF][START_REF] Murray | benefits and challenges posed by the worldwide expansion of equestrian events. New standards for the population of competition horses and equine disease free zones (EDFZ) in countries[END_REF]. This was illustrated by the outbreak of equine influenza in Australia in 2007. Here, the authorities failed to contain the infection in quarantine following the importation of one or more infected horses [START_REF] Webster | Overview of the 2007 Australian Outbreak of Equine Influenza[END_REF]. The horse population is also not well-tracked, which complicates the control and surveillance of diseases. In the EU, the implementation of mandatory passports for horses in 2008 has improved the tracking of horses. However, the database that contains the information on animal movements and deaths is not regularly updated. This has two consequences.

Firstly, the exact number of horses and their geographical location is unknown, which is an obstacle for disease surveillance and control. Secondly, the exact number of horses transported between EU member states or within a country is still not available. Indeed, although the EU's Trade Control and Expert System (TRACES) (Commission Decision 2003) provides information on the number of horses imported to and within the EU, several movements are not recorded in the database due to the absence of mandatory transport notification.

The difficulties of implementing proper health regulations and tracking systems can be explained by the complex reality of the world of horses. The equine industry includes a myriad of activities (e.g., tourism, equestrian sports, breeding and slaughtering of horses) and the various stakeholders engaged in each activity do so with different expectations, ranging from professional to leisure [START_REF] Castejón-Montijano | Economic Impact of the Horse Industry: A Special Reference to Spain[END_REF].

Considering the potential health and financial risks posed by horses, it is especially important to develop novel approaches for the surveillance of exotic infectious diseases, such as VBDs. However, this also constitutes an additional challenge given the structure of the equine industry.

Early warning

A key point in controlling emerging or reemerging VBDs is early warning. Indeed, dealing with a disease outbreak in its early stages is easier and more economical than once it has become widespread (FAO-OIE-WHO Collaboration 2013; FAO-OIE- WHO Collaboration 2006). Early warning systems are timely surveillance systems aimed at predicting the probability that an outbreak is spreading to new areas in order to trigger prompt public health interventions (FAO-OIE-WHO Collaboration 2006). Different strategies such as active and/or passive surveillance are used to ensure the timeliness of detection.

Active surveillance

Active surveillance refers to the active role of health authorities in data collection. The advantage is that active sampling may detect a disease without the observation of clinical signs. However, one of the major drawbacks is that, to detect rare diseases like a newly introduced exotic disease, active sampling has to be very large and redundant, which can be very costly [START_REF] Doherr | Monitoring and Surveillance for Rare Health-Related Events: A Review from the Veterinary Perspective[END_REF]. To mitigate costs, it is possible to implement a specific type of active surveillance, known as risk-based surveillance. Risk-based surveillance is defined by Stärk and colleagues [START_REF] Stärk | Concepts for risk-based surveillance in the field of veterinary medicine and veterinary public health: Review of current approaches[END_REF] as the allocation of surveillance activities based on the probability of events with or without consideration of the consequences of the event, the management of the event, or the process of communication of the event. The term "targeted surveillance" is also used [START_REF] Doherr | Monitoring and Surveillance for Rare Health-Related Events: A Review from the Veterinary Perspective[END_REF][START_REF] De Koeijer | Factors that influence the age distribution of BSE cases: potentials for age targeting in surveillance[END_REF][START_REF] Salman | Animal Disease Surveillance and Survey Systems[END_REF]. The simple idea behind the concept is to collect samples from the segments of the population that have the highest probabilities of being infected, thus increasing the probability of disease detection [START_REF] Salman | Animal Disease Surveillance and Survey Systems[END_REF]. In this way, this process decreases the required sample size without reducing the probability of detecting the disease. Risk-based surveillance is based on the concept of looking for something where it is most likely to be found; this approach thus requires reliable and thorough prior information on at-risk populations in order to ensure the appropriate representativeness of the sampling (FAO 2014;[START_REF] Oidtmann | Risk-based methods for fish and terrestrial animal disease surveillance[END_REF][START_REF] Stärk | Concepts for risk-based surveillance in the field of veterinary medicine and veterinary public health: Review of current approaches[END_REF].

Passive surveillance

In many countries, passive surveillance is one of the most common forms of surveillance for rare and exotic diseases. The term refers to any passive disease reporting systems in which veterinarians, farmers, or any other stakeholders notify authorities when they have sick animals. These surveillance systems are used to identify numerous diseases since they have several significant advantages: they cover a large part of the animal population and the costs associated with data collection and analysis are relatively low [START_REF] Doherr | Monitoring and Surveillance for Rare Health-Related Events: A Review from the Veterinary Perspective[END_REF]FAO 2014;[START_REF] Salman | Animal Disease Surveillance and Survey Systems[END_REF]. However, the performance of passive surveillance systems suffers from frequent under-reporting due to the lack of stakeholder awareness regarding a disease of interest. This may result in a failure to identify the disease [START_REF] Hadorn | Comparative Assessment of Passive Surveillance in Disease-Free and Endemic Situation: Example of Brucella Melitensis Surveillance in Switzerland and in Bosnia and Herzegovina[END_REF]) especially when it manifests in few or unspecific clinical signs [START_REF] Doherr | Monitoring and Surveillance for Rare Health-Related Events: A Review from the Veterinary Perspective[END_REF]). In addition, potential fears of the disease's consequences may also incite stakeholders to not report suspected cases (FAO 2014;[START_REF] Salman | Animal Disease Surveillance and Survey Systems[END_REF]. Under-reporting is especially problematic regarding the surveillance of exotic diseases, as exotic diseases have a low probability of occurrence, their symptoms usually not well known by practitioners, and the consequences of reporting an exotic disease in a new area may be dramatic.

Early warning in horse population

For the early detection of exotic VBDs in horses, both active and passive approaches could theoretically be implemented. However, as previously highlighted, one of the major drawbacks of the active approach is that it can be very costly, especially when a disease is rare like exotic VBDs [START_REF] Doherr | Monitoring and Surveillance for Rare Health-Related Events: A Review from the Veterinary Perspective[END_REF].

Risk-based active sampling could be implemented, but the equine industry suffers from a lack of accurate data regarding the populations at risk (e.g., details of animal movements, population size and location) which might complicate the planning and the implementation of such an active surveillance system. The efficiency of the classical passive surveillance approach in the early detection of an outbreak may also be limited due to the high probability of under-reporting, especially for exotic diseases.

Instead of relying on classical active or passive surveillance to detect new outbreaks, then, new approaches for estimating the probability of outbreak occurrence may constitute a promising way to improve the early detection of VBDs in horses. Different approaches can be considered in estimating this probability: classical risk assessment and syndromic surveillance.

Risk assessments

Risk assessments are the component of risk analysis that estimates the risks associated with a hazard, probability of hazard occurrence and its consequences (OIE 2010). Applied to exotic diseases, they are well-known tools for describing the probability of pathogen entry and spread within an area. The probability of entry is defined as the probability that a pathogen enters in a given area, considering all potential pathways of introduction and without considering the later steps of transmission (OIE 2014). The probability of "spread" is a vaguer concept and can include different sub-definitions, as presented by de Vos and colleagues [START_REF] De Vos | Risk Assessment Framework for Emerging Vector-Borne Livestock Diseases[END_REF]): (1) the probability of transmission, which is defined as the probability that the pathogen is able to spread to susceptible hosts in the area at risk, (2) the probability of establishment, which is the probability that the pathogen is able to spread to susceptible hosts and to susceptible vectors given the conditions of introduction, and (3) the probability of spread, which is the probability that the pathogen is able to spread in time and space, considering both local and long-distance dispersal. Regarding the specific issue of early detection, the probability of spread is irrelevant, as it is related more to the assessment of a disease's impact when early surveillance has already failed to detect and control an outbreak. Conversely, the probabilities of transmission and establishment are especially interesting for early detection as they indicate the time period and the most suitable area for early spread of a pathogen. In particular, the probability of establishment, which takes into account the place and time of entry, is an interesting parameter with which to evaluate the likelihood of an infection actually leading to local spread.

The above approach gives a probability of outbreak occurrence based on risk factors such as the suitability of an environment and climate for disease transmission, or the presence of risky practices (e.g., importation of animals from infected area). It can be used by decision makers for risk mitigation and/or to enhance stake-holders' awareness of rare or emerging diseases through risk maps, as has already been proposed for some endemic VBDs (e.g., surveillance of West Nile virus in California [START_REF] Brown | California Mosquito-borne Virus Surveillance & Response Plan[END_REF] (http://www.westnile.ca.gov/) or tick-borne diseases in Europe [START_REF] Beugnet | FleaTickRisk: a meteorological model developed to monitor and predict the activity and density of three tick species and the cat flea in Europe[END_REF] (http://www.fleatickrisk.com/FR/Pages/Home.aspx)).

Syndromic surveillance

To enhance traditional passive surveillance systems, methods based on the analysis of pre-diagnostic and unspecific routinely collected data were developed at the beginning of the 21 st century. Such approaches, referred to as syndromic surveillance, aim to identify the early, often weak, signal of an outbreak in the absence of an accurate identification of the disease by medical practitioners or laboratories. There is no single and commonly accepted definition for syndromic surveillance but it is commonly accepted that it focuses on data collected prior to clinical diagnosis or laboratory confirmation [START_REF] Katz | Redefining syndromic surveillance[END_REF][START_REF] Shmueli | Statistical Challenges Facing Early Outbreak Detection in Biosurveillance[END_REF]. First developed in human medicine, it is now also widely used in veterinary medicine [START_REF] Dórea | Veterinary syndromic surveillance: Current initiatives and potential for development[END_REF]; indeed, a recent review by Dupuy and colleagues (Dupuy et al. 2013a) identified at least 27 syndromic surveillance systems or initiatives in 12 European countries. However, regarding horses, few syndromic surveillance initiatives are in place and only two have been explicitly identified: one in UK with Equine quarterly surveillance reports (DEFRA/AHS/BEVA 2015) and another another in The Netherlands with the GD monitor system [START_REF] Rockx | Syndromic surveillance in the Netherlands for the early detection of West Nile virus epidemics[END_REF].

Syndromic surveillance provides a risk of outbreak occurrence based on the abnormal evolution of a health-related indicator. Such approaches can be used to rapidly detect a well-known disease or new pathogen without a priori consideration and they thus promise to strengthen surveillance of VBDs in horses. However, because they rely on health-related indicators, syndromic surveillance usually has a low specificity (variations in the indicator might be due to disease or to another event) and it is not able to take into account other epidemiological information available for a disease, such as environmental risk factors.

B. RESEARCH QUESTION

In the present work we explore various sources of information that shed light on the probability of occurrence of a newly introduced epidemic, focusing on exotic VBDs in horses. This is approached from various ends: is there a probability of entry? is there a probability of establishment? and is there a change in clinical signs, or other health-related indicator, that may signal such an epidemic?

The risk assessment for pathogen entry and establishment gives a risk profile of outbreak occurrence based on risk factors. However, an outbreak may also occur (with low probability) in a lower risk area instead of a higher risk area. The value of risk assessment for early detection is therefore more as supporting evidence than as formal evidence of an outbreak.

Similarly, syndromic surveillance gives a risk of outbreak occurrence based on the abnormal evolution of a health indicator. However, an outbreak may also occur without modification of such indicators. Even when significant modification is detected, the signal is often very unspecific and might occasionally be due to random fluctuation or to the effects of another outbreak or similar event. Again, then, the value of syndromic surveillance for early detection is more as supporting evidence than as formal evidence of an outbreak.

Risk assessments and syndromic surveillance can both suggest the possibility of a newly introduced epidemic, but they do not prove the presence of the disease. Using these approaches in concert, however, can increase the amount of evidence available and can be a way to improve confidence in predictions of newly introduced epidemics. In doing so, the interaction between risk assessments and syndromic surveillance must be considered carefully as these techniques are not fully independent. Indeed, for example, increased awareness via risk assessments might change the value of syndromic surveillance, because awareness will lead to increased reporting of data and thus to more numerous false alarms.

All these risk indicators are highly variable over time and space due to the unique nature of VBDs, which have a strong spatiotemporal pattern that is influenced by climatic and environmental factors [START_REF] Altizer | Seasonality and the Dynamics of Infectious Diseases[END_REF][START_REF] Gage | Climate and Vectorborne Diseases[END_REF][START_REF] Reisen | Landscape Epidemiology of Vector-Borne Diseases[END_REF]. Variability can also arise as a result of other non-biological fluctuations related to features of international trade, animal production, and so on. Spatial and temporal analyses must thus be performed in order to provide accurate data on the probability of occurrence of a newly introduced VBD.

To address the challenges of establishing early warning systems for VBDs in horses, the present work explores spatiotemporal risk assessments and syndromic surveillance, alone and in concert. In particular, we describe the limits and advantages of both methods in order to arrive at a new and more valuable approach for early warning systems.

C. CASES STUDIES

As case studies, we focus on three emerging vector-borne diseases found in French horses: African horse sickness, equine encephalosis, and West Nile fever.

French equine industry

Equine population

In France there are between 900,000 and 1,000,000 horses, which are mainly used for sport and leisure.

The horse population, as estimated by IFCE-SIRE, is more concentrated in Basse-Normandie (10% of the population) (IFCE -les Haras nationaux 2011) (see Figure 1). However, the exact number of horses and their geographical locations are unknown.

Figure 1: Estimated geographical distribution of horses population (ICFE-SIRE)

Organization of the equine industry

The equine industry in France is an important sector: it represents 4.3% of the full-time-job-equivalent in the agricultural sector and produces around 12 billion euros of revenue per year, mainly generated by horse-race betting operations [START_REF] Lebrun | Les enjeux et les perspectives de la filière équine en France[END_REF]. Furthermore, France is the world's fourth-largest exporter of horses and its equine industry is growing, with an increase in both the number of breeders and the size of the breeding population since the last decade (IFCE -les Haras nationaux 2011).

Nonetheless, the French equine industry is fragmented, with different organizations in charge of the various sub-industries: racing, sport and leisure, breeding, and butchery.

Horse racing industry

-'France galop': Grants authorization to train and ride horses for gallop racing; updates racing regulations and stud book organization -'Cheval français': Grants authorization to train and ride horses for harness racing; updates racing regulations and stud book organization -'Fédération nationale des courses françaises': Responsible for harmonization of racing regulations -10 regional federations promote purebred horses

Disease surveillance in French horses

The French surveillance system for equine diseases is mainly passive. The diseases for which mandatory reporting to the French ministry is in place are reported in Table 2. In addition to this classical passive reporting system, the French network for the surveillance of equine diseases, or 'RESPE'

(http://www.respe.net/), collects declarations from veterinary practitioners registered as sentinels throughout France. RESPE, which was established in 1999, also issues alerts on equine diseases, such as information on diseases detected in French horses or in neighboring countries. More than 500 sentinel veterinarians are involved and cover 92 out of 96 French regions (see Figure 2). The veterinarians fill out a standardized questionnaire online and send standardized samples for laboratory diagnosis.

Table 2: Mandatory notifiable diseases to the French ministry. Category 1 = diseases of serious concern for public health and/or for the industry and that require preventive and control measures for the general interest, Category 2 = other diseases that also require preventive and control measures for the collective interest.

Category 1

Horse specific: equine infectious anemia, African horse sickness, western and eastern equine encephalitis viruses, Venezuelan equine encephalitis virus Non-horse specific: rabies, botulism, brucellosis, anthrax, Aujeszky's disease, tuberculosis, Japanese encephalitis, West Nile virus, vesicular stomatitis virus

Category 2

Equine viral arteritis, contagious equine metritis, glanders, trichinosis Active testing of horses is performed by private partners prior to sale and by public partners prior to export for three diseases: equine viral arteritis, equine infectious anemia, and contagious equine metritis.

Active surveillance is also performed by private and public partners on breeding stock for certain breeds and on all stallions used for semen collection. No further active surveillance system exists for the surveillance of equine diseases in France.

Figure 2: Geographic distribution of the French sentinel veterinarians involved in RESPE.

Diseases of interest

African horse sickness

Like the Bluetongue and Schmallenberg viruses, African horse sickness (AHS) is a Culicoides-borne disease, and it has recently been highlighted as a potential threat for Europe [START_REF] Zimmerli | African horse sickness and equine encephalosis: must Switzerland get prepared][END_REF])(MacLachlan and Guthrie 2010). The disease is caused by a virus belonging to the Orbivirus genus of the Reoviridae family [START_REF] Mellor | African horse sickness[END_REF]. There are nine different serotypes that confer some degree of crossprotective immunity [START_REF] Mellor | African horse sickness[END_REF]. The virus is considered endemic in sub-Saharan countries, with rare outbreaks in North Africa and western Asia (MacLachlan and Guthrie 2010). The last AHS outbreak in Europe occurred between 1987 and 1990 in the Iberian Peninsula and resulted from the importation of infected zebras (Rodriguez et al. 1992a).

AHS is a non-zoonotic disease that affects all extant Equidae, although morbidity and mortality vary among species: as many as 90% of infected horses die within one week, while infection is largely subclinical in zebras [START_REF] Mellor | African horse sickness[END_REF][START_REF] Wilson | Adaptive strategies of African horse sickness virus to facilitate vector transmission[END_REF]. It is considered to be one of the most devastating diseases that affect equids. Four forms of the disease exist: horse sickness fever (moderate fever and no mortality), cardiac form (subcutaneous edema, particularly of the head, neck, chest, and supraorbital fossae, mortality 50%), mixed form (combination of the cardiac and pulmonary forms, mortality 70%) and pulmonary form (sudden death, severe dyspnea, mortality 95%) [START_REF] Mellor | African horse sickness[END_REF]. The incubation time is from 3 to 15 days [START_REF] Theiler | Notes on a fever in horses simulating horse-sickness[END_REF].

Equine encephalosis

Equine encephalosis (EE) is caused by a virus of the Orbivirus genus of the Reoviridae family, and encompasses seven different serotypes [START_REF] Dhama | Equine encephalosis virus (EEV): A Review[END_REF][START_REF] Viljoen | The Characterization of Equine Encephalosis Virus and the Development of Genomic Probes[END_REF]. Similarly to AHS, EE has been recently highlighted as a potential threat for Europe (MacLachlan and Guthrie 2010; [START_REF] Zimmerli | African horse sickness and equine encephalosis: must Switzerland get prepared][END_REF]. Indeed, AHS and EE viruses are similar in many aspects: both are non-zoonotic Culicoidesborne members of genus Orbivirus that share the same vectors [START_REF] Venter | A Comparison of the Vector Competence of the Biting Midges, Culicoides (Avaritia) Bolitinos and C. (A.) Imicola, for the Bryanston Serotype of Equine Encephalosis Virus[END_REF][START_REF] Venter | African Horse Sickness Epidemiology: Vector Competence of South African Culicoides Species for Virus Serotypes 3, 5 and 8[END_REF] and more or less the same geographical distribution. Like AHS, EE is also considered to be endemic in sub-Saharan countries, with rare outbreaks in North Africa and western Asia [START_REF] Mildenberg | Equine Encephalosis Virus in Israel[END_REF][START_REF] Wescott | Evidence for the Circulation of Equine Encephalosis Virus in Israel since 2001[END_REF]. The last major outbreak was reported in Israel in 2009 [START_REF] Mildenberg | Equine Encephalosis Virus in Israel[END_REF]). EE has never been observed in Europe [START_REF] Dhama | Equine encephalosis virus (EEV): A Review[END_REF].

The epidemiology of EE is similar to AHS but the pathogenicities of the two viruses are different. The incubation time of EE is shorter (2-6 days [START_REF] Theiler | Notes on a fever in horses simulating horse-sickness[END_REF])) and its transmission rate is higher [START_REF] Lord | Transmission patterns of African horse sickness and equine encephalosis viruses in South African donkeys[END_REF]. Moreover, despite the fact that EE was initially described as a "fever in horses simulating horsesickness" [START_REF] Theiler | Notes on a fever in horses simulating horse-sickness[END_REF], the symptoms of the two diseases are different. In particular, the mortality rate of EE is always low. In contrast to AHS, which causes severe cardiac and pulmonary symptoms, EE is characterized by a wide range of symptoms, such as abortions during the first 5-6 months of gestation, respiratory signs (e.g., nasal discharge, cough), and encephalitis [START_REF] Dhama | Equine encephalosis virus (EEV): A Review[END_REF].

West Nile virus

West Nile virus (WNV) is a mosquito-borne arbovirus belonging to the genus Flavivirus (family Flaviviridae)

and mainly transmitted by mosquitoes from the genus Culex (family Culicidae). Two distinct lineages exist: lineage 1 causes outbreaks throughout the world, while lineage 2 was limited to Africa until 2008, when it was introduced to Europe. Since the discovery of WNV in 1937 in Uganda [START_REF] Smithburn | A Neurotropic Virus Isolated from the Blood of a Native of Uganda[END_REF], the geographic distribution of the virus has expanded and the disease is now considered endemic in Africa, Asia, Europe, Australia, the Caribbean, and the Americas [START_REF] Campbell | West Nile Virus[END_REF][START_REF] Ozdenerol | Exploring the Spatio-Temporal Dynamics of Reservoir Hosts, Vectors, and Human Hosts of West Nile Virus: A Review of the Recent Literature[END_REF]. In Europe, WNV emerged in the 1960s and several outbreaks have subsequently been documented in many

European countries [START_REF] Calistri | Epidemiology of West Nile in Europe and in the Mediterranean Basin[END_REF]. Even if the virus is now endemic in large parts of Europe, the number of reported outbreaks is presently increasing in Southern and Eastern Europe (e.g., Italy, Greece, Bulgaria, Croatia, Serbia, Albania)(Di [START_REF] Sabatino | Epidemiology of West Nile Disease in Europe and in the Mediterranean Basin from 2009 to 2013[END_REF]. This increase in the number of outbreaks, combined with the recent introduction and spread of lineage 2 in Europe (which has been associated with severe cases in humans, horses, and birds [START_REF] Bakonyi | Lineage 1 and 2 Strains of Encephalitic West Nile Virus, Central Europe[END_REF][START_REF] Calzolari | New Incursions of West Nile Virus Lineage 2 in Italy in 2013: The Value of the Entomological Surveillance as Early Warning System[END_REF][START_REF] Hernández-Triana | Emergence of West Nile Virus Lineage 2 in Europe: A Review on the Introduction and Spread of a Mosquito-Borne Disease[END_REF])), contribute to the growing concern about WNV in Europe.

The enzootic cycle of WNV is driven by its continuous transmission to susceptible bird species through adult mosquitoes. Its main hosts are birds, but the virus also affects more than 30 non-avian species. The susceptibilities of birds to WNV infection differ, with those in the order Passeriformes being most susceptible, followed by birds in the order Charadriiformes and domestic geese (order Anseriformes).

Psittacine and gallinaceous birds are less susceptible. WNV in birds is usually asymptomatic, but may cause nonspecific clinical signs, neurological signs, and death [START_REF] Pérez-Ramírez | Experimental Infections of Wild Birds with West Nile Virus[END_REF][START_REF] Steele | Pathology of Fatal West Nile Virus Infections in Native and Exotic Birds during the 1999 Outbreak in New York City, New York[END_REF]. Of non-avian species, the most affected are humans and horses [START_REF] Kramer | West Nile Virus Infection in Birds and Mammals[END_REF][START_REF] Van Der Meulen | West Nile virus in the vertebrate world[END_REF]. In horses the clinical signs of WNV are almost exclusively neurological and reflect its pathology in the central nervous system [START_REF] Cantile | Clinical and Neuropathological Features of West Nile Virus Equine Encephalomyelitis in Italy[END_REF][START_REF] Castillo-Olivares | West Nile virus infection of horses[END_REF]. In humans two presentations of the disease are reported: uncomplicated WN fever (headache and myalgia, often accompanied by gastrointestinal symptoms) and WN meningoencephalitis (typical meningitis or encephalitis) [START_REF] Campbell | West Nile Virus[END_REF][START_REF] Colpitts | West Nile Virus: Biology, Transmission, and Human Infection[END_REF].

D. OUTLINES OF THE WORK

Chapter 1 presents the context of this work and the associated research question. Chapter 2 gives first a brief presentation of the methods used for spatiotemporal quantitative risk assessments of the entry and establishment of VBDs in France, then presents spatiotemporal risk analyses that were performed to assess the probabilities of AHS and EE entry and establishment. Two routes of viral entry were considered together and two methods were used to assess the probability of viral establishment.

Chapter 3 first provides an overview on current approaches in syndromic surveillance. Then, an application of a classical method is presented which explores the impact of pre-processing methods on surveillance system performance. Finally, we discuss the application of Bayes' rules to syndromic surveillance with the goal of generating a quantitative output from syndromic surveillance and combining this with other epidemiological information.

Chapter 4 presents the combination of risk assessments with syndromic surveillance data using a Bayesian approach. We present a combination of various sources of epidemiological information, which originate from different syndromic surveillance systems and/or from syndromic surveillance and risk analysis.

Chapter 5 concludes with a discussion of the reliability and transparency of these complex surveillance systems and their usefulness in supporting decision-making.

CHAPTER II: QUANTITATIVE RISK ASSESSMENTS

This chapter explores quantitative risk assessments as a way to assess the risk of potential newly introduced VBDs in horses. Early detection of an exotic vector-borne pathogen can reduce the impact of the disease. It relies on two factors: the probability of pathogen entry and the probability of pathogen transmission and establishment. In fact, the probability of spatial and numeric spread is irrelevant to this process, as it is related more to the assessment of a disease's impact after early detection has already failed to detect and prevent the outbreak. The parameters needed to assess these probabilities are specific to each VBD, given that a vector's biology is closely linked to season and environment. A brief overview of the methods used for quantitative risk assessments of a VBD's entry, transmission, and establishment is presented in Chapter II.A. This review highlighted that combination of probability of entry, probability of transmission and probability of establishment is still rarely implemented in animal health, as is a thorough study of multiple routes of pathogen entry. Building on this review, we thus developed a quantitative model to assess the probability of entry and establishment of AHS, one of the most devastating equine diseases known (Chapter II.B). We implemented spatiotemporal analysis to take into account the close link between VBDs and season/environment, and to consider other non-biological fluctuations related to features of international trade and animal production. Then, we evaluated the feasibility of adapting this model to other VBDs in horses (Chapter II.C). For that purpose, we focused on equine encephalosis (EE), as this disease is similar to AHS. The respective probabilities of entry into France were compared for each disease. Finally, we discuss the advantages and drawbacks of our model in assessing the risks of newly introduced VBDs in horses (Chapter II.D).

A. OVERVIEW

This section aims to present the general principle of risk assessment and explain how the probabilities of pathogen entry, transmission, and establishment can be assessed in the specific context of VBDs. We restrict ourselves to quantitative risk assessment and to the most popular methods for risk estimation.

General principle of risk assessment

Definitions and objectives

Risk assessment is the component of risk analysis that estimates the risk associated with a hazard (OIE 2014). The OIE has defined a hazard as a "biological, chemical, or physical agent in, or condition of, an animal or animal product with the potential to cause an adverse health effect" and a risk as "the likelihood of the occurrence and the likely magnitude of the biological and economic consequences of an adverse event or effect to animal or human health".

The purpose of risk assessment is not so much to predict the introduction of a hazard but rather to help managers to better understand the associated risks (e.g., relative contributions of various factors, current areas of distribution, pathways for introduction, effectiveness of risk prevention actions). Risk assessment is clearly separated from risk management, but actively collaborates to achieve the ultimate goal:

implement measures that ensure the appropriate level of protection [START_REF] Giovannini | The Use of Risk Assessment to Decide the Control Strategy for Bluetongue in Italian Ruminant Populations[END_REF]OIE 2014).

Risk assessment may focus on different components, such as assessment of the entry, exposure, or consequences of a VBD, or on an estimation of the total risk by combining the results of these separate components in an overall assessment. To our knowledge, only a few papers in the animal health literature have linked these different probabilities in a quantitative manner: in a literature search, only three papers were found that addressed a combination of the probability of entry of a virus and its probability of establishment (EFSA 2009;[START_REF] Napp | Assessment of the risk of a bluetongue outbreak in Europe caused by Culicoides midges introduced through intracontinental transport and trade networks[END_REF][START_REF] De Vos | Risk of introducing African horse sickness virus into the Netherlands by international equine movements[END_REF]. Similarly, a comprehensive approach to the routes of entry is rarely used; we found only one paper that analyzed a combination of routes of virus entry [START_REF] Kilpatrick | Quantitative Risk Assessment of the Pathways by Which West Nile Virus Could Reach Hawaii[END_REF]).

The entry assessment is conducted using the probability that the pathogen of interest enters the area at risk via any possible pathway, without regard to later steps of transmission.

The exposure assessment includes analysis of various factors, as presented by de Vos and colleagues (de

Vos et al. 2011):

(1) the probability of transmission, which is defined as the probability that the pathogen is able to spread to susceptible hosts in the area at risk, (2) the probability of establishment, which is the probability that the pathogen is able to spread to susceptible hosts and to susceptible vectors (and vice versa) given the conditions of introduction, and (3) the probability of extended spread, which is the probability that the pathogen is able to spread in time and space, considering both local and long-distance dispersal.

The consequence assessment rates the impact of the disease and includes health, economic, social, ethical, and environmental considerations [START_REF] Vose | Risk Analysis: A Quantitative Guide[END_REF]. Disease persistence to next season won't be considered in this work.

Method

The preliminary step of any risk assessment is to identify the hazard of interest. Hazard identification is fundamental in defining the objective of the risk assessment and must be carefully implemented [START_REF] Vose | Risk Analysis: A Quantitative Guide[END_REF]).  Risk assessment should be flexible enough to deal with the complexity of real-life situations.

 The risk assessment should be based on the best available information that is in accord with current scientific thinking. The assessment should be well-documented and supported with references to the scientific literature and other sources, including expert opinion.

 Consistency in risk assessment methods should be encouraged and transparency is essential in order to ensure fairness and objectivity, consistency in decision making, and ease of understanding by all interested parties.

 Risk assessments should document the uncertainties, the assumptions made, and the effect of these on the final risk estimate.

 The risk assessment should be amenable to updates when additional information becomes available.

Risk assessments can be either qualitative or quantitative, and both approaches are valuable. Qualitative assessments describe the risk in words (e.g., low, moderate, high), whereas quantitative assessments express the risk in numeric terms. Qualitative assessments are performed when no proper evaluation of the order of magnitude of uncertainties is possible while these uncertainties are typically high. Since there is no quantitative evaluation, there is also no proper mathematical model. Qualitative assessments are often used for routine decision making (OIE 2014). However, qualitative assessments do not provide sufficient information to accurately discriminate between small and large risks [START_REF] Cox | Some Limitations of Qualitative Risk Rating Systems[END_REF].

Quantitative assessments provide more detailed information on the risk and can be more useful in distinguishing periods and areas at higher risk. However, the performance of a quantitative risk analysis is limited by the quality of data available. In addition, quantitative risk assessment can be deterministic or stochastic. Deterministic approaches produce a single outcome from a given set of parameters, uncertainty can be included but stochastic effects are usually ignored or crudely estimated. Stochastic approaches directly calculate the risk while also taking into account uncertainty and/or variability due to stochastic variation in input parameters. They produce a probability distribution of possible outcomes distinguishing impact via uncertainty and stochasticity.

Probability of entry

Definition

The probability of entry was previously referred to as the probability of release (OIE 2010). In 2014, the new version of the OIE's Terrestrial Animal Health Code (OIE 2014) specified this a bit further and adopted the following definition: "Entry assessment consists of describing the biological pathway(s) necessary for an importation activity to introduce pathogenic agents into a particular environment, and estimating the probability of that complete process occurring".

Estimation for VBDs

Routes of entry

The first step of the assessment of pathogen entry is to identify the potential routes available for introduction of the pathogen. Considering the specific case of VBDs, de Vos and colleagues (de Vos et al.

2011) listed the following pathways which should be considered in assessing the probability of VBD entry:

 Entry of infected live animals via importation of livestock, zoo animals, pets, wildlife, or migratory birds;

 Entry of an infected vector or its eggs or larvae through expansion of the vector's habitat or transport with wind, tires, plant materials, transport vehicles, animals, humans, manure, or soil;

 Import of contaminated biological material, such as semen, ova, embryos, serum, plasma, and modified live vaccines;

 Import of contaminated animal products such as meat, milk, eggs, bush meat, and animal byproducts (feathers, animal proteins, animal fats);

 Entry of infected humans.

The importation of animals and transport of materials or other products can be legal or illegal. Illegal imports could contribute substantially to the probability of entry, but are obviously difficult to estimate and to quantify, and will therefore not be discussed further in this work [START_REF] Chaber | The Scale of Illegal Meat Importation from Africa to Europe via Paris[END_REF][START_REF] Hartnett | A Quantitative Assessment of the Risks from Illegally Imported Meat Contaminated with Foot and Mouth Disease Virus to Great Britain[END_REF][START_REF] Smith | Zoonotic Viruses Associated with Illegally Imported Wildlife Products[END_REF].

Calculation

The scenario tree, or scenario pathway, approach is commonly used to estimate the probability of pathogen entry [START_REF] Vose | Risk Analysis: A Quantitative Guide[END_REF]. Several examples are available for vector-borne pathogens, in particular for Rift Valley fever [START_REF] Abdo-Salem | Risk Assessment of the Introduction of Rift Valley Fever from the Horn of Africa to Yemen via Legal Trade of Small Ruminants[END_REF], West Nile fever [START_REF] Bessell | Quantifying the Risk of Introduction of West Nile Virus into Great Britain by Migrating Passerine Birds[END_REF][START_REF] Douglas | A quantitative risk assessment of West Nile virus introduction into Barbados[END_REF][START_REF] Kilpatrick | Quantitative Risk Assessment of the Pathways by Which West Nile Virus Could Reach Hawaii[END_REF]), equine infectious anemia [START_REF] Asseged | The risk of introduction of equine infectious anemia virus into USA via cloned horse embryos imported from Canada[END_REF], and bluetongue [START_REF] Hoar | Probability of introduction of exotic strains of bluetongue virus into the US and into California through importation of infected cattle[END_REF].

Other examples are also available for non-vector-borne pathogens like classical swine fever [START_REF] Bronsvoort | Quantitative assessment of the likelihood of the introduction of classical swine fever virus into the Danish swine population[END_REF]) and foot-and-mouth disease [START_REF] Yu | A risk-assessment model for foot and mouth disease (FMD) virus introduction through deboned beef importation[END_REF]).

The principle is first to describe all consecutive steps that result in disease entry. The complexity of these steps can vary according to the routes of entry considered [START_REF] De Vos | Risk Assessment Framework for Emerging Vector-Borne Livestock Diseases[END_REF]. For example, when an infected animal is legally imported, the animal must be viraemic (or latently infected) and the infection not detected during import procedure. However, when an infected wild bird enters the country via migratory routes, the only step to be considered in the probability of pathogen entry is that the animal is viraemic or latently infected. Each step has a conditional probability of occurrence and the probability of entry is calculated by multiplying the probabilities of all steps along the tree.

Model calculations can be used to quantitatively combine all these probabilities. These are especially useful when there is uncertainty and/or variability due to the presence of stochastic parameters, which is often the case in risk analysis.

Probabilities of transmission and establishment

Probability of transmission

Definition

The probability of transmission can be evaluated by calculating the basic reproductive number (R 0 ) (see for example [START_REF] De Koeijer | Factors that influence the age distribution of BSE cases: potentials for age targeting in surveillance[END_REF] and [START_REF] Fischer | The transmission potential of Rift Valley fever virus among livestock in the Netherlands: a modelling study[END_REF])), which represents the expected number of secondary cases produced, in a completely susceptible population, by a "typical" infected individual during its entire period of infectiousness [START_REF] Diekmann | On the Definition and the Computation of the Basic Reproduction Ratio R 0 in Models for Infectious Diseases in Heterogeneous Populations[END_REF]). The probability of transmission is thus not a probability but the number of new cases generated from one initial infected case.

If R 0 > 1, then, on average, each infected animal will generate more than one infected animal, and the infection will increase exponentially. If R 0 < 1, an infected animal is not able to infect more than one other animal, on average, and the infection should die out.

Due to the ease of interpretation of R 0 , it is very useful in distinguishing at-risk situations from those not at risk. This is one of the reasons why it has become an important parameter in risk assessment. In particular, R 0 is often used to assess the transmission of exotic infectious diseases for which, by definition, the only infected individual in a population is the introduced one.

Estimation for VBDs

Numerous approaches are available to estimate R 0 , but with vector-borne infection, the estimation of R 0 is slightly more complicated than for diseases with direct transmission. Indeed, with VBDs there is not only one population of infected/susceptible individuals to be considered, but at least two: hosts and vectors.

Thus two transmission steps must be assessed: one infectious host with a fully susceptible vector population, and one infectious vector with a fully susceptible host population.

The following parameters must be considered to assess the probability of VBD transmission (de Vos et al.

2011):

 Host density;

 Vector abundance;

 Biting rate;

 Transmission probability per bite from host to vector and from vector to host;

 Vector biology (e.g., survival rate, extrinsic incubation period).

Moreover, the vector-related data are highly dependent on environmental and climatic factors. Thus the R 0 for VBDs also depends on the time period and the geographical location in which the pathogen enters the area at risk.

Classical models for the assessment of VBD transmission probabilities are based on systems with one host and one vector or with two hosts and one vector. More details can be found, for example, in studies conducted on malaria [START_REF] Macdonald | The Measurement of Malaria Transmission[END_REF][START_REF] Ponçon | A Quantitative Risk Assessment Approach for Mosquito-Borne Diseases: Malaria Re-Emergence in Southern France[END_REF], African horse sickness [START_REF] Backer | Transmission and Control of African Horse Sickness in The Netherlands: A Model Analysis[END_REF][START_REF] Lord | Vector-borne diseases and the basic reproduction number: a case study of African horse sickness[END_REF], Rift valley fever [START_REF] Fischer | The transmission potential of Rift Valley fever virus among livestock in the Netherlands: a modelling study[END_REF], and bluetongue virus [START_REF] Brugger | Bluetongue Disease Risk Assessment Based on Observed and Projected Culicoides obsoletus spp. Vector Densities ». Édité par Simon Gubbins[END_REF][START_REF] Gubbins | Assessing the risk of bluetongue to UK livestock: uncertainty and sensitivity analyses of a temperaturedependent model for the basic reproduction number[END_REF][START_REF] Hartemink | Mapping the basic reproduction number (R0) for vectorborne diseases: A case study on bluetongue virus[END_REF]de Koeijer et al. 2011). However, other authors have also proposed approaches based on two-host, two-vector models [START_REF] Turner | Two-Host, Two-Vector Basic Reproduction Ratio (R(0)) for Bluetongue[END_REF].

Probability of establishment

Definition

The probability of establishment represents what happens in terms of pathogen survival and growth during a transition phase between a pathogen's entry and its actual spread. Establishment can be considered the initial spread of the disease and is expressed as the probability that "the infection has passed from a host via a vector to an indigenous host, while the basic reproduction number, R 0 , is higher than 1" (de [START_REF] De Vos | Risk Assessment Framework for Emerging Vector-Borne Livestock Diseases[END_REF].

First, the probability of establishment depends on the route of pathogen entry. Beyond this, it depends on environmental and climatic conditions and therefore on the time period and the location in which the pathogen enters the area at risk.

Estimation for VBDs

Methods such as those already presented in the previous section on the probability of entry assessment (i.e. the scenario tree method) can be used to estimate the probability of establishment. As previously presented, the principle is to describe all consecutive steps that result in disease establishment.

For VBDs, the following steps must be taken into particular consideration (de [START_REF] De Vos | Risk Assessment Framework for Emerging Vector-Borne Livestock Diseases[END_REF]):

 Pathway for introduction: route of exposure of indigenous host or vector;

 Time of disease entry: temperature, humidity, and other parameters that may influence pathogen transmission;

 Geographic location of disease entry: host density, vector abundance;

 Vector-host interaction: biting rate, transmission probability per bite from vector to host and from host to vector.

Studies conducted on African horse sickness (de [START_REF] De Vos | Risk of introducing African horse sickness virus into the Netherlands by international equine movements[END_REF], bluetongue [START_REF] Napp | Assessment of the risk of a bluetongue outbreak in Europe caused by Culicoides midges introduced through intracontinental transport and trade networks[END_REF], and epizootic hemorrhagic disease (EFSA 2009) provide examples of the assessment of the probability of VBD establishment using different routes of pathogen introduction (e.g., infectious host or infectious vector).

Conclusion

Quantitative risk assessments are common methods used to assess the risk posed by exotic pathogens.

Various methods are available to implement risk assessment. Notably, different components of risk assessment (i.e. probabilities of entry, transmission, and establishment) can be assessed independently or together according to the objective of the risk assessment. Considering the case of VBDs, specific parameters have to be taken into account to deal with the two steps of virus transmission (from vector to host and from host to vector). In particular, the time and the area of pathogen entry are important in assessments of the probabilities of pathogen transmission and establishment as a vector's biology is closely linked to season and environment. However, analyses that combine the probabilities of entry, transmission, and establishment are still rarely implemented in animal health; the same is true regarding studies of combinations of different routes of entry. The development of such models could be a way to better understand and manage the risk associated with a disease.

B. PROBABILITIES OF ENTRY AND ESTABLISHMENT

Introduction

In this section we present a spatiotemporal assessment of the probability of introduction of African horse sickness (AHS) to France. We developed a model that combined the probability of entry with the probability of establishment and included two routes of virus entry, expecting that such a model would enable a greater understanding of the risk associated with AHS in France compared to risk assessments involving only a single probability parameter or a single route of introduction. [START_REF] Mildenberg | Equine Encephalosis Virus in Israel[END_REF][START_REF] Wescott | Evidence for the Circulation of Equine Encephalosis Virus in Israel since 2001[END_REF]. Likewise, the epidemiology of these diseases are also similar, with both sharing the same vectors [START_REF] Venter | A Comparison of the Vector Competence of the Biting Midges, Culicoides (Avaritia) Bolitinos and C. (A.) Imicola, for the Bryanston Serotype of Equine Encephalosis Virus[END_REF][START_REF] Venter | African Horse Sickness Epidemiology: Vector Competence of South African Culicoides Species for Virus Serotypes 3, 5 and 8[END_REF], although EE has a higher transmission rate [START_REF] Lord | Transmission patterns of African horse sickness and equine encephalosis viruses in South African donkeys[END_REF].

However, the two viruses differ in pathogenicity: AHS is one of the most devastating diseases in equids, with a mortality rate approaching 90% [START_REF] Mellor | African horse sickness[END_REF], whereas EE induces only sporadic symptoms with a correspondingly low mortality rate [START_REF] Dhama | Equine encephalosis virus (EEV): A Review[END_REF]. At first glance, the epidemiology and transmission patterns of AHS and EE are very similar; however, more detailed information on the respective probabilities of entry of the two diseases is needed.

The aim of this study was to determine the extent to which AHS and EE differ in their probabilities of entry, despite their similar patterns of epidemiology and transmission. We also identified the most appropriate measure for risk mitigation for each disease. The probabilities of entry into France of both AHS and EE were evaluated and compared for two routes of virus entry: an infectious host imported via legal trade and an infectious vector imported via the large animal trade.

Method

Model for risk assessment of viruses entry

The probability of entry is defined as the probability that a virus reaches an area, without consideration of later steps of transmission (OIE 2014). The stochastic spatiotemporal model of AHS introduction presented in the previous section (Chapter 2, section B) (Faverjon et al. 2015b) was used to assess the probability of AHS entry. The model was adapted by Evelyn Pamela Martinez Lopez, a Master's student from CVI, to assess the probability of EE introduction to the Netherlands and subsequently adapted by us to assess the probability of EE entry into France. Two pathways were considered: the introduction of an infectious host via legal trade and the introduction of an infectious vector through the large animal trade.

Parameters

The models for AHS and EE entry differ only in the disease parameters. The parameters not related to the diseases, such as transport time, were identical to those defined in the previous section (Chapter 2, section B) (Faverjon et al. 2015b). The disease-specific parameters were, for AHS, those used in the previous section (Chapter 2, section B) (Faverjon et al. 2015b) and, for EE, the parameters used by Evelyn Pamela Martinez Lopez. The differences between the diseases are reported in Table 3 andTable 4. All other parameters are identical in both models; in particular, there is no quarantine and no laboratory test implemented for either disease for horses traveling within the EU. (Faverjon et al. 2015b); The parameters used for equine encephalosis have been estimated following the same assumptions than those used in (Faverjon et al. 2015b) but adapted according to the specificities of the disease presented in [START_REF] Aharonson-Raz | Isolation and Phylogenetic Grouping of Equine Encephalosis Virus in Israel[END_REF] [START_REF] Crafford | A group-specific, indirect sandwich ELISA for the detection of equine encephalosis virus antigen[END_REF] [START_REF] Crafford | A competitive ELISA for the detection of group-specific antibody to equine encephalosis virus[END_REF] [START_REF] Mildenberg | Equine Encephalosis Virus in Israel[END_REF]) [START_REF] Paweska | Vector Competence of Culicoides Species and the Seroprevalence of Homologous Neutralizing Antibody in Horses for Six Serotypes of Equine Encephalosis Virus (EEV) in South Africa[END_REF]) [START_REF] Venter | Vector Competence of Selected South African Culicoides Species for the Bryanston Serotype of Equine Encephalosis Virus[END_REF])

African

Cumulative incidence

High risk

Horse: Pert(4x10 -6 , 5.02x10 -4 , 1x10 -3 ) Donkey: 1.2x10 -2 Zebra: 1.6x10 -2

All equidae: 1-exp(Uniform(0.29,0.67))

Low risk 2x10 -4 0.0951

Very low risk 2x10 -4 0.0487

Input data

To calculate the probability of virus release, the numbers of bovines and equines transported to France were obtained from TRACES, the TRAde Control and Expert System, which monitors the transport of animals and products of animal origin both into and within the EU. In our analysis, we only included animals whose final destination was France.

What-if scenarios

To evaluate the impact of manageable parameters on the probability of entry of AHS and EE into France, we used the average annual number of animals imported into France between 2010 and 2012 to evaluate different scenarios and compare them to the default. Seven scenarios were tested: five tested the effects of changes to existing legislation, and two evaluated the consequences of changing import procedures from non-EU countries. A description of the scenarios is available in Table 5.

Scenario 4

No serological test implemented

Scenario 5

Vector protection implemented on all animals coming from low risk area

Scenario 6

No legal importation from high risk region

Scenario 7

No legal importation from low risk region and non-EU states

Calculations

Model calculations were performed in Microsoft Office Excel 2010 with @Risk 6.1 (Palisade Corporation 2013); 10,000 iterations were run. The sensitivity analysis tool in @Risk was used to evaluate the impact of stochasticity and uncertainty in the input parameters on model results. The correlations between the values of the input parameters and the pathway-specific probabilities of introduction were calculated (Spearman's rank correlation coefficients).

The sensitivity of the model to input parameter values could be expected as very similar across all regions and months because we used the same model and input parameter estimates in every case, with the exception of the bovine-to-equine ratio, the temperature data, and vector abundance. The values of these three parameters varied substantially across regions and months (e.g., in a given month, vector abundance could vary greatly in one region and little in another; the bovine-to-equine ratio also varied across regions). Parameters subject to larger amounts of variation are more likely to substantially influence model results more than those subject to lesser amounts of variation. When determining the overall probability of introduction, we thus chose to focus our sensitivity analysis on the combinations of region and time period that were associated with the highest levels of risk and/or uncertainty.

Results

Spatiotemporal probability of entry

The overall annual median probability of EE entry in France was much higher than that for AHS for both pathways and for each of the three years considered (EE: PW-host = 0.9 and PW-vector = 0.4 to 0.5, AHS:

PW-host = 3x10 -3 and PW-vector = 1.4 x10 -2 to 3.6x10

-2

). The route most susceptible to virus entry differed between diseases: for AHS, infectious vectors represented the route by which entry into France was most likely, while for EE, infectious hosts represented the most at-risk route of entry (see figure 3).

Seasonal effects were similar for both diseases, with a lower-risk period from January to June. This was the result from the assumption fact that the low-and very-low-risk regions (i.e. the exporting regions)

were considered to be unlikely to experience AHS and EE outbreaks during this time and that animal import from high-risk regions is very rare in general (see Figure 3).

Equine encephalosis

African horse sickness

Probability of entry varied greatly across space and time (see for example Figure 4 and Figure 5) but, over the three years considered, some areas consistently had a higher probability of virus entry, e.g., the southern and north-western regions of France. These areas were the most at-risk for both diseases and both entry pathways (see Figure 6).

Sensitivity analysis

The parameters with the greatest impact on the output differed between diseases and pathways. A summary of the input parameters with the greatest influence on the results is presented in Figure 7 and

African horse sickness Equine encephalosis

Probabilities of entry bellow 10 -4 over the three years Probabilities of entry between 10 -4 and 10 -3 over the three years Probabilities of entry between 10 -3 and 10 -2 over the three years Probabilities of entry between 10 -2 and 10 -1 over the three years Probabilities of entry above 10 -1 over the three years

AHS EEV

Figure 8 : Correlation of the model input parameters with the probability of entry of AHS and EE via an infectious vector. Results are presented for Basse Normandie in July 2012. Only input parameters with at least one correlation ≥ |0.1| have been included in the table. Parameters with black star are the uncertain parameters. The others are the variable parameters.

What-if scenarios

The what-if scenarios tested had similar effects on both diseases when the routes of introduction were considered separately (see Table 6). For example, the probability of importing an infectious vector decreased when systematic vector control was implemented during quarantine (a change of more than -40% for both diseases). Instead, changes to the length of the quarantine period and the use, or not, of laboratory tests had only a minor impact on the probability of introducing an infectious host (and obviously no impact on the importation of an infectious vector). Although the impact of the what-if scenarios was broadly similar (again, when considering each route of introduction separately) one difference should however be pointed out: a strategy of prohibiting imports from high-risk regions was much more successful in controlling AHS risk than EE risk. Indeed, in this scenario, the probability of importing an infectious vector decreased by 31.67% for AHS and by 3.40% for EE, and the probability of importing an infectious host decreased by 3.53% for AHS and 0.03% for EE.

When both entry pathways were considered together, the impact of the what-if scenarios on the overall probability of disease entry differed between AHS and EE. For example, when testing regulations were implemented in all low-risk countries, the overall probability of AHS introduction decreased by 4.99%

while the probability of EE introduction decreased by 15.35%. Similarly, the systematic implementation of vector control on animals coming from low-risk countries had a greater impact on AHS probability of entry than on EE probability of entry (-46.13% for AHS and only -2.07% for EE). The most influential protective measures were thus disease-specific. To reduce the probability of AHS introduction, the most efficient protective measure was to implement vector protection on all animals coming from low-risk regions. To reduce the probability of EE introduction, the most effective measure was to implement the same regulation in all low-risk regions: quarantine before import for horses coming from both EU and non-EU countries, which resulted in a 15.36% reduction in the probability of disease entry.

-0,96 0,14

-1 -0,8 -0,6 -0,4 -0,2 0 0,

Discussion

Our study showed that the probabilities of entry for AHS and EE into France are similar in terms of seasonality and, in both cases, the highest-risk period is from July to December. This is mainly due to a decrease in the estimated risk from exports from low-risk countries from January to June, when the probability of having an outbreak was calculated as negligible (outbreaks never reported). The regions most susceptible to AHS and EE entry were also similar, with the highest probabilities of virus entry in the southern and northwestern regions of France.

However, the probabilities of AHS and EE entry differed in magnitude, with the latter much higher than the former. In addition, the main probability contributors also differed between diseases. For AHS, the most important pathway for virus entry was through an infectious vector, but for EE, the appearance of an infectious host was the most important contributor to the overall probability. These patterns were due to the less-strict trade regulations concerning EE (i.e. no serological tests in low-risk non-EU states), the higher probability of EE occurrence in low-risk regions (mean value 0.14) compared to AHS (mean value 0.016), the difficulties of detecting EE symptoms during clinical inspection, and longer high-risk periods for EE, which can be explained by the longer asymptomatic period of EE, during which time the disease is not reported in the exporting country. These aspects together explain why preventive measures for high risk areas are more effective for AHS than for EE.

The sensitivity analysis revealed that the fraction of infectious Culicoides during an EE outbreak in high-risk regions had a significant impact on EE entry via increasing the number of infectious vectors. This parameter was estimated as a constant in the AHS model due to the limited information available and thus did not appear in the sensitivity analysis. However, this result for EE suggests that the impact of this parameter would be not negligible for AHS entry. Considering the probability of virus entry via an infectious host, the time for seroconversion was highlighted as an important input parameter for EE (coeff. correlation equal to 0.31), but not for AHS (coeff. correlation equal to 0.01). This result can be explained by the increased relative importance of serological tests in detecting EE, as this disease is mainly asymptomatic. In addition, there was much more uncertainty regarding estimates of the time for seroconversion for EE than there was for AHS. This also contributed to the importance of this parameter in the EE model.

The what-if scenarios tested here showed that the most effective protective measures were not the same for the two diseases, because the main probability contributors differed. Thus, even if the impact of each scenario was similar between diseases for a given route of introduction, its impact on the overall probability of disease introduction varied. To specifically decrease the probability of importing an infectious host, the most efficient measure for both diseases was to implement the same regulations in all low-risk countries, EU and non-EU states alike. This pattern can be explained by the fact that relatively few horses are imported into France from either high-risk or low-risk non-EU states (respectively 0.08% and 2.8% of the total number of imported horses to France) compared to the number of horses imported from low-risk EU states (34.4% of total imports to France). These results were consistent with those obtained by de Vos and colleagues (de Vos et al. 2012). To specifically decrease the probability of importing an infectious vector, the most efficient measure was, as expected, the implementation of systematic vector control during quarantine, which is currently only mandatory for horses coming from high-risk areas.

The model allowed us to distinguish which disease posed the greatest threat in a given time and place even though, a priori, the diseases are similar in term of biological origin and epidemiological patterns.

Our method also clearly identified the main probability contributors and the most efficient measures for risk mitigation. However, it does not take into account the assessment of the consequences of each disease, which would be useful in objectively allocating the limited resources for disease surveillance. For example, the probability of EE entry appears higher than that of AHS, but the consequences of AHS introduction would be more severe, given the pathogenicity of the disease. To aid in the allocation of resources, then, other approaches should be considered (e.g., [START_REF] Cardoen | Evidence-based semiquantitative methodology for prioritization of foodborne zoonoses[END_REF][START_REF] Havelaar | Prioritizing Emerging Zoonoses in The Netherlands[END_REF][START_REF] Krause | How Can Infectious Diseases Be Prioritized in Public Health?[END_REF][START_REF] Mckenzie | Development of methodology to prioritise wildlife pathogens for surveillance[END_REF][START_REF] Ruzante | A Multifactorial Risk Prioritization Framework for Foodborne Pathogens[END_REF][START_REF] Valenciano | Définition des priorités dans le domaine des zoonoses non-alimentaires[END_REF])).

D. DISCUSSION AND CONCLUSION

Discussion

The approach used in this chapter provided a complete and detailed picture of the probability of having an outbreak. In particular, the spatiotemporal risk analysis highlighted important spatiotemporal variations in probability of introcution. This is consistent with the non-homogeneity of the horse population and movements and with the link between VBDs and climate/environment. Performing a spatiotemporal analysis is thus useful for identifying the regions and time periods that are most at risk. In addition, by combining the probability of entry and probability of establishment for two routes of virus introduction, we provided a more complete picture of the risk posed by a pathogen compared to risk assessments that involve only a single route of introduction or a single probability. The risk maps provided in section B (figure 3 in the paper) present a good illustration of these differences: the spatiotemporal probabilities are different according to the probability of release/entry, the probability of establishment, the probability of introduction, and the routes of virus introduction under consideration.

Our method can be easily adapted to other Culicoides-borne diseases, as illustrated by the work conducted on equine encephalosis (section C). However, the method can also be easily adapted to other vector-borne diseases as long as vector-related data (extrinsic incubation period, survival rate, abundance, etc.) and host-related data (viremia, incubation period, etc.) are available (keeping in mind, of course, that more adaptations would be required for models of diseases that are less similar to AHS). In particular, the probability of virus establishment in our example was quite simple to estimate, but could be more complicated for diseases with more complex transmission cycles (e.g., diseases with vertical transmission, multiple hosts and vector species, and/or vectors with a slow biological cycle, such as ticks). Careful consideration must thus be taken in adapting the model to another disease. This is especially true given our finding that even very similar diseases, such as EE and AHS, lead to quite different risk assessment outputs (see section C).

Despite its advantages, the approach applied in this chapter is still rarely implemented in animal health.

The low number of publications found in the literature that combine routes of pathogen entry and probabilities of entry and establishment can be explained by two factors. Firstly, the propagation of bias and uncertainty that results from combining multiple data sources [START_REF] Hoffman | Propagation of Uncertainty in Risk Assessments: The Need to Distinguish Between Uncertainty Due to Lack of Knowledge and Uncertainty Due to Variability[END_REF] can complicate the interpretation of results. Secondly, each process requires a different estimate of probability and different measures of risk mitigation, which some researchers prefer to keep separate [START_REF] Stevens | Mapping the Likelihood of Introduction and Spread of Highly Pathogenic Avian Influenza Virus H5N1 in Africa, Ghana, Ethiopia, Kenya and Nigeria using Multicriteria Decision Modelling[END_REF]. Indeed, a large amount of data is needed to build such a complex spatiotemporal risk model. These data were hard to obtain, and not initially ready to use. When data are routinely collected, most of the time they are not formatted for use in the context of risk assessment, and thus an important step of data preprocessing is often needed. As an example, the TRACES database contains data on horse movements, but it was not straightforward to extract the relevant information. The method implemented in this chapter is thus time-and data-consuming, which constitutes one of the major obstacles to its wider implementation in risk estimation. This limitation may also restrict efforts to update the model and its outputs.

Conclusion

The approach used in this chapter provided a complete and detailed picture of the probability of experiencing an outbreak. However, a low probability does not mean that an outbreak is not occurring, and risk assessments do not predict with certainty the origin of an infection. This approach merely gives an estimate of the likelihood and the most likely sources of an outbreak. To ensure the early detection of a newly introduced disease, it would also be useful to consider other approaches for estimating the probability of experiencing an outbreak.

CHAPTER III: SYNDROMIC SURVEILLANCE

This chapter explores the possibility of implementing a syndromic surveillance approach to assess the probability of occurrence of a newly introduced VBD in horses. There is no single commonly accepted methodology for the execution of syndromic surveillance. We thus started by summarizing current methods and definitions used in syndromic surveillance and, in particular, in veterinary syndromic surveillance (Chap III.A). Based on this short review, we developed a syndromic surveillance system for the early detection of West Nile virus (WNV) (Chap III.B). WNV was chosen because it is currently a major concern in Europe for both human and equine populations. The syndromic surveillance system was developed using nervous symptoms in horses that are known to be early indicators of WNV. The output of this syndromic surveillance system was simple to understand, but also potentially complicated to use when data were close to the alarm threshold. In addition, it was difficult to combine the output with other epidemiological knowledge such as disease seasonality or environmental risk factors, parameters which are fundamental when working with VBDs like WNV. Indeed, how can we interpret a small outbreak occurring within the vector season versus a large outbreak occurring outside the vector season? To address this question, we tested an application of Bayes' rules to syndromic surveillance (Chap III.C). The objective was firstly to use syndromic surveillance to provide a quantitative assessment of the probability that an outbreak is in progress, and secondly to be able to combine syndromic surveillance with other epidemiological knowledge. The advantages and drawbacks of both approaches (classical and Bayesian approaches) in the assessment of the probability of a current VBD outbreak are discussed in the final section (Chapter III.D).

A. OVERVIEW

This section aims to present current methods and definitions used in syndromic surveillance and, in particular, in veterinary syndromic surveillance.

Overall principle of syndromic surveillance

1.1. History

Syndromic surveillance and human health

Syndromic approaches first gained momentum in human health applications, when the bioterrorist anthrax attacks of 2001 in the USA drew attention to the need for early detection of pathogen introduction [START_REF] Buehler | Syndromic Surveillance and Bioterrorism-related Epidemics[END_REF][START_REF] Nordin | Simulated Anthrax Attacks and Syndromic Surveillance[END_REF]. Concomitant outbreaks of new emerging infectious diseases, such as West Nile virus in 1999 [START_REF] Henderson | Lessons from the West Nile Viral Encephalitis Outbreak in New York City, 1999: Implications for Bioterrorism Preparedness[END_REF]) and SARS in 2002 [START_REF] Abdullah | Lessons from the Severe Acute Respiratory Syndrome Outbreak in Hong Kong[END_REF], reinforced the necessity of developing more timely surveillance systems. Real-time surveillance systems were then developed based on the automatic collection and transmission of pre-diagnostic and unspecific data, under the primary assumption that the behavior of these data change when a population's health is affected (Mandl et al. 2004a).

Syndromic surveillance was thus first used to enhance traditional passive surveillance, which is ineffective in detecting rare or emerging diseases due to the limited ability of clinicians to recognize the signs of unknown, or poorly known, diseases [START_REF] Shaffer | Using pre-diagnostic data fom veterinary laboratories to detect disease outbreaks in companion animals[END_REF]). However, a syndromic approach is now also applied in the monitoring of well-known diseases such as human flu [START_REF] Ginsberg | Detecting Influenza Epidemics Using Search Engine Query Data[END_REF][START_REF] Hiller | Syndromic Surveillance for Influenza in the Emergency Department-A Systematic Review[END_REF]) in order to implement protective measures early and limit the impact of the disease.

Syndromic surveillance and animal health

In veterinary medicine, the development of syndromic surveillance systems followed a parallel path to that in human medicine. In particular, the recent focus on the 'One medicine' concept has contributed to increased awareness of early disease detection in animal populations [START_REF] Dórea | Veterinary syndromic surveillance: Current initiatives and potential for development[END_REF]). However, compared to human medicine, syndromic surveillance in veterinary medicine poses its own unique problems. The great diversity of animal species and the types of production that must be considered constitute an impediment to the development of syndromic surveillance systems due to the lack of common vocabulary, practices, and data collection systems [START_REF] Shephard | The development of a syndromic surveillance system for the extensive beef cattle producing regions of Australia[END_REF]. In addition, animal data are subject to more variation stemming from non-disease factors, as a decision to seek care for livestock is mainly driven by a cost/benefit relationship and not, as in human medicine, by disease severity [START_REF] Kosmider | A stastistical system for detecting Salmonella outbreaks in British livestock[END_REF]. Moreover, data regarding animal health are still scarce due to less frequent data collection and less developed data standards. All of these elements complicate efforts to monitor animal diseases.

Although the number of syndromic surveillance systems or initiatives is increasing (at least 27 systems were identified in 12 European countries in 2013 (Dupuy et al. 2013a)), fully operational and validated systems are still rare in veterinary medicine [START_REF] Dórea | Veterinary syndromic surveillance: Current initiatives and potential for development[END_REF].

Definition and objectives

The term 'syndromic surveillance' derives from the word 'syndrome', a set of clinical signs and symptoms that are correlated with each other. However, any data can be used, provided they are sensitive to changes in disease incidence in a population and contain an early signature of a disease outbreak.

Syndromic surveillance can thus use either real syndromic data (e.g., data from emergency departments [START_REF] Hiller | Syndromic Surveillance for Influenza in the Emergency Department-A Systematic Review[END_REF], estimates of mortality in cattle [START_REF] Perrin | Using the National Cattle Register to estimate the excess mortality during an epidemic: Application to an outbreak of Bluetongue serotype 8[END_REF])) or other health-related data (e.g., milk yield [START_REF] Madouasse | Evaluation of a Continuous Indicator for Syndromic Surveillance through Simulation. Application to Vector Borne Disease Emergence Detection in Cattle Using Milk Yield[END_REF], search query data on Google [START_REF] Dugas | Influenza Forecasting with Google Flu Trends[END_REF][START_REF] Dugas | Google Flu Trends: Correlation With Emergency Department Influenza Rates and Crowding Metrics[END_REF][START_REF] Ginsberg | Detecting Influenza Epidemics Using Search Engine Query Data[END_REF]) and Twitter [START_REF] Gesualdo | Influenza-like Illness Surveillance on Twitter through Automated Learning of Naïve Language[END_REF][START_REF] Signorini | The Use of Twitter to Track Levels of Disease Activity and Public Concern in the U.S. during the Influenza A H1N1 Pandemic[END_REF])).

The Triple-S project defines syndromic surveillance as "the real-time (or near real-time) collection, analysis, interpretation and dissemination of health related data to enable the early identification of the impact (or absence of impact) of potential human or veterinary public health treats which require effective public health action" (Triple S Project 2011). Beyond this, there is no single and commonly accepted definition for syndromic surveillance. The main underlying objectives can nonetheless be summarized with the following points [START_REF] Katz | Redefining syndromic surveillance[END_REF]):

-Early detection of and response to an outbreak, or at least detection of a probability of an outbreak high enough to warrant further investigation;

-Use of continuously acquired pre-diagnostic information;

-Possible applications during an outbreak, through the provision of tools for following the course of outbreaks;

-Providing assurance that an outbreak is not in progress;

The primary objective of all syndromic surveillance systems is thus to detect the signal, even a weak one, of an outbreak prior to its formal diagnosis.

Overall approach

There is no commonly accepted method or framework for the implementation of a syndromic surveillance system, and different approaches can be used. However, following preliminary steps, three main steps should be always implemented: 1) description and preprocessing of the data, 2) choice and implementation of an appropriate detection algorithm, and 3) evaluation of the system's performance.

Figure 9 summarizes the overall process of implementing a syndromic surveillance system. Each component is detailed in subsequent sections.

Figure 9 : Overall method to implement syndromic surveillance.

Preliminary steps

Definition of objectives

Like for all surveillance system, the first step of any syndromic surveillance system is to set clear objectives (i.e., disease(s) of interest, system users, desired balance between the sensitivity, specificity, and timeliness of detection). The geographic, demographic, and temporal coverage of the system must be also carefully assessed [START_REF] Vial | A practical approach to designing syndromic surveillance systems for livestock and poultry[END_REF]. This step is essential as it will influence the performance of the surveillance system and its future organization.

Overview of data available

The essential data needed to achieve all surveillace objectives while minimizing the amount of data collected should be defined [START_REF] Vial | A practical approach to designing syndromic surveillance systems for livestock and poultry[END_REF]. Then, as one of the key objective of syndromic surveillance system is to use of continuously acquired pre-diagnostic information, an inventory of the data sources available has to be made and evaluated in order to identify the data which can be used by the system.

Preliminary steps

Data description and preprocessing

Development of detection algorithm

Detecting signal: comparing observed and predicted values

System's performance evaluation

Data preprocessing Data description

Historical baseline modelling and prediction

Definition of objectives Definition of syndrome Overview of data available

Definition of syndrome

Then, it is important to set a clear definition for the group of clinical signs, or any other data considered, that constitutes an event of interest. This step is essential and has to be carefully considered, as it will influence the performance of the surveillance system [START_REF] Ivanov | Accuracy of three classifiers of acute gastrointestinal syndrome for syndromic surveillance[END_REF][START_REF] Shaffer | Using pre-diagnostic data fom veterinary laboratories to detect disease outbreaks in companion animals[END_REF][START_REF] Vial | A practical approach to designing syndromic surveillance systems for livestock and poultry[END_REF]. Various methods can be used for data classification. For example, Dupuy and colleagues (Dupuy et al. 2013b) used multiple factor analysis, while Dórea and colleagues (Dórea et al. 2013b) used naïve Bayes learning and decision trees. This preliminary step poses unique problems in veterinary syndromic surveillance compared to human medicine. In particular, standards for data classification are not unified in veterinary medicine and each veterinary syndromic system develops and validates its own classification system [START_REF] Dórea | Veterinary syndromic surveillance: Current initiatives and potential for development[END_REF]. This lack of standardized data constitutes a challenge in the definition of syndrome groups and of the rules for characterizing events of interest.

Data description and preprocessing

Data description

After the definitions of the syndrome and events have been determined, the data must be carefully analyzed in order to identify their main variations and characteristics. Potential aberrations due to past outbreaks or other events must be identified. The data must also be decomposed in order to identify systematic and stochastic variations. When considering time series, one must take into account systematic variations due to trends (long-term movements in the time series) or seasonality (cyclic variations). This preliminary work is important in order to determine which detection algorithm will be best-adapted to the data and if data preprocessing will be necessary (see Table 7).

Data preprocessing

Depending on the results of data decomposition, data can also be preprocessed. Two main examples of data preprocessing are presented: removal of aberrations and stationarity transformation.

Aberrations removal

As a result of past outbreaks or other events, raw data may contain unusual values (to which we refer as "aberrations") which can disturb data modeling. To improve data modeling, and thus outbreak detection, these aberrations can be removed, either manually, based on historical data from previous outbreaks, or automatically, based on implemented procedures.

In particular, considering the specific case of time series data, Tsui and colleagues [START_REF] Tsui | Value of ICD-9 coded chief complaints for detection of epidemics[END_REF] proposed removing data points above the 95% confidence interval of model predictions. This was based on the assumption that, after fitting the entire dataset to a regression model, data points above the 95% confidence interval of model predictions represent data from an epidemic.

Another option is to use a reweighting procedure to reduce the influence of high baseline counts, as proposed by Farrington and colleagues [START_REF] Farrington | A Statistical Algorithm for the Early Detection of Outbreaks of Infectious Disease[END_REF]. A weighting function is used on empirical grounds to assign very low weights to counts with large residuals. The residuals (s i ) are obtained based on the initial estimates (μ i ) and the dispersion parameters (φ). The weight of each value (w i ) equals a constant γ. If s i is above 1, and γ*s i -2 if s i is below 1, the weighted data are refitted.

Stationarity transformation

The detection of outbreaks can sometimes be implemented only on stochastic variations of the data. This is especially true for time series which can be transformed into a stationary process. Such a transformation is essential in order to implement certain detection algorithms, such as control charts. In a stationary process, systematic variations have been removed from the data in order to keep only the stochastic variations.

Detection algorithms

There is no commonly accepted classification for algorithms used to detect abnormal patterns, but they are often presented according to the nature of the clusters they identify, i.e. temporal, spatial, or spatiotemporal clusters [START_REF] Buckeridge | Understanding Detection Performance in Public Health Surveillance: Modeling Aberrancy-detection Algorithms[END_REF]. As our work centers on equine populations, in which spatial information is rarely available and/or accurate, we focus in this section on temporal methods for cluster detection. Following a summary of how to choose the most appropriate detection algorithm, we briefly present the algorithms commonly used in the detection of temporal clusters.

Choice of detection algorithm

The choice of the algorithm for detecting a signal is fundamental in determining the quality of detection.

The choice must be based on [START_REF] Dórea | Veterinary syndromic surveillance: Current initiatives and potential for development[END_REF]):

the type of data available: single or multiple time series, data monitoring with rates or counts, long-term historical data available or not;

the nature of the disease considered: sudden or slow increase in the number of cases;

the desired balance between the sensitivity, specificity, and timeliness of detection.

The main detection algorithms used in temporal cluster detection are historical limits, control charts, and regression methods. A recent review showed that regression methods were the most popular methods used in veterinary syndromic surveillance in Europe (Dupuy et al. 2013a). Indeed, among the 23 systems found, eight used regression methods (of which four used autoregressive moving average models (referred to as "time series methods") and the remaining four used other methods), four systems used historical limits, and only one used control charts. Control charts are, however, more frequently used outside Europe [START_REF] Dórea | Veterinary syndromic surveillance: Current initiatives and potential for development[END_REF].

The popularity of regression methods might be explained by their ability to easily deal with data involving trends or seasons. Nevertheless, the drawback is that these methods require a long historical baseline, which is often not available. Conversely, control charts do not require a long historical baseline, but they also require preconditioning to remove seasonality, trends, and other variations, which adds complexity to the analysis. Historical limits algorithms are the simplest methods but they suffer from numerous drawbacks which may compromise outbreak detection (e.g., no adjustment for trends or disease clusters).

A summary of the main advantages and limitations of these different detection algorithms is presented in Table 7.

Historical limits

One simple method to detect outbreaks is based on historical limits and was first applied in the United

States by Stroup and colleagues [START_REF] Stroup | Detection of Aberrations in the Occurrence of Notifiable Diseases Surveillance Data[END_REF]).

An alarm is triggered when:

𝑋 0 μ > 1 + 2 × 𝜎 𝑥 μ
where X o is the number of cases in the most recent four-week interval and μ and σ x are the mean and the standard deviation, respectively, of the previous 15 historical four-week periods (from X 1 to X 15 ).

This method is simple to implement but presents major bias due to a lack of adjustment for gradual trends or disease clusters, a lack of consideration for reporting delays, and inconsistency in case inclusion criteria between current and historical data. Although a method for bias reduction was recently proposed [START_REF] Levin-Rector | Refining Historical Limits Method to Improve Disease Cluster Detection, New York City, New York, USA[END_REF], no real evaluation of the detection performance of a historical limits algorithm was conducted.

Control charts 4.3.1. Principle

Control charts are based on graphical representation of data and are commonly used when no solid baseline is available. Control charts rely on cumulative differences between observed data in a time window and a threshold (Mandl et al. 2004a), which is set at some multiple of the standard deviation of the sample's mean [START_REF] Carpenter | Evaluation and Extension of the Cusum Technique with an Application to Salmonella Surveillance[END_REF][START_REF] Hutwagner | A Simulation Model for Assessing Aberration Detection Methods Used in Public Health Surveillance for Systems with Limited Baselines[END_REF]. The value of the multiplier is chosen to optimize tradeoffs between sensitivity, specificity, and timeliness in order to meet the objectives of surveillance. However, the assumptions behind these methods are that the data are independent and distributed according to a known hypothesis, assumptions that are not met by most surveillance data [START_REF] Lotze | Implementation and comparison of preprocessing methods for biosurveillance data[END_REF]. In order to use control charts, then, significant preconditioning must be applied to transform the data into a stationary process.

Methods

Different kinds of control charts are available: Shewhart charts, cumulative sums (CUSUM), and exponential weighted moving average (EWMA) methods.

Shewhart charts are appropriate when a single peak is expected, and are simply based on the difference between observed values and average values calculated within a moving window [START_REF] Shewhart | Economic Control of Quality of Manufactured Product[END_REF]. Only the last mean recorded value is used for anomaly detection.

The CUSUM and EWMA methods rely on cumulative differences between observed data in a time window and a threshold (Mandl et al. 2004a). They are better-adapted to detect small but repeated lags between observed and expected values. Model parameters are empirically set to the best balance between sensitivity, timeliness, and specificity that is chosen to meet the objectives of the surveillance.

The CUSUM method is based on the calculation of a cumulative asymmetric sum and is especially useful in detecting outbreaks that are longer than one time unit (O'Brien and Christie 1997). It is sensitive to small shifts in deviations from the mean and also detects deviations more quickly than some other statistical process control methods. Two examples of the use of CUSUM are presented in [START_REF] Maciejewski | LAHVA: Linked Animal-Human Health Visual Analytics[END_REF][START_REF] Shaffer | Using pre-diagnostic data fom veterinary laboratories to detect disease outbreaks in companion animals[END_REF]), who both used CUSUM methods to detect syndromic aberrations in pets. This method is based on the equation:

C t = max {0, (D t + C t-1 )}
where t is the current time point and D t is the standardized difference between the current observed value and the expected value. The differences are accumulated daily (for each point t, the statistic incorporates the value at point t-1) over the baseline but reset to zero when the standardized value is negative.

The EWMA method is based on exponential smoothing and is especially useful in the detection of a gradual increase in a signal [START_REF] Hunter | The exponentially weighted moving average[END_REF]. One example of the application of EWMA methods to the detection of aberrations in veterinary laboratory data is presented in (Dórea et al. 2013a). EWMA is based on the equation:

E t = (1 -λ) t E 0 + ∑ t i=1 (1 -λ) t λI t
where λ is the smoothing parameter (>0) that determines the relative weight of current data to past data, I t is the observed value at time t, and E 0 is the starting value.

Regression methods

Principle

Regression methods can be used when long-term historical data are available (e.g., [START_REF] Kosmider | A stastistical system for detecting Salmonella outbreaks in British livestock[END_REF]); (Dórea et al.); [START_REF] Perrin | Using the National Cattle Register to estimate the excess mortality during an epidemic: Application to an outbreak of Bluetongue serotype 8[END_REF]). They utilize statistical methods for fitting a model to observed data in order to make predictions. The benefit of such an approach is that seasonal effects and trends that are observed in the dataset can be readily incorporated into the equation. The models are usually assessed based on an analysis of residuals and goodness-of-fit, and compared using AIC and root-mean-squared error within and outside the calibration period. In veterinary syndromic surveillance, these methods are still mainly used to perform retrospective analyses in order to assess their potential for prospective modeling [START_REF] Dórea | Veterinary syndromic surveillance: Current initiatives and potential for development[END_REF].

Regression models

Typical models are regression-type models (e.g., generalized linear models), autoregressive moving average (ARMA) models, and exponential smoothing. The different regression models are briefly presented in this section.

 Linear and Generalized linear models

Linear models (LMs) and generalized linear models (GLMs) are common tools for fitting data. In syndromic surveillance, they are especially useful when time series show trends and/or seasonal variations and when explanatory variables are used. Indeed, these types of information can be directly included in the model without additional data preprocessing. Two examples of their use in veterinary syndromic surveillance are shown in [START_REF] Perrin | Using the National Cattle Register to estimate the excess mortality during an epidemic: Application to an outbreak of Bluetongue serotype 8[END_REF]) and [START_REF] Kosmider | A stastistical system for detecting Salmonella outbreaks in British livestock[END_REF], who applied Poisson regression on cattle-related data (mortality and number of laboratory isolations of Salmonella, respectively).

 Autoregressive moving average models

Autoregressive moving average models (ARMA) are based on two processes: one for the auto-regression (AR) and another for the moving average (MA) [START_REF] Box | Time Series Analysis: Forecasting & Control[END_REF]. ARMA models require data to be stationary, i.e. without trends and with a mean and variance that do not change over time. If the data are not stationary, a common solution is to use a difference variable to transform the time series into a stationary process. Another option is to use an autoregressive integrated moving average (ARIMA) or seasonal ARIMA (SARIMA) model. The first aims to incorporate non-stationarity in the mean and the second attempts to take into account seasonal variations [START_REF] Box | Time Series Analysis: Forecasting & Control[END_REF].

 Exponential smoothing

Exponential smoothing involves exponentially decreasing the weights of observations over time, such that oldest observations have the smallest weight [START_REF] Gardner | Exponential Smoothing: The State of the Art[END_REF]. The forecast is continuously revised according to more recent observations. The EWMA, or exponential weighted moving average, approach is the simplest form of exponential smoothing and is used when data do not have trends and/or seasonality.

Instead, if trends are present, double exponential smoothing is used.

Triple exponential smoothing, also called Holt-Winters exponential smoothing (HW), aims to take into account both trends and seasonality. The seasonality can be either multiplicative or additive, but there can be only one type of seasonal pattern. If more than one kind of 'seasonal' pattern is present (e.g., monthly and daily seasonality), another smoothing method must be chosen. HW incorporates three components: a level term, a trend term, and a seasonality term, respectively defined by the smoothing constants α, β, and γ. The main advantage of this technique is that it is easily automatable and adaptable to local changes in the data [START_REF] Lotze | Implementation and comparison of preprocessing methods for biosurveillance data[END_REF]. One example of the use of HW in veterinary syndromic surveillance is found in (Dórea et al. 2013a).

Threshold values

The threshold values that trigger an alarm are typically a multiple of the standard error of the prediction (Mandl et al. 2004a), based on Serfling's approach [START_REF] Serfling | Methods for current statistical analysis of excess pneumonia-influenza deaths[END_REF]). This constant is determined by the best compromise between sensitivity and specificity for a given case, as illustrated, for example, by Muscatello et al. [START_REF] Muscatello | Prospective Surveillance of Excess Mortality due to Influenza in New South Wales: Feasibility and Statistical Approach[END_REF]. The authors explored excess mortality due to influenza and discussed the optimal threshold to balance the false positive alarm rate and true positive alarm rate. In general, a value between 2-and 3.5-times the standard error is often chosen to ensure the false alarm rate is below 5% (Mandl et al. 2004a).

Farrington and colleagues [START_REF] Farrington | A Statistical Algorithm for the Early Detection of Outbreaks of Infectious Disease[END_REF]) also proposed the use of an exceedance score based on the upper limit of the 99% prediction interval. An alarm is triggered when:

𝑋 𝑖 = (𝛾-𝜇 𝑖 ) (𝑈-𝜇 𝑖 )
> 1 U i is the upper limit of the 99% prediction interval, μ i is the initial estimated value, and γ is a constant.

Assessment of performance

Assessment of syndromic surveillance systems is essential for determining the validity of conclusions. The assessment can be either qualitative or quantitative. However, in veterinary syndromic surveillance, assessment of the system's performance is still rarely carried out [START_REF] Dórea | Veterinary syndromic surveillance: Current initiatives and potential for development[END_REF]. Moreover, when assessment is performed, it mainly focuses on data quality rather than real system performances (Dupuy et al. 2013a).

Performance metrics

Quantitative evaluation of a syndromic surveillance system's performance can be implemented in a similar way to the evaluation of the performance of individual diagnostic tests. Sensitivity, specificity, predictive positive values, and predictive negative values are commonly used as evaluation metrics of outbreak detection algorithms [START_REF] Buckeridge | Algorithms for rapid outbreak detection: a research synthesis[END_REF][START_REF] Choi | Comparison of Various Statistical Methods for Detecting Disease Outbreaks[END_REF]. Regarding sensitivity, two approaches can be considered: the outbreak-day approach and the outbreak-detection approach (Mandl et al. 2004b). The outbreak-day approach considers each day (or time period considered) within an epidemic period to be an independent case. A true positive alarm is thus produced for each outbreak-day detected. The outbreakdetection approach considers each outbreak to be a single entity and thus, a true positive alarm is produced when at least one outbreak-day is detected. Various other quantitative parameters can be used to compare detection algorithms, according to the objectives of the surveillance system (see Table 8).

In their "Framework for evaluating public health surveillance systems for early detection of outbreaks", Bühler et al. [START_REF] Bühler | Framework for Evaluating Public Health Surveillance Systems for Early Detection of Outbreaks[END_REF]) suggested a list of criteria, such as usefulness, flexibility, and acceptability, to qualitatively describe and evaluate each system component. Regarding veterinary syndromic surveillance, other criteria should be added, including population coverage, automation of data capture and transfer, benefit to users, detection efficiency of programmed algorithms, and contribution to claims of disease freedom [START_REF] Dórea | Veterinary syndromic surveillance: Current initiatives and potential for development[END_REF].

Predictive negative value

Probability that no alarm corresponds to a true absence of an outbreak

ROC curve

Plots sensitivity (or true positive rate) against 1-Specificity (or false positive rate) for a range of algorithm settings Area under ROC curve Summarizes the detection performance of an algorithm. Values larger than 0.5 indicate that the algorithm is better than a random detection scheme.

AMOC curve

Plots a summary measure of time-to-alarm (given an outbreak is occurring) against the false positive rate

FROC curve

Plots the fraction of outbreak detected against the false positive detection rate ARL Expected time until the first detected event -ARL0; the expected time-to-alarm when there is an ongoing outbreak at the initiation of surveillance -ARL1

PSD

Probability of an alarm before some critical point in the outbreak given that the outbreak is detected

Time lag

Average number of weeks between the first of a consecutive number of outbreaks and the first alarm raised by each method

Missing rate

Number of missed outbreaks/total number of outbreaks

Test data

Generally, models are built using a calibration period and their predictions are then tested using a validation period. The role played by validation data in algorithm research is a crucial one and determines the validity of conclusions, especially when attempting a quantitative assessment of the system's performance [START_REF] Buckeridge | Algorithms for rapid outbreak detection: a research synthesis[END_REF]. Authentic baseline and outbreak data can be used but the scarcity of such data means that it is often not possible to generate a quantitative assessment of the detection algorithm. Simulations of background data and/or outbreaks are therefore often required.

To simulate the background of a time series, different methods can be implemented. One of the simplest methods is to set the predicted value for each time period as the mean of a Poisson distribution. This distribution is then sampled randomly to determine the value for a week of a given year, as proposed by Dórea et al. (Dórea et al. 2013a). For outbreak data, most studies have used naturally occurring signals from one or more real outbreaks to evaluate outbreak detection performance [START_REF] Buckeridge | Outbreak Detection through Automated Surveillance: A Review of the Determinants of Detection[END_REF].

However, given the limited availability of high-quality data from known outbreak periods, such signals can also be simulated. The methods for doing so range from simple mathematical functions to more complex stochastic simulation. Outbreak simulation has to consider the duration of an outbreak, spacing between outbreaks, temporal progression, outbreak magnitude, and spatial features (Mandl et al. 2004b). The advantages and disadvantages of each set of tests are presented in the Table 9.

Conclusion

There is no single commonly accepted method or framework for the implementation of a syndromic surveillance system, and different approaches can be used to detect temporal clusters of abnormal events. However, three main steps should always be included: 1) description and preprocessing of the data, 2) choice of an appropriate detection algorithm, and 3) assessment of the system's performance.

Considering the use of syndromic surveillance in veterinary medicine, some specific points can be highlighted. Firstly, it can be challenging to define syndromes and abnormal events due to the lack of standards of data classification. Secondly, the most commonly used detection algorithms are control charts which, despite their limitations, are useful when a long-term baseline is not available. Regression methods are a priori more robust and flexible but are often only used for retrospective analyses because of the absence of long-term historical data. Finally, assessment of system performance in veterinary syndromic surveillance remains rare and, when it is performed, it mainly focuses on data quality rather than system performance.

Introduction

The Currently, the collected data are mainly used to produce alerts when cases with positive laboratory diagnoses are identified. The data are also used for basic syndromic surveillance: an alarm is triggered when four syndromes are reported in the same week, or three declarations reported in each of two consecutive weeks. This alarm threshold was set arbitrarily and alarms may result in the initiation of epidemiological investigations depending on the context of the declarations. However, the reliability of this threshold has never been assessed and the ability of the RESPE nervous syndrome database to serve as a routine syndromic surveillance system is currently unknown.

Nervous syndromes in horses are considered to be an early indicator of WNV outbreaks [START_REF] Leblond | West Nile Virus Outbreak Detection Using Syndromic Monitoring in Horses[END_REF]. Using routinely collected RESPE data in an early detection surveillance system could lead to the timelier implementation of protective measures, thereby limiting the consequences of a WNV outbreak for both equine and human populations. Therefore, there is a need to assess the capacities in which the RESPE nervous database can be used to detect WNV outbreaks.

The RESPE nervous syndrome dataset presents several aberrations that can be mainly explained by EHV-1 and EHV-sp outbreaks. As discussed in Chapter III.A, different methods can be used to remove these unusual data (manual or automatic procedures). To date, though, little work has been done on the potential impact of the choice of pre-processing method on a surveillance system's ultimate performance.

In this section, we use several preprocessing methods and detection algorithms to model time series data from the RESPE nervous symptoms database. The objectives were (i) to evaluate the impact of these methods and algorithms on system performance, and (ii) to assess whether or not these data can be used as a routine syndromic surveillance system for the detection of WNV outbreaks.

Methods

Data characterization

In the RESPE database, nervous symptoms in horses are defined as any signs of impairment of the central nervous system, i.e. ataxia, paresis, paralysis and/or recumbency, and/or behavioral disorder. Cases, or an unusual cluster of cases, with "atypical" expression (colic, lameness, excitement, falling, muscular atrophy) can also be considered after the most common etiology of these symptoms has been excluded, since these signs can sometimes be the clinical manifestation of an affected central nervous system. Nervous disorders with evidence of traumatic or congenital origins are excluded.

Data on nervous symptoms in horses were available from RESPE for every calendar day from January 1 st , 2006 to December 31 st , 2013, totaling 532 declarations. An initial data characterization was performed using the daily data in order to identify explainable patterns such as global linear trends and seasonality.

However, in the remainder of the study, the time series was aggregated into weekly counts due to the low per-day count. Monthly aggregation was not considered, as the main objective of this surveillance system was early detection.

Tests for WNV and EHV are routinely carried out on horses that present nervous symptoms, and the database contains 80 positive laboratory results, mainly for EHV-1 (only two positive cases of ELISA-IgG

West Nile virus). The EHV-1 positive cases were either isolated cases -i.e. not associated with other positive cases -or from a cluster of cases that could represent a true outbreak.

Data pre-processing

We split the data into two time periods: data from 2006 to 2010 were used to train the model (see next section) and data from 2011 to 2013 were used to validate the model.

The raw time series used for model training was called TS0. We investigated three options for the removal of aberrations present in TS0 in order to obtain an outbreak-free baseline. In the first method, we retained only the 452 cases with no positive laboratory results (TS1). The second method consisted of removing all data linked to historical EHV-1 outbreaks, based on information from the RESPE website (TS2). This method did not remove single positive cases but only the positive cases associated with a cluster of other positive cases. In our third method, extreme values from TS0 were removed using the approach of Tsui and colleagues (2001) [START_REF] Tsui | Value of ICD-9 coded chief complaints for detection of epidemics[END_REF], which assumes that, after the data have been fitted to a regression model, data points above the 95% confidence interval of the model prediction represent an outbreak (TS3). The authors used Serfling's regression model [START_REF] Serfling | Methods for current statistical analysis of excess pneumonia-influenza deaths[END_REF], which is a linear regression model that uses sine and cosine terms to account for seasonal variation. With our own data, we followed the proposal of Dórea and colleagues (Dórea et al.) and used a Poisson regression, which they considered an appropriate method to capture baseline activity while minimizing the influence of aberrations present in the dataset. The data were thus first fitted to a Poisson distribution and then values above the 95% confidence interval were removed. In TS1, TS2, and TS3, the values of weeks considered to be part of an outbreak were not removed but instead replaced by the average of the four previous weeks.

The four time series are shown in Figure 11. The explainable patterns (such as global linear trends and seasonality) were investigated in each time series (TS0, TS1, TS2, and TS3) in order to assess the impact of preprocessing methods on the dataset. We generated summary statistics by month and year, and performed moving average and autocorrelogram analysis [START_REF] Lotze | Implementation and comparison of preprocessing methods for biosurveillance data[END_REF].

Forecasting

Forecasting was attempted using generalized linear regression models (GLMs) that were appropriate for count data (Poisson and negative binomial (NB) regressions) and Holt-Winters generalized exponential smoothing (HW). For GLMs the evaluated models included different types of seasonality through the use of sinod models with 1, 2, or 3 periods/year and season or month as factorial variables. To account for differences between years, we calculated the average counts for 53 consecutive weeks (histmean). To ensure that an ongoing outbreak would not influence the estimate, we used a 10-week guard band for the calculation of histmean.

Training data from 2006 to 2010 (TS0, TS1, TS2, TS3) were used to train the models, while data from 2011 to 2013 were used to validate the quality of the predictions. Alternative GLMs were evaluated for training data using the Akaike information criterion (AIC) [START_REF] Bozdogan | Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions[END_REF]. For HW, the optimal parameters were determined through minimization of the squared prediction error [START_REF] Kalekar | Time series forecasting using holt-winters exponential smoothing[END_REF]).

The best models were then evaluated and compared using the autocorrelation and partial autocorrelation functions of the residuals (ACF and PACF, respectively) and the root-mean-squared error (RMSE). ACF and PACF are used to find repeating patterns (e.g., seasons) in a dataset. ACF is the linear dependence of a variable on itself at two points in time and PACF is the autocorrelation between two points in time after removing any linear dependence between them [START_REF] Box | Time Series Analysis: Forecasting & Control[END_REF]. RMSE is a measure of the difference between the values predicted by a model and the values actually observed from the environment that is being modeled [START_REF] Chai | Root Mean Square Error (RMSE) or Mean Absolute Error (MAE)? -Arguments against Avoiding RMSE in the Literature[END_REF]. This criterion was calculated for the differences between the observations and the predicted values within both the calibration period (RMSE c ) and the validation period (RMSE v ). In either case, the lower the criterion, the better the predictive performance of the model.

Detection algorithm

Finally, all eight combinations of pre-processing (4) and forecasting methods (2) were evaluated on their ability to detect simulated disease outbreaks: GLM applied to TS0, TS1, TS2, and TS3; and HW applied to TS0, TS1, TS2, and TS3. A six-week guard band was used to ensure that previous outbreaks would not influence the estimate of the baseline. The outbreak detection method used was based on a multiple of the standard error of the prediction. The action threshold was defined as the predicted number of cases in a given week plus a constant multiple of the standard error of the model prediction. If the actual observed value was above the threshold, an alarm was triggered. The constant multiple was empirically defined according to the best balance between sensitivity and specificity.

Baseline data from 2011, 2012, and 2013 were used for the assessment of the detection algorithms' performance. We simulated WNV outbreaks based on historical data from three previous European outbreaks: French outbreaks in 2000 [START_REF] Murgue | West Nile outbreak in horses in southern France, 2000: the return after 35 years[END_REF]) and 2004 [START_REF] Leblond | West Nile Virus Outbreak Detection Using Syndromic Monitoring in Horses[END_REF]) and an Italian outbreak in 1998 [START_REF] Autorino | West Nile virus Epidemic in Horses, Tuscany Region, Italy[END_REF]. The average weekly count of nervous-symptom cases in horses was calculated from the three historical outbreaks for an epidemic period covering a total of 11 weeks, from the first positive case detected to the last positive case detected (see Figure 12). The number of cases for each week of an epidemic period was sampled randomly between the extreme values obtained from historical data. To test our detection method, three simulated outbreaks were randomly inserted in the baseline data from 2011, 2012, and 2013, with at least 15 weeks between each outbreak in order to avoid overlap (see example in Figure 13). The process was repeated 25 times, for a total of 75 years containing a total of 75 outbreaks.

Quantitative assessment

We first calculated sensitivity based on the number of outbreaks detected out of all inserted outbreaks and denoted this Se_out. An outbreak was detected when it triggered at least one true alarm, defined as a week that produced an alarm and that was a part of an epidemic period. Se_out was calculated as:

Se_out = Out / (Out + No_Out)
where Out is the number of outbreaks detected and No_Out is the number of outbreaks not detected.

We also calculated Se_wk, the sensitivity based on the number of weeks in an epidemic period in which an alarm was triggered. Se_wk and specificity (Sp) were calculated as:

Se_wk = TP / (TP+ FN) Sp = TN / (TN + FP)
where TP is the number of true positive alarms, TN the number of true negative alarms, FP the number of false positive alarms, and FN the number of false negative alarms.

A receiver operating characteristic (ROC) curve was generated in R by testing various alarm thresholds, and the area under each curve (AUC) was also calculated [START_REF] Hanley | The Meaning and Use of the Area under a Receiver Operating Characteristic (ROC) Curve[END_REF]. The time to the first true alarm within an epidemic period was also evaluated in order to assess the efficiency of early detection.

Implementation

Models were implemented in R x64 version 3.0.2. Dynamic regression was performed with the functions glm (package {stats}), glm.nb (package {MASS}), and stlf (package {forecast}). The expected numbers of counts at time t were estimated with the predict functions of the respective packages. The expected numbers of outbreak-related cases were estimated with the fitdist function of the package {fitdistrplus}.

AUCs were estimated with the auc function of the package {flux}.

Results

Baseline characterization

For the initial data characterization, we worked with the daily time series data. The autocorrelograms showed high autocorrelation at lag 7, 14, 21, etc., indicative of a day-of-week effect. Not surprisingly, the number of declarations was significantly lower on Saturday and Sunday.

At the weekly level, all baselines except TS2 showed a significant positive trend: TS0 had +0.07 declarations per month (p-value = 0.0001), TS1 had +0.06 declarations per month (p-value = 0.01), and TS3 had +0.07 declarations per month (p-value = 0.000). However, this trend was mainly due to the first years of data collection (see Figure 14). A significant seasonal effect was also present in all time series: the number of declarations appeared highest in November, December, and January compared to other months. However, this seasonality was weak and principally apparent in the raw TS0 data, due to EHV-1 and EHV-sp outbreaks present in the dataset during the winters of 2008, 2011, and 2013 (see Figure 14).

Smoothing and forecasting

From 2006 to 2010, the data from each time series were fitted to their respective appropriate regression model, using variables that accounted for seasonal effects. For the Poisson as well as the NB regression, the best fit was obtained for all time series with the simple model:

Number_of_cases ~ sin(2π*week/53) + cos(2π *week/53) + log(histmean)

NB and Poisson regressions performed equally well for all time series, with the exception of TS0 (raw data), for which the NB model provided a better fit (AIC 749 vs. 761).

The details of differences between the smoothing performance of the best generalized linear models obtained and HW are presented in Table 10 andTable 11. In all regression methods used, TS0 produced the worst results, while TS1 generated the best fitting parameters. TS2 and TS3 yielded intermediary results, with better performances for TS3 than for TS2.

Table 10 : Smoothing and forecasting performance of GLMs. ACF and PACF are, respectively, the autocorrelation and partial autocorrelation functions of the residuals. Residuals are theoretically assumed to have an ACF and PACF that have no correlation for all lags. RMSEc and RMSEv are measures of rootmean-squared error within the calibration period and the validation period, respectively. In both cases, lower values are better.

ACF and PACF

Outbreak detection

The results showed that, for a given method, there was no difference between the different time series tested. However, the generalized linear model always outperformed the Holt-Winters method in terms of detection performance (see details in Table 12).

The AUCs of all methods and time series were low, but it is important to note that the sensitivity used here was based on the number of weeks within an epidemic period that produced an alarm (Se_wk). By using instead the percentage of outbreaks detected (with at least one alarm) among all the outbreaks inserted (Se_out), the AUCs for all combinations of time series and methods improved to 0.95.

With the generalized linear model, the optimal balance between Se_wk, Se_out, Sp, and the time-todetection within an epidemic period was obtained when the alarm threshold exactly equaled the value of the standard error of the model prediction (see details in Table 13). This alarm threshold detected more than 95% of the inserted outbreaks, with an average time to the first true alarm of less than 3 weeks from the start of the outbreak, with the exception of TS0. Specificity varied according to the smoothing method used, but ranged from 0.80 to 0.94 for all generalized linear models. Alarm thresholds that were based on a value higher than the standard error of the model prediction (K>1) had the same detection rate but took more time to produce the first true alarm (> 3 weeks). Instead, an alarm threshold based on a value lower than the standard error of the model prediction (K<1) had the same detection rate and required less time to produce the first true alarm, but resulted in the lowest specificity of all models (from 0.71 to 0.57). The alarm threshold equal to the standard error of the model prediction (K=1) detected from 3 to 6 nervous cases depending on the time series, the smoothing method, and the time period considered.

With the Holt-Winters approach, the optimal balance between Se_wk, Se_out, Sp, and the time-todetection in an epidemic period was obtained when the alarm threshold equaled the standard error of the model prediction multiplied by a constant of 0.5 (see details in Table 14). This alarm threshold detected more than 95% of the inserted outbreaks and the average time-to-detection was less than 3 weeks from the start of the outbreak. The associated specificity had an average value of 0.87. Alarm thresholds that were based on constants higher than 0.5 had the same detection rate but needed more time to produce the first true alarm (> 3 weeks).

Table 12 : System's detection performances. Se_wk = sensitivity based on detection of each week which is a part of an epidemic period, Sp = specificity based on the number of true negative and false positive alarms, ROC = receiver operating characteristic, AUC = Area Under the receiver operating characteristic curve. Table 13 : system's detection performances for time series fitted with generalized linear models. K = constant multiple of the standard error of the model prediction, Se_wk = sensitivity based on detection of each week which is a part of an epidemic period, Se_out = sensitivity based on the number of outbreaks detected, Sp = specificity based on the number of true negative and false positive alarms, Average time of detection = Average number of weeks needed to produce the first alarm within an outbreak.

AUC

K

Discussion

As expected, the preprocessing methods that were used to remove past outbreaks present in the dataset modified the seasonality of the time series. Indeed, outbreaks of EHV-1 that were present in TS0 were mainly reported during winter, which is consistent with reports of seasonal patterns of disease outbreaks from a recent consensus statement [START_REF] Lunn | Equine Herpesvirus-1 Consensus Statement[END_REF]. Removing these outbreaks from the TS0 data decreased the impact of season on the baseline and improved the smoothing performance of the two forecasting methods tested. The raw data (TS0) produced the worst results compared to all time series in which outbreaks were removed. Regarding the impact of preprocessing methods on system performance, no impact was observed when Holt-Winters smoothing was used. Conversely, the detection performance differed between time series fitted with glm: TS0 obtains always the worst results (longest time-todetection and lowest Se_wk/Sp).

RESPE currently uses raw data (TS0) and an alarm threshold of four declarations per week for the detection of outbreaks. According to the analysis performed in this study with TS0, this alarm threshold is close to the standard error of our model prediction using GLMs (between four and five cases, depending on season). The current detection performance of the RESPE system is thus: weekly sensitivity close to 0.48, specificity close to 0.94, and average time-to-detection close to 3.13 weeks. These values are lower than those obtained here with preprocessed data (TS1, TS2, TS3) and reveal the importance of data preprocessing in improving outbreak detection for syndromic surveillance.

When we use values of Se_wk to evaluate overall system's performance, it is clear that the syndromic surveillance system suffers from low sensitivity. This is not surprising as, during a WNV outbreak, the number of cases observed per week of the outbreak is generally low, especially during the initial and final stages of the outbreak (see figure 12). When considering the system's ability to detect an outbreak as a single entity (Se_out), all combinations of time series and methods used were able to detect more than 95% of the inserted outbreaks. However, compared to HW, GLM enabled earlier outbreak detection, with a better Se_wk, for a given Sp. In the end, the best performances were obtained using GLMs associated with preprocessing methods TS1, TS2, or TS3, and an alarm threshold set to the standard error of the model prediction. With these settings, the surveillance system can detect 96% of outbreaks, with an average time-to-detection of 2.16 to 2.75 weeks, weekly sensitivity (Se_wk) between 0.56 and 0.62, and specificity ranging from 0.80 to 0.86. A K value (multiple of the standard error) between 2 and 3.5 is often chosen to ensure a false alarm rate below 5% (Mandl et al. 2004a) but, in our case, this threshold increased the time-to-detection to between 3 and 5 weeks, an undesirable outcome when striving for early detection. In this study, we did not determine which time series (TS1, TS2, or TS3) was the most efficient, as such a decision would be made in real life by decision makers and would depend on the objectives of the surveillance.

Our study shows that the RESPE data on nervous symptoms in horses can be used as an alarm system for WNV outbreaks in France and the full assessment of system's performance was possible thanks to simulated data. This is the first time that a real assessment of system performance has been implemented

for WNV surveillance. Previous early warning systems developed for WNV only identified risk factors of WNV outbreaks, but did not evaluate the detection performances of those systems [START_REF] El Adlouni | Effects of climate on West Nile Virus transmission risk used for public health decision-making in Quebec[END_REF]Bellini et al. 2014a;[START_REF] Brown | California Mosquito-borne Virus Surveillance & Response Plan[END_REF][START_REF] Chaskopoulou | Detection and Early Warning of West Nile Virus Circulation in Central Macedonia, Greece, Using Sentinel Chickens and Mosquitoes[END_REF][START_REF] Gosselin | The Integrated System for Public Health Monitoring of West Nile Virus (ISPHM-WNV): a real-time GIS for surveillance and decision-making[END_REF][START_REF] Rosà | Early warning of West Nile virus mosquito vector: climate and land use models successfully explain phenology and abundance of Culex pipiens mosquitoes in northwestern Italy[END_REF][START_REF] Shuai | A GIS-driven integrated real-time surveillance pilot system for national West Nile virus dead bird surveillance in Canada[END_REF][START_REF] Valiakos | Use of Wild Bird Surveillance, Human Case Data and GIS Spatial Analysis for Predicting Spatial Distributions of West Nile Virus in Greece[END_REF]). Timeliness has occasionally been evaluated but only based on a limited number of real WNV outbreaks, and has not been associated with a further assessment of system performance [START_REF] Calzolari | New Incursions of West Nile Virus Lineage 2 in Italy in 2013: The Value of the Entomological Surveillance as Early Warning System[END_REF][START_REF] Chaintoutis | Evaluation of a West Nile virus surveillance and early warning system in Greece, based on domestic pigeons[END_REF][START_REF] Eidson | Dead bird surveillance as an early warning system for West Nile virus[END_REF][START_REF] Johnson | Geographic Prediction of Human Onset of West Nile Virus Using Dead Crow Clusters: An Evaluation of Year 2002 Data in New York State[END_REF][START_REF] Mostashari | Dead Bird Clusters as an Early Warning System for West Nile Virus Activity[END_REF][START_REF] Veksler | Assessment of methods for prediction of human West Nile virus (WNV) disease from WNV-infected dead birds[END_REF]. Only one attempt [START_REF] Leblond | West Nile Virus Outbreak Detection Using Syndromic Monitoring in Horses[END_REF]) to assess the sensitivity and specificity of surveillance has been made but the parameters of interest were only evaluated based on a limited number of outbreaks, which did not allow any conclusions to be drawn regarding overall system performance. The outbreaks were simulated using real data and should thus be consistent with the course of a real WNV outbreak. However, there is always the risk that the conditions used here to evaluate system performance were unrealistic, and thus other outbreaks, differing in magnitude and form, should be also tested in order to confirm our results.

Conclusion

A classical syndromic surveillance approach based on nervous symptoms in horses can be implemented using RESPE data in order to detect WNV outbreaks. The results produced in our study are better than those obtained with the current detection system and argue in favor of data preprocessing for the improvement of outbreak detection.

The output of the syndromic system produced here was a yes/no qualitative output: "No, there is no outbreak" or "Yes, something unusual is happening in the population". This output has the advantage of simplicity, but its interpretation/utilization may be complex when data are close to the alarm threshold.

This output also has a low specificity. Indeed, we can detect WNV but probably also equine herpesvirus. It would be interesting to combine the output from syndromic surveillance with other information to reach a better specificity. However, it is currently complicated to combine this output with other epidemiological knowledge, such as disease seasonality or environmental risk factors, parameters that are fundamental when working with vector-borne diseases like WNV. This dilemma will be addressed in the next section.

C. VALUE OF EVIDENCE

Introduction

To address the problems associated with the qualitative outputs of syndromic surveillance and the difficulties of combining syndromic surveillance with other epidemiological knowledge, we tested a new approach for outbreak detection based on Bayes' rule. Bayes' rule is already used in a wide range of disciplines to combine information and provide numerical estimation of a likelihood ratio. In the framework of Bayesian analyses, this likelihood ratio is used to test hypotheses and clearly specify the strength of forensic evidence for/against a hypothesis.

In the next section, we evaluate the applicability of the Bayesian likelihood ratio framework to the detection of outbreaks in syndromic surveillance. Two examples are considered: nervous syndromes in horses as an early warning of WNV outbreaks, and respiratory syndromes in horses for the detection of equine influenza. The objective was, first, to build a more objective, flexible, and easily interpretable output for syndromic surveillance and, second, to combine syndromic surveillance with other epidemiological knowledge.

This part of the work was implemented in collaboration with Gunnar Andersson (SVA, Sweden) and published in PLOSOne (see below). This work also resulted in one oral presentation at the annual conference of AEEMA ("Association pour l'étude de l'épidémiologie des maladies animales", a

Francophone association dedicated to veterinary epidemiology) and one publication in their journal, 'Bulletin Epidémiologie et Santé Animale' (text available in French in Appendix 10).

D. DISCUSSION AND CONCLUSION

Discussion

This chapter showed that syndromic surveillance based on data collected by RESPE is able to detect signals suggestive of the presence of an outbreak of WNV or equine influenza in French horses (through the monitoring of nervous and respiratory symptoms, respectively). Although the system appears to be effective, syndromic surveillance is still rarely implemented in horses, probably due at least in part to the lack of data available for this population (e.g., few centralized databases on horse health, mainly due to the diversity of activities in the equine industry). In Europe, we have only been able to identify three syndromic surveillance initiatives for horses, based on a recent review by Dupuy et al. (Dupuy et al. 2013a) and an additional literature search. One such initiative is present in the UK, associated with the Equine Quarterly Surveillance Reports (DEFRA/AHS/BEVA 2015), another is in the Netherlands [START_REF] Rockx | Syndromic surveillance in the Netherlands for the early detection of West Nile virus epidemics[END_REF], and the third is in Switzerland, linked to the Equinella network (https://www.equinella.ch/). At the time of writing, none of these systems (RESPE included) uses statistical tools to detect the signal of an outbreak prior to its formal diagnosis. Instead, the alarm threshold is typically set at an arbitrary level using raw data. However, our results indicate that data preprocessing and analysis improve detection performance compared to such subjective methods.

In syndromic surveillance, Bayesian approaches have previously been mainly used for spatiotemporal outbreak detection and/or to assess unknown posterior probabilities by using hierarchical Bayesian models that involve inferences [START_REF] Chan | Probabilistic Daily ILI Syndromic Surveillance with a Spatio-Temporal Bayesian Hierarchical Model[END_REF][START_REF] Banks | Bayesian CAR models for syndromic surveillance on multiple data streams: Theory and practice[END_REF], Neill et al. 2006, Schmidt and Pereira 2011[START_REF] Zou | Bayesian methodology for spatio-temporal syndromic surveillance[END_REF]). The simple Bayesian approach developed in this chapter is less robust, from a mathematical point of view, than full inference-based Bayesian models, which take into account the uncertainties of parameter estimation. However, our approach is also much easier to implement and to understand. This is an advantage compared to more complex approaches, which are often too complicated for decision makers who lack experience with these methods to understand [START_REF] Banks | Bayesian CAR models for syndromic surveillance on multiple data streams: Theory and practice[END_REF]). The simple Bayesian approach used here could thus be a good compromise between rigor and ease-of-understanding in presenting results.

In this chapter, two types of detection algorithms were tested: classical methods based on regression models and an algorithm based on the empirical Bayesian approach. Classical approaches generated good detection performance and were simple to apply, a great advantage in veterinary medicine where syndromic surveillance systems are still difficult to implement [START_REF] Shephard | The development of a syndromic surveillance system for the extensive beef cattle producing regions of Australia[END_REF]). However, compared to an empirical Bayesian approach, classical approaches have three main shortcomings: they do not provide a quantitative output, they are not able to easily take into account other epidemiological information available on a disease, and they are very unspecific. This last point, however, can be an advantage in detecting an unknown disease, as no a priori hypotheses are required. The empirical Bayesian approach is more disease-specific, but the drawback is that knowledge of the disease must be available. However, this is not a fundamental limitation to the approach, as a vague probability distribution can also be used. The choice of an approach should be made according to the objective of the surveillance and the data available. In addition, it would be useful to perform a formal and quantitative comparison of the detection performances of both approaches before reaching a conclusion about their advantages and drawbacks.

The representativeness of the RESPE data was not evaluated here, but was recently investigated by that organization [START_REF] Daix | Typologie des vétérinaires sentinnelles[END_REF]). The study identified 430 sentinel veterinarians who truly participated in the reporting system. They are not equally distributed all over France, but rather present in 92 (of 96) French regions and concentrated in areas with high horse densities. The questionnaires filled out by 63% of the active sentinel veterinarians revealed that 26% do not declare all suspect cases to RESPE. The reasons cited were: no consent from owner, omission, lack of time, and definitive diagnosis obtained without laboratory analysis. Most of the sentinel veterinarians reported seeing only a few suspect cases, which explained the low number of declarations reported per veterinarian. These elements suggest that the representativeness of the RESPE data is probably acceptable. However, it is unknown how these factors specifically affect the reporting of nervous and respiratory symptoms. Indeed, some veterinarians seem to declare only certain symptoms and not others. Therefore, it would be important to perform a detailed assessment of the RESPE system in order to ensure optimal outbreak detection performance.

Conclusion

This chapter describes a useful tool for determining if there is an ongoing VBD outbreak in French horses.

In particular, the Bayesian approach enabled us to merge syndromic surveillance with knowledge of risk factors, which can be especially useful for VBDs as they are closely related to season and environment.

Despite these advantages, an outbreak may also occur without generating a detectable signal in the syndromic surveillance system. This is of particular concern given the unknown representativeness of the data used. In addition, even if there is a significant signal, the lack of specificity in the system means that it could be a false alarm. It will thus be useful going forward to consider other approaches for estimating the probability of an outbreak in order to ensure the early detection of a newly introduced disease.

CHAPTER IV: MULTIPLE INDICATORS OF RISK

Risk assessments and syndromic surveillance provide an estimate of the probability of an outbreak, but they do not prove the presence of the disease. The accumulation of evidence from a combination of these approaches can be a way to improve confidence in the prediction that a newly introduced epidemic is in progress. More generally, combining all available information in a multivariate algorithm should give better results for outbreak detection than univariate methods do.

In this chapter, we explore the combination of multiple risk indicators in order to improve assessment of the probability of occurrence of a newly introduced VBD in horses. We first direct our attention to WNV, which infects a wide range of species and induces different types of symptoms. Therefore, combining information from different species or from different syndromic groups could help in outbreak detection.

We thus worked first on a multivariate syndromic surveillance system in order to improve the detection of WNV outbreaks (Chapter IV.A). However, as already highlighted, VBDs are closely linked to season and environment. In addition, the probability that an outbreak occurs is also linked to the probability that the disease enters an area. Combining syndromic surveillance with assessments of the probabilities of virus entry and establishment may thus also improve confidence in the prediction that a new VBD has been introduced. This approach has the potential to be much more useful than syndromic surveillance alone, as the latter may fail to detect an outbreak of a disease that causes few symptoms. To test this approach, we worked to combine syndromic surveillance data with quantitative risk analysis and we applied this approach to the detection of equine encephalosis (EE) outbreaks. We chose EE because it has few symptoms and should be more difficult to detect using a single approach than AHS and WNV, both of which manifest themselves in a more specific clinical picture (Chapter IV.B). The advantages and drawbacks of combining these risk indicators to detect VBDs in horses are also discussed (Chap. IV.C).

A. MULTISTREAM SYNDROMIC SURVEILLANCE

Introduction

One limit of univariate syndromic surveillance is that no single data source captures all the individuals involved in the outbreak, and that diseases may cause a wide variety of symptoms in different individuals [START_REF] Kulldorff | Multivariate Scan Statistics for Disease Surveillance[END_REF]). In addition, the data collected are often vague, and univariate syndromic surveillance systems can suffer from this lack of specificity. However, by simultaneously assessing information from different data sources related to different populations and/or symptoms, one can improve outbreak detection and, in particular, the specificity of the detection.

Multivariate syndromic surveillance can be purely temporal (see, for example, [START_REF] Schiöler | Multivariate outbreak detection[END_REF], [START_REF] Fan | Evaluation of Outbreak Detection Performance Using Multi-Stream Syndromic Surveillance for Influenza-Like Illness in Rural Hubei Province, China: A Temporal Simulation Model Based on Healthcare-Seeking Behaviors[END_REF][START_REF] Lau | Optimizing Use of Multistream Influenza Sentinel Surveillance Data[END_REF])), purely spatial, or spatiotemporal (see, for example, [START_REF] Kulldorff | Multivariate Scan Statistics for Disease Surveillance[END_REF]) and [START_REF] Greene | Gastrointestinal Disease Outbreak Detection Using Multiple Data Streams from Electronic Medical Records[END_REF]). Different methods exist for the aggregation of data sources, but the two main approaches are the reduction method and the parallel method [START_REF] Frisén | Evaluation of multivariate surveillance[END_REF][START_REF] Sonesson | Multivariate Surveillance[END_REF]. The reduction method considers several variables that are reduced to a single statistic, using for example the sum for each time period, p-value aggregation [START_REF] Roure | A study into detection of bio-events in multiple streams of surveillance data[END_REF], or multivariate control charts [START_REF] Macgregor | Statistical process control of multivariate processes[END_REF][START_REF] Stoto | Evaluating statistical methods for syndromic surveillance[END_REF]). The parallel method uses multiple univariate systems which are then assessed in parallel. An alarm is triggered if any of the univariate systems gives an alarm (e.g., (Fan et al. 2014, Schiöler and[START_REF] Schiöler | Multivariate outbreak detection[END_REF]). The reduction approach gives a better detection performance when all changes occur simultaneously in the different processes under consideration. When the changes occur separately, the parallel approach yields better results [START_REF] Frisén | Evaluation of multivariate surveillance[END_REF].

In this section, we consider a multivariate syndromic surveillance system applied to the detection of West Nile virus outbreaks. WNV typically affects different hosts, which makes it a particularly interesting case in determining if multivariate surveillance can improve outbreak detection. To combine the different variables, we used a reduction method based on a Bayesian approach.

This work resulted in a scientific paper submitted to Vector-borne and zoonotic diseases (see below for the main text).

INTRODUCTION

West Nile virus (WNV) is a mosquito-borne arbovirus mainly transmitted by mosquitoes from the genus Culex (family Culicidae). Its main hosts are birds but the virus also affects various non-avian species including horses and humans, with dramatic consequences for public health and for the equine industry, i.e. potentially fatal encephalitis in humans and horses [START_REF] Campbell | West Nile Virus[END_REF][START_REF] Castillo-Olivares | West Nile virus infection of horses[END_REF]. In Europe, WNV emerged in the 1960s and several outbreaks have been documented since that time [START_REF] Calistri | Epidemiology of West Nile in Europe and in the Mediterranean Basin[END_REF]. Even if the virus is now considered endemic in a large part of Europe, the number of reported outbreaks is presently increasing in southern and eastern Europe, particularly in Italy, Greece, and Bulgaria (Di [START_REF] Sabatino | Epidemiology of West Nile Disease in Europe and in the Mediterranean Basin from 2009 to 2013[END_REF]. This increasing number of outbreaks, combined with the recent introduction and spread in Europe of WNV lineage 2, which induces severe symptoms in humans, horses, and birds [START_REF] Bakonyi | Lineage 1 and 2 Strains of Encephalitic West Nile Virus, Central Europe[END_REF][START_REF] Calzolari | New Incursions of West Nile Virus Lineage 2 in Italy in 2013: The Value of the Entomological Surveillance as Early Warning System[END_REF][START_REF] Hernández-Triana | Emergence of West Nile Virus Lineage 2 in Europe: A Review on the Introduction and Spread of a Mosquito-Borne Disease[END_REF], has resulted in growing concern about WNV in Europe. In addition, the implementation of prevention plans for WNV outbreaks is difficult [START_REF] Zeller | West Nile Virus: The Need to Strengthen Preparedness in Europe[END_REF] because the environmental factors and meteorological interactions underlying the increase in WNV circulating in mammals are still poorly understood. To improve early detection of WNV outbreaks, then, the major challenge is to develop more integrated and quantitative approaches [START_REF] Beck | Flaviviruses in Europe: Complex Circulation Patterns and Their Consequences for the Diagnosis and Control of West Nile Disease[END_REF]Bellini et al. 2014b).

Syndromic surveillance is currently a popular approach for the early detection of health-related phenomena [START_REF] Dórea | Veterinary syndromic surveillance: Current initiatives and potential for development[END_REF]) and has already been implemented for WNV. In Europe, the surveillance of nervous syndromes in horses has been shown to detect early indicators of WNV outbreaks (Leblond et al. 2007;[START_REF] Saegerman | Clinical Sentinel Surveillance of Equine West Nile Fever, Spain[END_REF] and is one of the most cost-effective surveillance systems in the European context [START_REF] Chevalier | West Nile Virus in Europe: A Comparison of Surveillance System Designs in a Changing Epidemiological Context[END_REF]). In the USA, instead, increased mortality in wild birds is one of the most timely indicators of virus activity [START_REF] Brown | California Mosquito-borne Virus Surveillance & Response Plan[END_REF]. Mortality in wild birds had rarely been reported in Europe until the recent explosive spread of lineage 2 in 2008-2009 in Hungary and Austria, which suggests that this parameter could be also incorporated into future monitoring systems in Europe [START_REF] Bakonyi | Explosive spread of a neuroinvasive lineage 2 West Nile virus in Central Europe, 2008/2009[END_REF]. This is consistent with recent experimental infections of European wild birds with various WNV strains, which generated an average mortality rate of 43% (Del Amo et al. 2014a;Del Amo et al. 2014b;[START_REF] Dridi | Experimental infection of Carrion crows (Corvus corone) with two European West Nile virus (WNV) strains[END_REF][START_REF] Sotelo | Pathogenicity of two recent Western Mediterranean West Nile virus isolates in a wild bird species indigenous to Southern Europe: the red-legged partridge[END_REF][START_REF] Ziegler | Pathogenesis of West Nile Virus Lineage 1 and 2 in Experimentally Infected Large Falcons[END_REF]. Apart from mortality in wild birds and nervous symptoms in horses, WNV is also associated with mortality in horses, which could constitute another signal of a WNV outbreak. Combining all available information in a multivariate algorithm should give better results for outbreak detection than univariate methods alone. However, at the time of writing, multivariate syndromic surveillance has never been implemented for the detection of WNV outbreaks.

The aim of our study was to evaluate the performance of a multivariate syndromic surveillance system in detecting WNV using three datasets: nervous syndromes in horses and mortality in horses and wild birds.

We focused on the French Mediterranean coast, which is a particularly high-risk area for WNV outbreaks.

Indeed, in France, WNV has only ever been identified in this area, which is home to mammalian and avian hosts, bridging vectors, and large protected wetlands with numerous migratory birds.

MATERIALS AND METHODS

Data sources

Nervous syndromes in horses

Data on nervous syndromes in horses are collected through the passive surveillance system "RESPE". This

Mortality in horses

Data on mortality in horses have been centralized since 2010 in the "EDI-SPAN" database, managed by all the French fallen stock companies and the French Ministry of Agriculture [START_REF] Perrin | Assessment of the utility of routinely collected cattle census and disposal data for syndromic surveillance[END_REF]). As WNV does not produce perinatal mortality, we only considered the 8 742 dead adult horses collected around the French Mediterranean coast between 2010 and 2014. The time series of mortality in adult horses is designated DeadHorse in subsequent sections.

Mortality in wild birds

Data on mortality in wild birds are collected through the event-based surveillance system "SAGIR", the national French surveillance network of diseases in wild birds and mammals, which collects declarations from field workers (e.g., hunters, technicians from departmental hunting federations, and environmental inspectors from the French National Hunting and Wildlife Agency (ONCFS)). Surveillance relies on diagnosis at a local veterinary laboratory [START_REF] Decors | Le réseau Sagir: un outil de vigilance vis-à-vis des agents pathogènes exotiques[END_REF]. Between 2007 and 2013, 292 dead wild birds were collected and necropsied around the French Mediterranean coast. The time series of the number of necropsied wild birds is designated DeadBird in subsequent sections.

Data modeling and simulation

Baselines

All time series were aggregated weekly. Using visual examination, abnormal peaks were observed only in Dynamic regression was performed with the functions glm (package {stats}) and glm.nb (package {MASS}).

The expected number of counts at time t was estimated with the predict functions of the respective packages.

Models were evaluated using the Akaike information criterion (AIC) [START_REF] Bozdogan | Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions[END_REF], and the adjusted deviance (deviance/degree of freedom) was used as a measure of goodness-of-fit (GOF). The agreement between predicted and observed values was assessed according to the root-mean-squared error [START_REF] Chai | Root Mean Square Error (RMSE) or Mean Absolute Error (MAE)? -Arguments against Avoiding RMSE in the Literature[END_REF]. The criterion was assessed within the calibration period (RMSE c ) and within the validation period (RMSE v ). In either case, the lower the value, the better the predictive performance of the model.

For each time series, the best regression model was used to predict the expected value of each week of the next simulated year. Distribution of cases for each week was defined as a Poisson distribution with lambda equals to the predicted value for the same week. Weekly samples from 100 fictive years were generated by random sampling from the previous distributions as proposed by Dórea et al. (Dórea et al. 2013a).

WNV outbreaks

Data on real WNV outbreaks are scarce, so we thus used simulated outbreaks to evaluate our detection system. For each syndrome, the distribution of the number of cases during an outbreak was estimated with the fitdist function of the package {fitdistrplus}. Time series for each syndrome during 100 fictive outbreaks were simulated by randomly sampling the corresponding distribution. One simulated outbreak was inserted in each simulated baseline. The outbreaks related to nervous cases in horses were randomly inserted, followed by the corresponding outbreaks related to wild bird mortality, such that the time lag between the first dead bird and the first nervous case in horses due to WNV was 0, 1, or 2 weeks [START_REF] Kulasekera | West Nile virus infection in mosquitoes, birds, horses, and humans, Staten Island, New York[END_REF]. The corresponding horse mortality outbreaks were inserted such that half of the affected horses died the week of onset of clinical signs and half died the week after [START_REF] Bunning | Experimental infection of horses with West Nile virus[END_REF][START_REF] Cantile | Clinical and Neuropathological Features of West Nile Virus Equine Encephalomyelitis in Italy[END_REF][START_REF] Trock | West Nile virus outbreak among horses in New York State, 1999 and 2000[END_REF][START_REF] Ward | Characteristics of an outbreak of West Nile virus encephalomyelitis in a previously uninfected population of horses[END_REF].

The weekly counts of cases of five real European WNV outbreaks (Anonymous 2007;[START_REF] Autorino | West Nile virus Epidemic in Horses, Tuscany Region, Italy[END_REF][START_REF] Kutasi | Equine Encephalomyelitis Outbreak Caused by a Genetic Lineage 2 West Nile Virus in Hungary: Lineage 2 West Nile Virus Encephalomyelitis[END_REF][START_REF] Leblond | West Nile Virus Outbreak Detection Using Syndromic Monitoring in Horses[END_REF][START_REF] Murgue | West Nile outbreak in horses in southern France, 2000: the return after 35 years[END_REF] were fitted to the NB distribution and the resulting distribution of the additional number of nervous cases due to WNV during an outbreak was NB(mu=3.12, theta=1.150). The mortality among horses clinically affected by WNV was fitted to a normal distribution (mean=0.384, standard deviation=0.128) based on [START_REF] Autorino | West Nile virus Epidemic in Horses, Tuscany Region, Italy[END_REF][START_REF] Leblond | West Nile Virus Outbreak Detection Using Syndromic Monitoring in Horses[END_REF][START_REF] Murgue | West Nile outbreak in horses in southern France, 2000: the return after 35 years[END_REF][START_REF] Ward | Characteristics of an outbreak of West Nile virus encephalomyelitis in a previously uninfected population of horses[END_REF]). The NervSy dataset did not provide the real number of clinically affected horses, so we assumed that only 50% of horses with nervous symptoms were declared to RESPE.

To estimate the real number of clinically affected horses, we simulated RESPE declarations of nervous symptoms associated with 100 WNV outbreaks and doubled the counts of horses obtained. The related weekly count of dead adult horses was then deduced and fitted to the NB distribution NB(mu=3, theta=2.005). The distribution of the weekly number of dead birds was estimated by expert opinion to be NB(mean=2.23,theta=3.34).

Outbreak detection

Bayesian framework

Bayesian hypothesis testing is based on two mutually exclusive hypotheses which can be expressed in the syndromic surveillance context as H 1, "there is an ongoing outbreak of WNV (or another disease with similar symptoms)", and H 0 , "there is no ongoing outbreak" [START_REF] Andersson | Using Bayes' Rule to Define the Value of Evidence from Syndromic Surveillance[END_REF]. The relative probability of the two hypotheses can be expressed as a ratio (O pri ) which represents our a priori belief about the disease status:

Eq.1

When evidence in favor (or not) of each hypothesis is observed, we can build the a posteriori belief about the disease's status (O post ):

Eq.2

where P(H 1 |E x ) is the probability of H 1 given the evidence E observed in time series x and P(H 0 |E x ) is the probability of H 0 given the evidence E observed in time series x.

Using this general framework with the application of Bayes' theorem, O post can be calculated as:

Eq.3 where V x is the value of evidence, P(E x |H 1 ) is the probability of observing the number of reported cases of syndrome x in a particular week given that H 1 is true, and P(E x |H 0 ) is the probability of observing the number of reported cases of syndrome x in a particular week given that H 0 is true.

In order to estimate P(E x |H 1 ) and P(E x |H 0 ), information on the probability distribution for the number of reported cases in non-outbreak and outbreak situations is used. The probability of E x (observation of n cases in time series x) during an outbreak is calculated as:

Eq.4

where P base (i) is the probability of drawing i cases from the baseline distribution in time series x and P out (i) is the probability of drawing i cases from the outbreak distribution in time series x based on the shape of the outbreak, as previously simulated.

) (

) ( 0 1 H P H P O pri  ) | ( ) | ( 0 1 x x pos t E H P E H P O  ) ( ) ( ) | ( ) | ( 0 1 0 1 H P H P H E P H E P O V O x x pr i x pos t          n i out base x i n P i P H E P 0 1 ) ( ) ( ) | (

Combining time series

When the three time series were combined, V tot incorporated evidence from NervSy, DeadHorse, and DeadBird, respectively denoted as E NervSy , E DeadHorse , and E DeadBird . Assuming that the three sources of evidence were independent, V tot was calculated as: Eq.5 and O post_tot was calculated as:

Eq.6

Performance assessment

Sensitivity (Se) and specificity (Sp) were calculated as: Eq.7 Se = TP / (TP+ FN)

Eq.8 Sp = TN / (TN + FP)

where TP is the number of true positive alarms, TN the number of true negative alarms, FP the number of false positive alarms, and FN the number of false negative alarms.

The receiver operating characteristic (ROC) curve was generated in R by testing various alarm thresholds, and the areas under the curves (AUC) were calculated with the auc function of the package {flux}. A larger AUC represented a better detection performance.

RESULTS

Modeling time series and simulating data

For all time series the best fits were obtained for NB distributions. The resulting models' parameters are summarized in table 1 and corresponding baselines and predictions are shown in figure 1. The probabilities of observing n cases and the resulting value of V (p(E|H 1 )/ p(E|H 0 )) during a non-outbreak (p(E|H 0 )) and an outbreak (p(E|H 1 )) situation for each time series are summarized in figure 2.

Outbreak detection

We estimated the respective performance of each univariate system (NervSy, DeadHorse, and DeadBird)

in
V V V H E E E P H E E E P V     ) | , , ( ) | , , ( 0

  

detection performances whereas models using DeadHorse were not able to discriminate between outbreak and non-outbreak situations (AUC≈0.50).

The best results for multivariate outbreak detection were obtained for analyses that combined NervSy with DeadBird data, which gave similar results to a combination of the three time series (figure 3 andtable 2). The results of using NervSy combined with DeadBird were also better than those obtained with each time series alone. For example, for a specificity set at 0.80, the sensitivity of the detection reached 0.80 with the combined NervSy and DeadBird series whereas it was 0.67 with NervSy and 0.60 with DeadBird alone.

DISCUSSION

Our results indicated that the best detection performance was obtained using multivariate syndromic surveillance based on reports of nervous symptoms in horses (NervSy) and wild bird mortality (DeadBird).

To our knowledge, this is the first time that multivariate syndromic surveillance has been implemented for WNV detection. However, when using a univariate detection method, NervSy was the best indicator of WNV outbreaks. This is consistent with the number of expected cases during an outbreak compared to the baseline of each time series considered (i.e. high number of case for NervSy, moderate number of cases for DeadBird, and low number of cases for DeadHorse). Indeed, models based only on the DeadHorse data resulted in poor detection performance at the regional level because mortality in horses is mainly due to causes other than WNV. However, before ruling on the usefulness of this datasource for WNV surveillance, it would be interesting to test whether an outbreak generates local clusters of deaths in horses that may be used as a signal of a VNW outbreak. However, the quality of geographical information of reported cases are currently insufficient to test this hypothesis. This is the first time that a real assessment of system performance has been implemented for WNV surveillance. Previous early warning systems developed for WNV only identified risk factors of WNV outbreaks, but did not evaluate the detection performances of those systems [START_REF] El Adlouni | Effects of climate on West Nile Virus transmission risk used for public health decision-making in Quebec[END_REF]Bellini et al. 2014a;[START_REF] Brown | California Mosquito-borne Virus Surveillance & Response Plan[END_REF][START_REF] Chaskopoulou | Detection and Early Warning of West Nile Virus Circulation in Central Macedonia, Greece, Using Sentinel Chickens and Mosquitoes[END_REF][START_REF] Gosselin | The Integrated System for Public Health Monitoring of West Nile Virus (ISPHM-WNV): a real-time GIS for surveillance and decision-making[END_REF][START_REF] Rosà | Early warning of West Nile virus mosquito vector: climate and land use models successfully explain phenology and abundance of Culex pipiens mosquitoes in northwestern Italy[END_REF][START_REF] Shuai | A GIS-driven integrated real-time surveillance pilot system for national West Nile virus dead bird surveillance in Canada[END_REF][START_REF] Valiakos | Use of Wild Bird Surveillance, Human Case Data and GIS Spatial Analysis for Predicting Spatial Distributions of West Nile Virus in Greece[END_REF]). Timeliness has occasionally been evaluated but only based on a limited number of real WNV outbreaks, and has not been associated with a further assessment of system performance [START_REF] Calzolari | New Incursions of West Nile Virus Lineage 2 in Italy in 2013: The Value of the Entomological Surveillance as Early Warning System[END_REF][START_REF] Chaintoutis | Evaluation of a West Nile virus surveillance and early warning system in Greece, based on domestic pigeons[END_REF][START_REF] Eidson | Dead bird surveillance as an early warning system for West Nile virus[END_REF][START_REF] Johnson | Geographic Prediction of Human Onset of West Nile Virus Using Dead Crow Clusters: An Evaluation of Year 2002 Data in New York State[END_REF][START_REF] Mostashari | Dead Bird Clusters as an Early Warning System for West Nile Virus Activity[END_REF][START_REF] Veksler | Assessment of methods for prediction of human West Nile virus (WNV) disease from WNV-infected dead birds[END_REF]. Only two attempts to assess the sensitivity and specificity of surveillance have been made [START_REF] Andersson | Using Bayes' Rule to Define the Value of Evidence from Syndromic Surveillance[END_REF][START_REF] Leblond | West Nile Virus Outbreak Detection Using Syndromic Monitoring in Horses[END_REF]) but the parameters of interest were only evaluated based on a limited number of outbreaks, which did not allow any conclusions to be drawn regarding overall system performance.

To assess the surveillance systems and compare them, we simulated baselines and outbreaks using parameters from data observed in Europe (Anonymous 2007; [START_REF] Autorino | West Nile virus Epidemic in Horses, Tuscany Region, Italy[END_REF][START_REF] Bakonyi | Explosive spread of a neuroinvasive lineage 2 West Nile virus in Central Europe, 2008/2009[END_REF][START_REF] Leblond | West Nile Virus Outbreak Detection Using Syndromic Monitoring in Horses[END_REF][START_REF] Ward | Characteristics of an outbreak of West Nile virus encephalomyelitis in a previously uninfected population of horses[END_REF]. To expand upon this, patterns of outbreaks in other locations should be tested in order to evaluate the performance of multivariate syndromic surveillance in more varied situations. Particular attention should be paid to patterns of mortality of wild birds, as the dynamics of wild bird mortality during a WNV outbreak have only been poorly investigated in Europe.

The Bayesian approach seems well adapted for multivariate WNV detection and can be used for other diseases. Indeed, Bayesian hypothesis testing is based on two mutually exclusive hypotheses which can be expressed in the syndromic surveillance context as: H 1 , "there is an ongoing outbreak of WNV or of another disease with similar symptoms", and H 0 , "there is no ongoing outbreak". It would be theoretically possible to include every possible differential diagnosis for every syndrome (or group of syndromes) considered; however, such a system would be difficult to implement and maintain. It would thus be interesting to first examine the evidence from each time series individually and then together in order to identify which combination of datasets results in the strongest signal. It would be up to the relevant decision maker in a given situation to consider appropriate differential diagnoses and the actions that should be implemented for further investigation.

In our study, we considered three sources of evidence for WNV outbreak detection. Nevertheless, additional information can be utilized with Bayesian approaches, as it is easy to add such information.

Then, a next step in the early detection of WNV outbreaks should be to test the efficiency of the method with other data, such as the predicted abundance of mosquitoes [START_REF] Calistri | A Transitional Model for the Evaluation of West Nile Virus Transmission in Italy[END_REF][START_REF] Rosà | Early warning of West Nile virus mosquito vector: climate and land use models successfully explain phenology and abundance of Culex pipiens mosquitoes in northwestern Italy[END_REF], environmental risk factors [START_REF] Tran | Environmental predictors of West Nile fever risk in Europe[END_REF], and probability of introduction [START_REF] Bessell | Quantifying the Risk of Introduction of West Nile Virus into Great Britain by Migrating Passerine Birds[END_REF][START_REF] Brown | California Mosquito-borne Virus Surveillance & Response Plan[END_REF].

CONCLUSION

The proposed approach is suitable for performing multivariate syndromic surveillance of WNV outbreaks. Indeed, we found that a multivariate surveillance system using this approach performed better than a univariate approach in detecting WNV outbreaks in southern France. In particular, a combination of data regarding nervous symptoms in horses and wild bird mortality was the most efficient in detecting outbreaks. Such multivariate surveillance systems could be especially useful in serving as early warnings for possible human viral infections, considering that horses and birds are affected by WNV before humans [START_REF] Kulasekera | West Nile virus infection in mosquitoes, birds, horses, and humans, Staten Island, New York[END_REF][START_REF] Leblond | West Nile Virus Outbreak Detection Using Syndromic Monitoring in Horses[END_REF]. We propose that this methodology is generally applicable to other diseases for which multiple sources of evidence are available.

B. COMBINING QUANTITATIVE RISK ASSESSMENT AND SYNDROMIC SURVEILLANCE

Introduction

Risk assessment and syndromic surveillance can both indicate the possibility of a newly introduced epidemic but they do not prove the presence of the disease. Specifically, both approaches provide different risk estimations. Risk assessment identifies the respective probabilities of pathogen entry and establishment according to season and local environment. Syndromic surveillance determines the probability that an outbreak is in progress based on field observations. Combining both approaches will thus result in a posterior probability which should improve confidence in the prediction of an outbreak of a newly introduced VBD. The posterior probability is calculated according to Figure 15.

Figure 15: Combining syndromic surveillance and probability of disease introduction to obtain a posterior probability that there is an ongoing outbreak.

In particular, this approach can be useful for exotic diseases with few and unspecific symptoms. Indeed, veterinary practitioners are rarely able to detect such diseases and syndromic surveillance might be useful in enhancing the passive reporting system. However, the incidence of under-reporting is also expected to be high, which compromises the ability of syndromic surveillance to detect disease. Adding prior information on the probability of disease introduction can improve the detection of such diseases.

Among exotic diseases, equine encephalosis (EE) typically causes unspecific symptoms that are quite hard to detect, as illustrated by the example of Israel, where the disease was present for at least 10 years before it was first officially reported [START_REF] Wescott | Evidence for the Circulation of Equine Encephalosis Virus in Israel since 2001[END_REF]. In this study we combined syndromic surveillance with information on the probability of disease introduction in order to improve early detection of a potential EE outbreak.

This work will result in a scientific paper in preparation and we only present here preliminary results: Mats Gunnar Andersson*, Egil Andreas Joor Fischer* + , Céline Faverjon, Jörn Gethmann, Maya Gussmann, Yves Probability of disease entry Probability of disease establishment

Probability of disease introduction

Relative risk of ongoing outbreak according to syndromic surveillance Posterior probability van der Stede, Petter Hopp, René Bødker, Agnès Leblond. (2015). A joint risk score method for risk-based surveillance of vector-borne animal diseases. Manuscript in preparation

Material and Methods

Bayesian framework

The analyses were performed with weekly data using counts from a grid in France which consisted of 943 cells of 25x25 kilometers each.

To provide a comprehensive and single indicator of risk, we used spatiotemporal extension of the empirical Bayes' approach presented in previous sections (see Chapter III.C and Chapter IV.B). Bayesian hypothesis testing is based on two mutually exclusive hypotheses which can be expressed in the syndromic surveillance context as: H 1 , "there is an ongoing outbreak of EE (or another disease with similar symptoms) in grid cell g during week w" and H 0 , "there is no ongoing outbreak in grid cell g during week w" [START_REF] Andersson | Using Bayes' Rule to Define the Value of Evidence from Syndromic Surveillance[END_REF]. The relative probability of the two hypotheses can be expressed as a ratio (O pri ) that represents our a priori belief about the disease status:

) ( ) ( 0 1 H P H P O pri 
The probabilities of H 1 and H 0 were estimated based on the spatiotemporal quantitative model for the assessment of the probability of EE introduction developed in Chapter II.C. The value of evidence (V) was estimated using syndromic surveillance data. The main symptoms of EE in horses are respiratory and nervous symptoms [START_REF] Dhama | Equine encephalosis virus (EEV): A Review[END_REF]; we thus considered these two sources of data (NervSy and RespSy, respectively). We supposed both datasets to be independent and describe them in the next section. The corresponding value of evidence (V) was calculated as:

) | , ( ) | , ( ) | ( ) | ( ) | ( ) | (

  

where P(E X |H 1 ) is the probability of observing the number of reported cases of syndrome X in a particular week in a particular grid cell given that H 1 is true, and P(E X |H 0 ) is the probability of observing the number of reported cases of syndrome X in a particular week in a particular grid cell given that H 0 is true.

The a posteriori belief about the disease's status for each week and each grid cell (O post ) takes into account both the probability of disease introduction and the results of syndromic surveillance and was calculated as in (Faverjon et al. 2015a):

pri spSy NervSy spSy NervSy post O V E E H P E E H P O    ) , | ( ) , | ( Re 0 Re 1

Simulated EE outbreaks

Two outbreaks were simulated to test our model: one in Aquitaine, and another in Normandy. These regions were selected due to their large equine population. No spatiotemporal description of EE outbreaks is currently available, so we used other, indirect, information to estimate the number of expected cases and the spatiotemporal evolution of an EE outbreak.

First, we assumed that 80% of the susceptible population would be infected, based on the estimated prevalence of EE in the initial serological data from Israel in 2001 [START_REF] Wescott | Evidence for the Circulation of Equine Encephalosis Virus in Israel since 2001[END_REF]. To obtain the number of horses showing clinical signs for EE, we supposed that around 40% of the infected horses would show clinical signs and, of these, 90% would be respiratory symptoms and 10% neurological symptoms [START_REF] Aharonson-Raz | Isolation and Phylogenetic Grouping of Equine Encephalosis Virus in Israel[END_REF]. We then presumed that 25% of respiratory cases and 50% of neurological cases would be declared to RESPE. In the end, we estimated that, during an EE outbreak, the percentage of horses with respiratory or nervous symptoms due to EE and declared to RESPE was 7% and 1.6%, respectively, of the general equine population located in an area.

To obtain the distribution of horses that showed clinical signs per week, we used data collected during African Horse Sickness (AHS) outbreaks, because EE and AHS are very similar and share the same transmission patterns [START_REF] Dhama | Equine encephalosis virus (EEV): A Review[END_REF][START_REF] Lord | Transmission patterns of African horse sickness and equine encephalosis viruses in South African donkeys[END_REF]. Specifically, we used data from outbreaks in Western Cape in [START_REF] Cochrane | Effectiveness and efficiency: Random reflections on health services[END_REF], 2004, and 2011(Anonymous 2011;;[START_REF] Sinclair | An epidemiological investigation of the African horsesickness outbreak in the Western Cape Province of South Africa in 2004 and its relevance to the current equine export protocol[END_REF]). These outbreaks occurred in an area of South Africa that is under surveillance designed to act as an early warning system, but which lacks systematic vaccination campaigns performed to protect the free zone. Nevertheless, the number of vaccinated horses is considered to be high in this area [START_REF] Sinclair | An epidemiological investigation of the African horsesickness outbreak in the Western Cape Province of South Africa in 2004 and its relevance to the current equine export protocol[END_REF], which probably reduced the size of the outbreaks compared to a situation in which all horses are susceptible.

To estimate the spatial propagation of EE for the outbreak in "Aquitaine", we used the first six weeks of location data from a BTV-1 outbreak in southern France, as both viruses share the same vector, Culicoides [START_REF] Venter | A Comparison of the Vector Competence of the Biting Midges, Culicoides (Avaritia) Bolitinos and C. (A.) Imicola, for the Bryanston Serotype of Equine Encephalosis Virus[END_REF]. For the outbreak in "Normandy", we assumed that the spread of an EE outbreak would be similar in velocity to that observed during the last BTV-8 outbreak in France: from an index case, the outbreak gained around 10 kilometers per week (Pioz et al. 2008), with 50% of new cases occurring less than 5 km from the closest infected animal, and 95% within a radius of 31 km of the closest infected animal [START_REF] Hendrickx | A wind density model to quantify the airborne spread of Culicoides species during north-western Europe bluetongue epidemic, 2006[END_REF]. The distribution of cases has been made according to local equine population using data provided by IFCE-SIRE.

The spatiotemporal progression of the outbreak in Aquitaine is presented in Figure 16, while the outbreak in Normandy is available in Appendix 11.

Probability of EE introduction 2.3.1. Data source

To define our a priori belief about the disease status (O pri ), we reused the spatiotemporal quantitative model that was developed in Chapter II.C to assess EE introduction. The model served as a basis for estimations of the probability of disease entry and the probability of disease establishment. The spatiotemporal model of EE introduction uses monthly data at the regional scale (22 regions) for three consecutive years (2010, 2011, and 2012).

Data transformation

To transform the monthly and regional data into weekly, grid-based data, we assumed that the monthly regional probabilities of virus introduction were uniformly distributed in space and time within a given region and for a given month. The weekly probability of virus release in a grid cell, 𝑃(𝑖𝑛𝑡𝑟𝑜 𝑤𝑥 ), is thus defined for both routes of introduction as:

𝑃(𝑖𝑛𝑡𝑟𝑜 𝑤𝑔 ) = 1 -(1 -𝑃(𝑖𝑛𝑡𝑟𝑜 𝑘𝑚 )) 1 𝑤𝑒𝑒𝑘 𝑚 * 𝑔𝑟𝑖𝑑 𝑘
where w belongs to month m, g belongs to region k, week m equals the number of weeks in month m, grid k equals the number of grid cells in region k, and 𝑃(𝑖𝑛𝑡𝑟𝑜 𝑘𝑚 ) is the monthly regional probability of virus introduction via an infectious host or vector.

The probability of introduction sometimes equaled zero, due to a lack of importation or to a null probability of virus circulation in exporting countries. When combining this zero probability with the syndromic surveillance model, the final output was thus zero as well. We adopted a conservative approach and assumed that there is always a slight probability of virus introduction and transmission; we thus chose to replace these zero probabilities of introduction with a value equal to 10% of the lowest calculated probability of introduction.

Syndromic surveillance of EE

Data sources

To define the value of evidence (V), two types of syndromes were considered: nervous symptoms and respiratory symptoms in horses. Both sets of related data are collected by RESPE and have already been used and presented in Chapter III.C. The datasets without positive laboratory diagnoses were used to obtain an outbreak-free dataset. Syndromic surveillance data collected by RESPE are available on a daily basis and at the municipal level from 2006 to 2013.

Spatiotemporal detection

The algorithm used for spatiotemporal detection of clusters of cases was developed and implemented by Gunnar Andersson (SVA, Sweden) within the framework of the EMIDA-VICE European project [START_REF] Andersson | A joint risk score method for risk-based surveillance of vector-borne animal diseases[END_REF]. Briefly the seasonal variation of each syndrome/symptom, under outbreak-free conditions was first modelled for France as a whole. The probability distribution of the number of reported syndromes/symptoms around each grid-cell was subsequently modelled using the expected number of cases per host, and local host density as input. The host population horse population around each grid cell was based on data at commune level provided by IFCE-SIRE (IFCE -les Haras nationaux 2011)).

Presentation of the concept and first feedback

To evaluate and receive feedback on the proposed approach, the concept was presented during a two-day workshop organized by the EMIDA-VICE project in Paris in February 2015. Fourteen people not included in the VICE project from eight countries and one person representing EFSA were present. The participants were from research centers, state agencies, or veterinary services, and were all involved in surveillance (data collection and management), risk assessment, and/or risk management.

In addition to the general approach, we also presented the EE example. Practical exercises were provided to the participants to facilitate their understanding of the concept. Their comments and suggestions on the concept and method were collected.

Results

Multivariate syndromic surveillance

Models that made use of both syndromes (neurological and nervous) discriminated better between outbreak and non-outbreak situations than those that considered symptoms separately (see Figure 17).

Combining Risk assessment

The combination of the probability of disease introduction with syndromic surveillance results is presented in Figure 18. The results for the outbreak in Normandy are presented in Appendix 12.

In both cases, combining prior information on the probability of disease introduction (O pri ) with a multivariate syndromic surveillance system (V) allowed us to i) highlight a small number of cases occurring in an area at high probability for disease introduction, and ii) diminish the significance of a large number of cases occurring in an area at low probability for disease introduction.

Workshop output

The workshop organized by the EMIDA-VICE project presented our approach and the EE example to fourteen participants from eight European countries. The main conclusion of the workshop was that the approach was of great interest for combining different risk assessments. The participants highlighted the wide range of opportunities offered by this tool, but were of the opinion that this approach would mainly be used to increase awareness, rather than to implement active surveillance. Indeed, for the participants, the approach was helpful for demonstration and should facilitate risk communication (in particular when different scenarios are tested). The main constraint to the implementation of this approach was, according to the participants, the current lack of relevant and accurate data.

Despite these advantages, the approach also appeared quite complicated, and the participants advocated for the automatic generation of output, a user-friendly interface, a list of requirements to run the system, and an easy-to-use manual. Other criticisms were that the assumptions were not sufficiently explicit and the uncertainty was not displayed, which complicated the understanding and interpretation of results. The participants also advocated for the development of sensitivity and cost-efficiency analyses for this approach.

Week

Discussion and Conclusion

The results presented are only preliminary but they provide a good example of the concept. In this example, the approach was applied to detect a known disease (equine encephalosis), but it also presents multiple other opportunities. Indeed, any kind of prior knowledge can be used and thus the approach could also be implemented for diseases about which not a great deal is known a priori. Moreover, it can be used not only in the context of risk assessment, but also in that of risk management. For example, the approach can be used to test different risk scenarios and increase awareness, and thus support decisionmaking. It is particularly adapted for use in decision-making because it can be easily combined with decision theory, as presented in [START_REF] Andersson | Using Bayes' Rule to Define the Value of Evidence from Syndromic Surveillance[END_REF].

The feedback from the EMIDA-VICE workshop emphasized the potential of our approach but also highlighted a limitation to its practical implementation: the lack of relevant and accurate data. . Indeed, the approach requires a large amount of data (regarding, e.g., import of animals, temperature, vector abundances, declarations from veterinarians), which are currently very rarely available all together. At the European scale, at the time of writing, there is no agreement on data format or on the definition of terms, especially in syndromic surveillance. Current initiatives to collect and analyze data are thus rarely transferable between EU countries and the results of these programs are not comparable to each other.

Further efforts should be made to homogenize data collection and the definition of terms at the European level in order to facilitate the widespread use of the results of the different existing surveillance systems.

However, even if the lack of data is a concern, Bayesian framework allows us to deal with missing data by combining expert opinion with data driven models. The lack of relevant and accurate data is thus not a fundamental limitation of the approach.

In this study, the example of equine encephalosis served mainly to illustrate our concept. That is why we only considered a simple approach for outbreak detection. However, this approach had some limits. In particular, we assumed that the population at risk remained stable over time, and we detected clusters of cases based on the size of this baseline population. This assumption can be questioned, particularly regarding horses, which travel frequently and for which no accurate data exist on numbers and geographical localization. Other methods of cluster detection should be tested (for a summary of the main statistical methods available for testing clusters in space, time and space, and time*space (interaction), see the review by T. Carpenter [START_REF] Carpenter | Methods to investigate spatial and temporal clustering in veterinary epidemiology[END_REF]) and other detection parameters should be also considered to optimize outbreak detection. In particular regarding detection parameters, radius' size on outbreak detection, temporal units of detection and potential interactions among cluster parameters [START_REF] Olson | Real time spatial cluster detection using interpoint distances among precise patient locations[END_REF][START_REF] Ozonoff | Effect of Spatial Resolution on Cluster Detection: A Simulation Study[END_REF]. From the perspective of a real outbreak detection system, all these parameters should be carefully investigated and their appropriate values determined, in collaboration with decision makers, according to the objective of the surveillance and to the disease considered. Moreover, in this example we used respiratory and nervous symptoms observed in horses, but it could be interesting to evaluate other symptoms, such as spontaneous abortions, which are often present during EE outbreaks [START_REF] Dhama | Equine encephalosis virus (EEV): A Review[END_REF]. Testing combinations of other symptoms would thus be an important part of optimizing outbreak detection.

Using a Bayesian approach for combining evidence is not new, but it is still rarely implemented in disease surveillance. To our knowledge, there are only a few examples in the literature of this kind of data combination in disease surveillance. We can cite the work of Gustafson and colleagues [START_REF] Gustafson | Combining Surveillance and Expert Evidence of Viral Hemorrhagic Septicemia Freedom: A Decision Science Approach[END_REF], which proposed using the likelihood ratio to combine expert opinion with surveillance data in surveys of viral hemorrhagic septicemia, but the work of Burkom and colleagues [START_REF] Burkom | An Integrated Approach for Fusion of Environmental and Human Health Data for Disease Surveillance[END_REF]) is perhaps closer to our concept (i.e. combining health surveillance data and environmental sensors for monitoring waterborne diseases). Bayesian approaches are thus still new in disease surveillance and offer great opportunities, but, as highlighted during our workshop, further work must also be conducted. In particular, a full assessment of the tool is fundamental in order to know more about its sensitivity and reliability. Moreover, further developments should focus on making our approach more comprehensive and user-friendly, or it will likely not be adopted by decision-makers and other participants in disease surveillance.

C. DISCUSSION AND CONCLUSION

Discussion

The complementary approaches used in this chapter (i.e. multivariate syndromic surveillance and the combination of probability of introduction with syndromic surveillance) were both effective in providing a better estimation of the probability of an ongoing outbreak compared to estimates based on a single probability estimation. Similar methods are nonetheless rarely implemented in veterinary public health.

Multivariate syndromic surveillance is still a new approach and, at the time of writing, it has been reported from only one initiative in this field [START_REF] Höle | Statistical approaches to the surveillance of infectious diseases for veterinary public health[END_REF]), which used multivariate CUSUMs for rabies surveillance. Instead, combining syndromic surveillance with quantitative risk assessment is a completely innovative concept and, to date, no similar approach has been presented in the veterinary public health literature.

Multivariate risk assessment is heuristically better than univariate risk assessment. However, there are a number of practical issues that make multivariate assessment difficult to implement. For example, the multivariate syndromic surveillance systems developed in this chapter assumed that the data sources were independent and that changes during an outbreak occurred simultaneously in all data considered.

These assumptions were simple but justifiable with WNV surveillance that used nervous symptoms in horses, mortality in wild birds, and mortality in horses. However, adapting the approach to another disease may require different assumptions and thus models of greater complexity, in order to deal with interactions between risk sources [START_REF] Frisén | Evaluation of multivariate surveillance[END_REF]. This is not a fundamental limitation of the approach, but further complications in model implementation may place limits on its practical use. Similarly, we combined syndromic surveillance and risk assessment assuming that both were a priori independent, as they do not utilize the same data sources. However, this was not completely true, and in reality the simultaneous use of syndromic surveillance and risk assessment is not so simple. As an example, risk assessment can be used to enhance veterinary practitioners' awareness through the production of risk maps, as has already been proposed for some endemic VBDs (e.g., surveillance of West Nile virus in California [START_REF] Brown | California Mosquito-borne Virus Surveillance & Response Plan[END_REF] or tick-borne diseases in Europe [START_REF] Beugnet | FleaTickRisk: a meteorological model developed to monitor and predict the activity and density of three tick species and the cat flea in Europe[END_REF]). Enhancing awareness in this way plays an important role in improving the early detection of disease. However, syndromic surveillance is closely dependent on practitioners' awareness, and increased awareness can result in an increasing number of (potentially spurious) declarations, and thus more false alarms. When combining risk sources, then, one must be careful to take into account any possible correlation between them.

Conclusion

Using a combination of risk estimations provided a better estimation that an outbreak might be ongoing.

However, the interactions between risk estimations must be carefully considered, as they may have an impact on the complexity and the performance of the surveillance system. This is of particular concern regarding the practical implementation of such a combined surveillance system.

CHAPTER V: DISCUSSION

The objective of this work was to address the challenges of establishing early warning systems for VBDs in horses by using quantitative risk assessments and syndromic surveillance, alone and in concert. All the methods developed in this work provided estimates of the probability of a VBD outbreak in horses and may help to address the challenge of VBDs surveillance in horses. However, many questions were raised in the implemention of these approaches (i.e. quantitative risk assessments and/or syndromic surveillance).

In this chapter, we start by presenting a brief summary of the main results obtained regarding the specific case of VBDs in horses, and we balance these against our initial objective and work already conducted on this topic. Then, from a wider perspective, we address how our approaches may support decision making and how they relate to demonstrating the absence of disease. Finally, we discuss the practical implementation of such methods.

Early warning system of VBDs in horses

Quantitative risk assessment

In this work, we showed that combining the probabilities of entry and establishment and taking into account spatiotemporal aspects in a quantitative assessment of the probability of import were both essential in obtaining a complete view of the risk posed by a vector-borne pathogen. This is consistent with the close link between VBDs and their climate and environment. By combining two routes of pathogen entry, we were able to better understand the risk posed by a pathogen to the equine industry.

Additionally, although quantitative risk assessment is not a new method for assessing the probability of outbreak occurrence, spatiotemporal analyses and combinations of probabilities and of entry routes are still rarely implemented in animal health. Our work thus advocates for the wider use of these kinds of approaches in order to obtain a more detailed and complete picture of the risk. It could also be interesting to apply this method to studies of other pathogens. In particular, assessments of the probability of bluetongue virus introduction could be easily implemented, as this virus is Culicoides-borne and is similar to the viruses responsible for African horse sickness and equine encephalosis. This part of the work also highlighted some limits specific to the equine industry. In particular, the available data were sometimes inaccurate because the equine industry is fragmented and poorly tracked, and few databases exist. When data do exist, they are rarely centralized, which presents problems regarding accessibility and standardization. Further work should be conducted to improve the quality of data on horses. It would be particularly helpful to reinforce the tracking of horse movements and to continue with efforts to identify the location of horses using awareness campaigns or field surveys.

Syndromic surveillance

Syndromic surveillance of nervous symptoms in horses using an alarm threshold that was a multiple of the standard error of prediction was able to detect early signals of a WNV outbreak in French horses.

However, our study represents the first time that a full assessment of this system's performance has been carried out. Using a simple Bayesian approach, we were able to provide a quantitative evaluation of the probability of an outbreak and generate an easy-to-interpret output that was simple to combine with other epidemiological knowledge, such as disease seasonality. This is especially important for the surveillance of VBDs, which are closely related to season. The output can be also combined with socioeconomic information in order to facilitate a more transparent and evidence-based decision-making process. To date, syndromic surveillance has rarely been implemented in animal health and even less often for diseases in horses, a deficiency that our work seeks to address. In addition to the diseases studied here, syndromic surveillance could also be used to monitor for the presence of other exotic diseases that induce nervous symptoms in horses, such as Eastern and Western equine encephalitis, Venezuelan equine encephalitis, or Japanese encephalitis, which are of serious concern for public health.

It would also be interesting to explore other symptoms occurring in horses. Here, we considered only nervous and respiratory symptoms, but future surveillance systems could also use data on abortions, for example, to detect equine arteritis virus, another disease of interest for the equine industry. In the present work, we did not quantitatively compare the respective performances of both proposed approaches (i.e., classical approach with an alarm threshold that was a multiple of the standard error of prediction and Bayesian approach) in outbreak detection, but this step would also be important for future work.

Combining risk

To improve confidence in the prediction of an ongoing outbreak, we combined different sources of risk assessment, first by using multivariate syndromic surveillance. This approach provided better detection performance than univariate syndromic surveillance, but it is rarely implemented in veterinary public health. It could however be applied in a wide range of situations. Considering other VBDs that affect horse populations, it could be also used, for example, to monitor for Japanese encephalitis, by combining surveillance of nervous symptoms in horses with that of reproductive diseases in swine. As a further step in risk combination, we also combined assessments of the probability of introduction with syndromic surveillance. Such integrated surveillance systems already exist in animal health, in particular for WNV surveillance. For example, the system implemented in California provides updated risk maps in which all information is gathered together through a scoring system [START_REF] Brown | California Mosquito-borne Virus Surveillance & Response Plan[END_REF]; similar systems also exist in Canada [START_REF] Gosselin | The Integrated System for Public Health Monitoring of West Nile Virus (ISPHM-WNV): a real-time GIS for surveillance and decision-making[END_REF], Italy (Bellini et al. 2014a), and Greece [START_REF] Chaskopoulou | Detection and Early Warning of West Nile Virus Circulation in Central Macedonia, Greece, Using Sentinel Chickens and Mosquitoes[END_REF]). However, unlike our approach, these integrated surveillance systems do not provide a single and quantitative output that combines all the collected information. Our approach thus represents a promising way to build a surveillance system that can quantitatively combine several estimations of risk in a single risk indicator.

This method could be of particular use for the surveillance of VBDs, as it can include information on seasonality and environmental risk factors, which are both fundamental parameters of VBD biology. In addition, combining syndromic surveillance with other epidemiological information is a way to improve the specificity of detection and could thus strengthen the surveillance of VBDs. This approach could also be applied to various other exotic diseases, such as equine encephalitis or exotic strains of bluetongue virus. However, the study presented here of the combination of syndromic surveillance with risk analysis was only preliminary, and further work should be conducted, especially to investigate tradeoffs between system performance and system complexity.

Support decision-making

The present work was primarily interested in quantitatively combining different sources of risk (i.e. routes of pathogen entry, probabilities of entry and establishment, syndromic surveillance data sources, syndromic surveillance and risk assessment). Apart from the obvious benefits of producing more reliable information, such an approach is also a good way to further support decision making in veterinary public health, as shown, for example, during the workshop described in Chapter IV.B At the individual level, decision making is the cognitive process that leads to the selection of a course of action and ends with a final choice. Decision making is a part of risk management (OIE 2010) and is based on a complex combination of rational analysis and subjective opinion [START_REF] Damasio | Descartes' Error: Emotion, Reason, and the Human Brain[END_REF], Slovic et al. 2005). In public health, there is a consensus that decision making should be strictly rational and based on a combination of scientific evidence, available resources, and context [START_REF] Brownson | Evidence-Based Public Health[END_REF]. The concept of evidence-based practice dates from 1971 [START_REF] Cochrane | Effectiveness and efficiency: Random reflections on health services[END_REF]. It was initially developed for clinical medicine but the evidence-based philosophy has now also been adopted in public health. Evidence-based public health (EBPH) can be defined as a 'public health endeavour in which there is an informed, explicit, and judicious use of evidence that has been derived from any of a variety of science and social science research and assessment methods' [START_REF] Rychetnik | A Glossary for Evidence Based Public Health[END_REF]). EBPH and the related evidence-based veterinary public health (EBVPH) are still in their early stages [START_REF] Latham | Capacities, practices and perceptions of evidencebased public health in Europe[END_REF], although guidelines and tools have recently emerged from international agencies (see, for example, the European Centre for Disease Prevention and Control (ECDC 2011) and the Center for Disease Control and Prevention [START_REF] Jacobs | Tools for Implementing an Evidence-Based Approach in Public Health Practice[END_REF]). The fact remains, though, that in the real world, decisions in public health are rarely made using empirical-analytical models, but are often conjectures based on crises, hot issues, short-term opportunities, concerns of organized interest groups, political and practical judgments, and public concern [START_REF] Brownson | Evidence-Based Public Health[END_REF], Head 2010[START_REF] Rutherford | Public Health Triangulation: Approach and Application to Synthesizing Data to Understand National and Local HIV Epidemics[END_REF], Sanderson 2002).

Several factors explain the limited use of EBPH, such as the lack of understanding of evidence-based methodologies by policy makers and the lack of relevant data and formalized systems [START_REF] Brownson | Bridging the gap: Translating research into policy and practice[END_REF][START_REF] Dobbins | A Knowledge Transfer Strategy for Public Health Decision Makers[END_REF][START_REF] Latham | Capacities, practices and perceptions of evidencebased public health in Europe[END_REF][START_REF] Lomas | Research and Evidence-based Decision Making[END_REF][START_REF] Rutherford | Public Health Triangulation: Approach and Application to Synthesizing Data to Understand National and Local HIV Epidemics[END_REF]), but also the absence of agreement on how to interpret and compare different types of evidence [START_REF] Dobbins | Public Health Decision-Makers' Informational Needs and Preferences for Receiving Research Evidence[END_REF][START_REF] Latham | Capacities, practices and perceptions of evidencebased public health in Europe[END_REF], Tannahill 2008). Indeed, decision makers in EBPH and EBVPH often have to combine different types of evidence and the decision process can be very complex [START_REF] Ecdc | Evidence-Based Methodologies for Public Health: How to Assess the Best Available Evidence When Time Is Limited and There Is Lack of Sound Evidence[END_REF]. This problem has become particularly acute because the volume of information has increased exponentially and diverse sources of data are rarely presented together, making gathering, synthesizing, and interpreting them an increasingly challenging task [START_REF] Rutherford | Public Health Triangulation: Approach and Application to Synthesizing Data to Understand National and Local HIV Epidemics[END_REF].

By providing decision makers with a single risk indicator that synthesizes different risk assessments about the presence of an outbreak, we thus hope to promote the development of EBVPH. Our approach allowed us to easily combine in a single quantitative risk indicator as much evidence as needed. For example, in

Chapter IV we combined different syndromic surveillance data sources (i.e. multivariate syndromic surveillance), as well as considering syndromic surveillance together with the probability of pathogen entry. However, more complex models can be built that involve other risk estimations. The present work is thus especially relevant for efforts to facilitate decision making. In particular, the work conducted in Chapter III.C illustrates how risk analysis can fit easily with decision theory and cost-efficiency analysis, yet another way to help decision makers and to promote a more rational decision-making process in veterinary public health. Nevertheless, further work remains to be done on determining the cost of diseases and disease surveillance (Babo Martins and Rushton 2014).

Demonstrate freedom of disease

Although risk indicators never prove the presence of a disease, they suggest the likelihood of its existence in a particular place. This is of course particularly true for indicators of combined risks. It can thus be problematic for decision makers to prove freedom from disease in high-risk areas.

Demonstrating that a country is free from a disease is a complex issue, and it is rare to prove absolute freedom from disease (with the exception of highly contagious diseases for which, when there is no case, there is also no disease). According to the OIE Terrestrial Animal Health Code (OIE 2014), a free zone is defined as a zone in which the absence of the disease under consideration has been demonstrated by the requirements given in the Code for free status. Given that surveillance does not detect any infected animal (S-), the probability of freedom (D-) is estimated, with the final result that, if the disease is nevertheless present, its prevalence will be lower than a set threshold by a certain level of confidence.

Based on (Martin et al. 2007a;Martin et al. 2007b), the FAO manual on risk-based surveillance (FAO 2014) proposed a method for estimating the probability of freedom (Pfree) using Bayes' theorem and accumulated historical information. Pfree is calculated as:

𝑃𝑓𝑟𝑒𝑒 = 𝑃(𝐷 -|𝑆 -) = (1 -𝑃𝑟𝑖𝑜𝑟) × 𝑆𝑝 (1 -𝑃𝑟𝑖𝑜𝑟) × 𝑆𝑝 + 𝑃𝑟𝑖𝑜𝑟 × (1 -𝑆𝑒)
where Sp and Se are the specificity and sensitivity of the surveillance system and Prior is the prior probability that the country is infected.

However, the resulting probability of freedom is expected to be quite low. An accumulation of historical information about the probability of freedom over time is thus used to build a better estimate of this probability. Pfree for the previous time period is calculated and used as the prior for the current time period of evaluation. In other words, Pfree t calculated at time period t can be estimated with:

𝑃𝑓𝑟𝑒𝑒 𝑡 = (1 -𝑃𝑟𝑖𝑜𝑟 𝑡 ) × 𝑆𝑝 (1 -𝑃𝑟𝑖𝑜𝑟 𝑡 ) × 𝑆𝑝 + 𝑃𝑟𝑖𝑜𝑟 𝑡 × (1 -𝑆𝑒)
where Prior t is the resulting probability of two non-exclusive states: "the country was not free from the disease to begin with" and "the country became infected during the time period considered". Prior t is thus calculated as: 𝑃𝑟𝑖𝑜𝑟 𝑡 = 𝑃𝑓𝑟𝑒𝑒 (𝑡-1) + 𝑃𝑖𝑛𝑡𝑟𝑜 -𝑃𝑓𝑟𝑒𝑒 (𝑡-1) × 𝑃𝑖𝑛𝑡𝑟𝑜 Applying such an approach to the surveillance systems presented in this work is thus a way to calculate the probability of freedom using evidence that suggests the presence of the disease. In this case, Se and Sp are the sensitivity and specificity of the syndromic surveillance system and Pintro is the probability of disease introduction. It would also be possible to use either the combination of syndromic surveillance and risk analysis or each approach individually to demonstrate freedom from disease. Of course, such an approach would only be relevant for an exotic infection that spreads slowly and causes few symptoms. For example, in the work conducted here, this method could be used for equine encephalosis but not for African horse sickness.

Practical implementation of integrated surveillance systems

Providing decision makers with a single risk indicator that synthesizes the different risks related to an outbreak could potential be very useful, but also results in a complex surveillance system which can be complicated to put into practice.

Firstly, such a complex surveillance system requires a large amount of data, which is not always easy to obtain (e.g., animal movements, vector abundance, host geographical localization, declarations from field workers). In addition, even when data are available, they are often formatted in many different ways, especially at the European level (e.g., different definitions, different geographical units). This is of concern for the use of the data (i.e. a lengthy initial step of preprocessing is needed) but also for sharing the results with partners involved in disease surveillance. However, sharing surveillance results is particularly important for the European Union, where movements of animals and humans are not (or only poorly) tracked within the community. Disease surveillance in the EU therefore depends in part on reliable and up-to-date data-sharing among member countries. The lack of high-quality and standardized data constitutes a problem not only for the initial implementation of a system, but also for its maintenance. It is especially a concern for syndromic surveillance systems in which reporting has to be continuously stimulated in order to obtain data. Improvements in data collection may be encouraged, however, by proof that the data are important for disease surveillance. Although initial efforts, such as the present work, might be complicated to implement due to the lack of good data available, they can also be used to promote the need for better data collection.

Secondly, the complexity of a surveillance system may result in a reluctance to trust it on the part of decision makers, given the large amount of information and uncertainties involved. The Bayesian approach used in the present work partially solved this concern. This approach is transparent and offers an explicit separation of assumptions, scientific evidence, and criteria for decisions. However, further work should be conducted to ensure its proper communication and acceptance. Indeed, a complex system that combines different risk estimations requires several underlying assumptions, and, before any practical implementation of such a system, it would be necessary to thoroughly explain how to use it and interpret the output. In addition, future work must include a full assessment of system performance, the only guarantee of the reliability of the surveillance outputs. However, it remains challenging to evaluate multivariate surveillance methods due to the several dimensions and complex time relations involved [START_REF] Frisén | Evaluation of multivariate surveillance[END_REF]. One potential approach that could help would be the use of Monte Carlo simulations, as proposed by Frisén and colleagues [START_REF] Frisén | Evaluation of multivariate surveillance[END_REF].

Many different issues remain to be solved before such complex surveillance systems can be broadly applied in veterinary public health. However, the work conducted here shows that these approaches have huge potential and constitutes a promising initial step. Future work should focus on thorough assessments of system performance and effective communication to interested parties. However, as more data become available online and access to data improves, such systems will play an invaluable role in future disease monitoring efforts.

Conclusion

The present work proposed to improve the surveillance of vector-borne diseases in horses though different approaches that assessed the probability of occurrence of a newly introduced epidemic. First, we developed a model of quantitative risk assessment to improve estimates of the probability of pathogen introduction. In particular, we performed a spatiotemporal analysis, simultaneously analyzed two routes of virus entry, and also combined the probability of virus entry with the probability of virus establishment.

Second, we implemented and assessed syndromic surveillance systems based on two approaches: a classical approach with an alarm threshold based on the standard error of the prediction, and a Bayesian approach based on a likelihood ratio. The Bayesian approach was especially useful as it provided a quantitative assessment of the syndromic surveillance output and was able to combine different information. We therefore also used this approach to combine various sources of risk estimation in order to improve the assessement of the probability of occurrence of a newly introduced epidemic. We performed multivariate syndromic surveillance and also combined quantitative risk assessment with syndromic surveillance. Approaches that quantitatively combined evidence provided promising results. This work, based on risk estimations, strengthens the surveillance of VBDs in horses and has potential in supporting decision making. In the end, we hope to encourage the improvement of data collection and data sharing, stimulate the implementation of a full assessment of complex surveillance system performance, especially in terms of cost-efficiency, and promote the adoption of the approach by decision makers and other parties involved in disease surveillance through effective communication and training.

Appendix 1: Model calculation for PW-host. Details of calculation regarding the AHSV introduction via the import of an infectious host.

Every calculus below is made for an equine from species i imported from an area j to the free area k the month m. All the parameters used are detailed in the Additional file 2.

The probability of introduction for PW-host is the probability to import at least one infected host able to transmit the infection to at least one local host and is defined as: P(introH ijkm ) = 1 -[1 -P(relH ijkm ) × P(estH ijkm )] eq ijkm

Where P(relH ijkm ), the probability of release, depends of the importation procedure implemented and the periods where a host is infected and P(estH ijkm ), the probability of establishment, is defined as:

P(estH ijkm ) = 1 -[1 -𝐼 𝑉𝐻 × 𝑃(𝑠𝑢𝑟𝑣 𝑘𝑚 ) × 𝑏 𝑒𝑞𝑢𝑖 𝑘 × 𝐼 𝐻𝑉 ] 𝑐𝑢𝑙𝑖 𝑘𝑚
with culi km the number of vectors feeding on an infected viraemic imported host equals at BR km x Vir x C km For each category of exporting region, there is different import procedure implemented and thus different periods z where a host can be infected. For a given region j, there is a total of w different time periods z where the equine can be infected depending on the import procedure implemented for the region j. The different periods z for each region j are presented below:

-High risk countries: host can be infected 1) Before quarantine, 2) During quarantine but before the first serological test CF1, 3) During quarantine but between the both serological tests CF1 and CF2, 4) During quarantine but after CF2 and before clinical exam, or 5) After clinical exam.

-Low risk countries:

o Non EU country member: host can be infected 1) Before quarantine, 2) During quarantine but before CF1, 3) During quarantine but between CF1 and CF2, 4) During quarantine but after CF2 and before clinical exam, or 5) After clinical exam. o EU country member: host can be infected 1) Before clinical exam, or 2) After clinical exam.

-Very low risk countries:

o Non EU country member: host can be infected 1) Before clinical exam, or 2) After clinical exam. o EU country member: host can be infected 1) Before clinical exam, or 2) After clinical exam.

The probability of release by species i from region j to area k during a specific month m (P(relH ijkm )) is thus calculated as:

P(relA ijkm ) = ∑ [(length period z)×P(relA ijkmz )] w z=1 ∑ (length period z) w z=1
Where 𝑃(𝑟𝑒𝑙𝐻 𝑖𝑗𝑘𝑚𝑧 ) is the probability of release when the animal i is infected during the time period z. P(relA ijkmz ) is calculated for each period z as: P(relA ijkmz ) = P(inf ijmz ) × P(vir ijmz ) × (1 -P(CF1 iz )) × (1 -P(CF2 iz )) × (1 -P(clin ijmz )) × (1 -P(trans ijkz ))

1. 𝐏(𝐢𝐧𝐟 𝐢𝐣𝐦𝐳 ) = Probability for a host to be infected during period z in the month m in area j

The probability of infection during a certain period z (before or during the import procedure) depends on the fraction of this period z spend in each of the months m, m-1 and m-2.  Probability that the imported host is infected between q and cf1 If e -cf1 < 0 If q > 30 + e

= (1 -Prot vect ) × PO jm q -cf1 × [CI m-1 × (30 -cf1 + e) + CI m-2 × (q -30 -e)] If q < 30 + e = (1 -Prot vect ) × PO jm × CI m-1 if e -cf1 > 0 if q > 30 + e = (1-Prot vect ) × PO jm q-cf1 × [CI m × (e -cf1) + CI m-1 × 30 + CI m-2 × (q -30 -e)] if q < 30 + e = (1 -Prot vect ) × PO jm q -cf1 × [CI m × (e -cf1) + CI m-1 × (q -e)]
 Probability that the imported host is infected between cf1 and cf2 If e < cf2

= (1 -Prot vect ) × PO jm cf1 -cf2 × [CI m-1 × (30 -cf2 + e) + CI m-2 × (cf1 -30 -e)] If e > cf2 if cf1 > 30 + e = (1 -Prot vect ) × PO jm cf1 -cf2 × [CI m × (e -cf2) + CI m-1 × 30 + CI m-2 × (cf1 -30 -e)] if cf1 < 30 + e = (1 -Prot vect ) × PO jm cf1 -cf2 × [CI m × (e -cf2) + CI m-1 × (cf1 -e)]
 Probability that the imported host is infected after cf2 If e < cf2 Inf time = Period when a horse can be infected before the start of import procedure such as quarantine or clinical exam when there is no quarantine

If a quarantine applied: if HRP -q > 0, Inf time = HRP -q but if HRP -q < 0, Inf time = 0. If no quarantine applied: Inf time = HRP -clin

HRP = High risk period

The HRP is the time between virus introduction and the first formal detection. In low and very low risk region, we assumed that the first infected horse won't be detected but that the secondary cases will be.

Thus the time needed to detect the second case is estimated as the time required for two incubation periods plus the time till the next infectious blood meal of a vector. In low risk regions HRP 2 is assumed equal at 22 days (based on a temperature in the region j of 18°C). In very low risk region, HRP 3 is assumed equal at 60 days (based on a temperature in the region j of 12°C). As in high risk region the virus is supposed endemic, there is no real HRP 1 because an equine can be infected at any time (during or before quarantine). We thus choose to set a period of 30 days before the start of quarantine (thus 70 days before embarkation) as the earliest stage when a host can be infected.

D culi_inf = Day of vector becomes infected

To estimate the day where the vector becomes infected (D culi_inf ), we first only take into account the Culicoides susceptible to the infection. When a Culicoides is susceptible, one blood meal on a vireamic host is assumed sufficient for this vector to become infected [START_REF] Jones | The effet of repeated blood meals for Bluetongue on the infection rate of Culicoides variipennis[END_REF]. Assuming a uniform distribution of the viraemic host and a constant monthly temperature T jm in each departure area j, the moment (or day) of Culicoides infection follows a Uniform distribution between 1 (the Culicoides is infected the first day of its life) and 1/MR km (the Culicoides is infected the last day of its life).

CI ijm = Cumulative monthly number of infectious hosts i in each departure area j Equidae have a seasonal foaling period but the foaling season depends on the geographical area considered (North or South hemisphere). We thus assumed that CI ijm was a constant for all species in all departure region j. For low and very low risk regions, CI ijm was considered as equals at 2x10 -4 for all species based on AHSV epidemic in Spain (Rodriguez et al. 1992a;Rodriguez et al. 1992b) ). For donkeys and zebras, CI ijm in high risk region were respectively assumed equal at 1.2x10

-2 and 1.6x10 -2 based on rate of seroconversion in foals, the surviving foaling rate and the offspring rate [START_REF] Barnard | Circulation of African horsesickness virus in zebra (Equus burchelli) in the Kruger National Park, South Africa, as measured by the prevalence of type specific antibodies[END_REF] [START_REF] Penzhorn | Reproductive characteristics of a free-ranging population of Cape mountain zebra (Equus zebra zebra)[END_REF]. r jm = Prevalence of infected vectors during an outbreak in the region j We applied for the prevalence of infected vector the same process than for infected host. Thus r jm is considered as a constant in all region j. In high risk region r jm is assumed at 0.014 based on data from South Africa [START_REF] Scheffer | Comparison of two trapping methods for Culicoides biting midges and determination of African horse sickness virus prevalence in midge populations at Onderstepoort, South Africa[END_REF]. In low risk region, as for equidae the number of infectious animal is divided by 10 -2 between high risk regions and low risk regions, the rate was here estimated as 1.4x10 -4 . …/.. This approach was applied to time series on the number of horses showing nervous symptoms. The separation between prior beliefs about the probability of an outbreak and the strength of evidence from syndromic surveillance offers a transparent rational process suitable for supporting decision making. Furthermore, a Bayesian approach makes it possible to combine data from syndromic surveillance with results from predictive modeling and with information from other sources such as assessments of risks of disease introduction. La surveillance syndromique est un concept apparu à la fin des années 90 et est devenue de plus en plus populaire en santé humaine mais également ces dernières années en santé animale [START_REF] Dórea | Veterinary syndromic surveillance: Current initiatives and potential for development[END_REF]. Il n'existe à ce jour pas de définition unique et communément acceptée de la surveillance syndromique. Cependant, en général, la surveillance syndromique utilise des données pré-diagnostiques, souvent peu spécifiques, collectées en routine et analysées en temps réel [START_REF] Katz | Redefining syndromic surveillance[END_REF]. La surveillance syndromique a ainsi pour vocation de détecter précocement des maladies connues, comme la grippe saisonnière humaine [START_REF] Hiller | Syndromic Surveillance for Influenza in the Emergency Department-A Systematic Review[END_REF] ; [START_REF] Ginsberg | Detecting Influenza Epidemics Using Search Engine Query Data[END_REF]) ou inconnues, comme les attaques bioterroristes [START_REF] Buehler | Syndromic Surveillance and Bioterrorism-related Epidemics[END_REF]. La surveillance syndromique ne remplace pas les approches traditionnelles de surveillance des maladies mais elle est un outil complémentaire intéressant de par sa rapidité, sa flexibilité et son bon rapport coût-bénéfice.

Keywords

Les approches actuellement utilisées en surveillance syndromique cherchent d'abord à définir les propriétés normales de la série de données considérée lorsqu'aucun foyer de maladie n'est enregistré. L'objectif est de pouvoir ensuite détecter des évènements anormaux tels que des épidémies ou des épizooties. Les méthodes de détection traditionnelles produisent une alarme lorsque les données observées dépassent les valeurs attendues en l'absence d'épidémie. Les algorithmes utilisés définissent ainsi un seuil épidémique et fournissent une réponse finale de type oui/non : « non, aucune épidémie en cours », « oui, un évènement inhabituel est en cours ».

Cette

vision binaire d'une situation épidémiologique est simple mais elle n'est pas toujours suffisante et peut être compliquée à interpréter notamment lorsque les résultats de l'analyse sont dans une zone « grise » proche du seuil épidémique. De plus, ces résultats qualitatifs binaires sont également difficiles à combiner avec d'autres connaissances épidémiologiques, tels que le risque d'introduction ou la saisonnalité d'une maladie, qui entrent pourtant en compte lorsqu'une décision d'intervenir (ou non) doit être prise suite à la production d'une alarme. Développer des méthodes quantitatives transparentes, plus spécifiques, et facilement utilisables dans un processus de décision s'avère ainsi être un domaine de recherche prometteur.

OBJECTIFS DE L'ÉTUDE

L'objectif de ce travail est de tester l'applicabilité du cadre statistique bayésien pour la détection précoce d'épidémies en surveillance syndromique. Ces approches sont déjà utilisées notamment pour l'évaluation des pièces à convictions dans un cadre juridique [START_REF] Foreman | Interpreting DNA Evidence: A Review[END_REF] [START_REF] Drygajlo | Statistical methods and Bayesian interpretation of evidence in forensic automatic speaker recognition[END_REF] ; [START_REF] Morrison | The Likelihood-Ratio Framework and Forensic Evidence in Court: A Response to R v T[END_REF] ; [START_REF] Taroni | Bayesian Networks and Probabilistic Inference in Forensic Science[END_REF]].

Nous détaillerons dans un premier temps le cadre théorique de la méthode développée, puis nous présenterons une application concrète de la méthode au cas de la surveillance de la fièvre de West Nile (WN). Le virus West Nile est un arbovirus du genre Flavivirus (famille Flaviviridae). Il est principalement transmis par des moustiques du genre Culex (famille Culicidae). Les hôtes principaux sont les oiseaux mais le virus peut également affecter l'homme et plus de 30 espèces animales parmi lesquelles les équidés. Chez les personnes comme chez les chevaux, le virus peut provoquer des encéphalites mortelles et la présence de la maladie dans un territoire a ainsi des conséquences importantes en termes de santé publique et sur la filière équine.

Le virus a été identifié en Europe pour la première fois dans les années 60 et depuis, de nombreuses émergences ont été rapportées un peu partout sur le continent [START_REF] Calistri | Epidemiology of West Nile in Europe and in the Mediterranean Basin[END_REF]. Même si le virus est actuellement considéré comme endémique dans une grande partie de l'Europe [START_REF] Ozdenerol | Exploring the Spatio-Temporal Dynamics of Reservoir Hosts, Vectors, and Human Hosts of West Nile Virus: A Review of the Recent Literature[END_REF]), de plus en plus de cas sont rapportés ces dernières années dans le sud-est de l'Europe (exemple : Italie, Grèce, Bulgarie, Croatie, Serbie, Albanie) (Di [START_REF] Sabatino | Epidemiology of West Nile Disease in Europe and in the Mediterranean Basin from 2009 to 2013[END_REF]. L'impact de la maladie est plus limité en Europe que ce qui est observé en Amérique du Nord. Cependant, le nombre croissant d'émergences associé à la récente introduction de la lignée 2 en Europe font du virus WN une menace d'intérêt constant pour les pays européens [START_REF] Hernández-Triana | Emergence of West Nile Virus Lineage 2 in Europe: A Review on the Introduction and Spread of a Mosquito-Borne Disease[END_REF] ; [START_REF] Bakonyi | Lineage 1 and 2 Strains of Encephalitic West Nile Virus, Central Europe[END_REF]) [START_REF] Calzolari | New Incursions of West Nile Virus Lineage 2 in Italy in 2013: The Value of the Entomological Surveillance as Early Warning System[END_REF] . Cet odds correspond à la connaissance a posteriori sur le statut de la maladie dans le territoire. Il sera noté O post dans les paragraphes suivants.

INTÉGRATION DANS UN PROCESSUS DE DÉCISION

Le rapport de vraisemblance O post construit à partir du cadre statistique bayésien donne une appréciation quantitative de la probabilité de circulation de la maladie. Cependant, il est important de pouvoir déterminer à partir de quel seuil de probabilité il est utile (ou non) de déclencher une alarme et de mettre en place des mesures de contrôles et/ou d'investigation de la maladie.

La théorie de la décision évalue comment s'effectue une prise de décision rationnelle en présence d'incertitude [START_REF] Gittelson | Evolving from Inferences to Decisions in the Interpretation of Scientific Evidence[END_REF] Ainsi, l'utilité de mettre en place des actions de contrôle (U(A1)) et l'utilité de ne rien faire (U(A0)) peuvent être définies comme suit :

III -CAS PRATIQUE : SURVEILLANCE DE LA FIÈVRE DE WEST NILE

Ce cas propose d'utiliser la méthode développée afin de détecter les émergences de virus WN en France. Nous utiliserons pour cet exemple les données de syndromes nerveux chez les chevaux qui sont des indicateurs intéressants d'émergence de la maladie [START_REF] Leblond | West Nile Virus Outbreak Detection Using Syndromic Monitoring in Horses[END_REF]). Les données de syndromes nerveux sont collectées en routine depuis 2006 par le réseau d'épidémiosurveillance en pathologie équine (RESPE).

CONNAISSANCES A PRIORI

La fièvre de WN est une maladie à transmission vectorielle. La probabilité de circulation du virus à des niveaux épizootiques est ainsi fortement liée à la dynamique de population de son vecteur principal, les moustiques du genre Culex. Ainsi les épizooties de WN présentent une saisonnalité marquée avec de nombreuses occurrences rapportées en été et à l'automne, des cas moins fréquents au printemps et seulement quelques cas sporadiques en hiver.

En utilisant les données historiques relatives aux épizooties de WN rapportées en Europe ces dernières années, nous avons ainsi établi des O pri de la maladie, différents selon les saisons. Les probabilités de circulation relatives au printemps, automne/été et hiver sont ainsi respectivement de 1:5:0,04.

RÉSULTATS DE LA SURVEILLANCE SYNDROMIQUE

SITUATION NON-EPIZOOTIQUE

Pour déterminer la probabilité d'observer un nombre de cas n lorsque la maladie est absente, p(n|M-), nous avons utilisé les données collectées par le RESPE depuis 2006. Des traces d'épizooties sont cependant présentes dans ces données et sont principalement dues aux émergences d'herpesvirus de type 1. Afin de modéliser au mieux la série de données en situation nonépizootiques, nous les avons supprimées en utilisant uniquement les données provenant de chevaux qui n'ont pas obtenu de résultat de laboratoire positif. Les données de 2006 à 2010 ont été utilisées pour calibrer le modèle et les données de 2011 à 2012 pour le valider.

Plusieurs modèles ont été testés mais celui qui a obtenu les meilleures performances est celui utilisant une loi de poisson (AIC = 637,8 et GOF (déviance ajustée) = 1,156): Nombre de cas ~ sin(2π*t) + cos(2π*t) + log(histmean) où 'histmean' représente la moyenne des 53 semaines précédant t sans tenir compte des 10 semaines juste avant t afin de ne pas incorporer des données d'une épizootie éventuellement en cours.

SITUATION EPIZOOTIQUE

Afin de déterminer la probabilité d'observer un nombre de cas n lorsque la maladie est présente, p(n|M+), nous avons utilisé les données trouvées dans la littérature sur des épizooties de WN ayant entrainé des symptômes nerveux chez les chevaux. Nous avons ainsi utilisé les nombres de symptômes rapportés chez les chevaux lors des émergences françaises de 2000 [START_REF] Murgue | West Nile outbreak in horses in southern France, 2000: the return after 35 years[END_REF]) et 2004[START_REF] Leblond | West Nile Virus Outbreak Detection Using Syndromic Monitoring in Horses[END_REF]) et lors de l'épisode de WN en Italie en 1998 [START_REF] Autorino | West Nile virus Epidemic in Horses, Tuscany Region, Italy[END_REF].

Le nombre de cas observés en situation épizootique a été modélisé avec une loi négative binomiale de paramètre mu égal à 4,45 et theta égal à 0,94. Le nombre médian de cas attendus par semaine en cas d'épizootie a ainsi été estimé à 3 (IC 95 %: 0-18).

RAPPORT DE VRAISEMBLANCE

Le rapport de vraisemblance noté V correspond au rapport entre p(n|M+) et p(n|M-) et peut se représenter graphiquement comme présenté en figure 1. Si la méthode offre des perspectives prometteuses, certaines limites sont cependant à considérer. Le cadre statistique bayésien a ici été appliqué en estimant les probabilités a priori de manière probabiliste à partir des données disponibles et non par le biais d'inférence bayésienne. L'approche probabiliste est relativement simple à mettre en place et à présenter. Elle a cependant le défaut de ne pas complètement rendre compte de l'incertitude des hypothèses de départ. Des approches utilisant les méthodes d'inférence ont été proposées par plusieurs auteurs pour détecter des agrégats spatio-temporels de cas [START_REF] Banks | Bayesian CAR models for syndromic surveillance on multiple data streams: Theory and practice[END_REF] ; [START_REF] Zou | Bayesian methodology for spatio-temporal syndromic surveillance[END_REF]. Cependant, si ces approches sont techniquement réalisables et plus robustes d'un point de vue mathématique, elles restent encore assez théoriques et compliquées à présenter à un public non familier des méthodes bayésiennes tel que les décideurs politiques [START_REF] Banks | Bayesian CAR models for syndromic surveillance on multiple data streams: Theory and practice[END_REF].

Concernant l'exemple développé, il est important de noter que nous avons ici considéré que les semaines étaient indépendantes les unes des autres. Cette hypothèse simple a été choisie pour présenter au mieux la méthode et ne constitue pas une limite à son application. En effet, il est tout à fait possible de construire un système plus complexe considérant non pas les semaines de manière séparées mais les preuves cumulées sur plusieurs semaines. Par ailleurs, si un système de surveillance de WN fondé sur cette approche devait effectivement être implémenté, il faudrait nécessairement mieux préciser les estimations de nombre de cas utilisées, la saisonnalité des données ainsi que les estimations coûts-bénéfice.

V -CONCLUSION

L'utilisation du cadre statistique bayésien en surveillance syndromique est donc une approche prometteuse pour l'amélioration de la surveillance des maladies connues. Elle permet de synthétiser de manière quantitative les diverses sources d'informations épidémiologiques disponibles et de les intégrer aisément dans un processus de décision rationnel prenant en compte des analyses couts bénéfices. Des travaux ultérieurs pourront permettre de perfectionner la méthode et d'évaluer son intérêt dans des systèmes de surveillance complexes. L'ensemble des analyses détaillées est disponible dans l'article publié par Anderson, Faverjon et al. [START_REF] Andersson | Using Bayes' Rule to Define the Value of Evidence from Syndromic Surveillance[END_REF].

ABSTRACT

Emerging vector-borne diseases are a growing concern, especially for horse populations, which are at particular risk for disease spread. In general, horses travel widely and frequently and, despite the health and economic impacts of equine diseases, effective health regulations and biosecurity systems to ensure safe equine movements are not always in place. The present work proposes to improve the surveillance of vector-borne diseases in horses through the use of different approaches that assess the probability of occurrence of a newly introduced epidemic. First, we developed a spatiotemporal quantitative model which combined various probabilities in order to estimate the risk of introduction of African horse sickness and equine encephalosis. Such combinations of risk provided more a detailed picture of the true risk posed by these pathogens. Second, we assessed syndromic surveillance systems using two approaches: a classical approach with the alarm threshold based on the standard error of prediction, and a Bayesian approach based on a likelihood ratio. We focused particularly on the early detection of West Nile virus using reports of nervous symptoms in horses. Both approaches provided interesting results but Bayes' rule was especially useful as it provided a quantitative output and was able to combine different epidemiological information. Finally, a Bayesian approach was also used to quantitatively combine various sources of risk estimation in a multivariate syndromic surveillance system, as well as a combination of quantitative risk assessment with syndromic surveillance (applied to West Nile virus and equine encephalosis, respectively). Combining evidence provided promising results. This work, based on risk estimations, strengthens the surveillance of VBDs in horses and can support public health decision making. It also, however, highlights the need to improve data collection and data sharing, to implement full performance assessments of complex surveillance systems, and to use effective communication and training to promote the adoption of these approaches.

Key words: syndromic surveillance, West Nile, quantitative risk analysis, African horse sickness, equine encephalosis, vector-borne diseases, risk-based surveillance

RÉSUMÉ

Les maladies émergentes à transmission vectorielle sont une préoccupation croissante et particulièrement lorsqu'elles affectent les chevaux, une population spécirfiquement à risque vis-à-vis de la propagation de maladies. En effet, les chevaux voyagent fréquemment et, malgré l'impact sanitaire et économique des maladies équines, les règlementations sanitaires et les principes de biosécurité et de traçabilité censés assurer la sécurité des mouvements d'équidés ne sont pas toujours en place. Notre travail propose d'améliorer la surveillance des maladies à transmission vectorielle chez les chevaux en utilisant différentes méthodes pour estimer la probabilité d'émergence d'une maladie. Tout d'abord, nous avons développé un modèle quantitatif et spatio-temporel combinant différentes probabilités pour estimer les risques d'introduction de la peste équine et de l'encéphalose équine. Ces combinaisons permettent d'obtenir une image plus détaillée du risque posé par ces agents pathogènes. Nous avons ensuite évalué des systèmes de surveillance syndromique par deux approches méthodologiques: l'approche classique avec un seuil d'alarme basé sur un multiple de l'erreur standard de prédiction, et l'approche bayésienne basée sur le rapport de vraisemblance. Nous avons travaillé ici principalement sur la détection précoce du virus West Nile en utilisant les symptômes nerveux des chevaux. Les deux approches ont fourni des résultats prometteurs, mais l'approche bayésienne était particulièrement intéressante pour obtenir un résultat quantitatif et pour combiner différentes informations épidémiologiques. Pour finir, l'approche bayésienne a été utilisée pour combiner quantitativement différentes sources d'estimation du risque : surveillance syndromique multivariée, et combinaison de la surveillance syndromique avec les résultats d'analyses de risques. Ces combinaisons ont données des résultats prometteurs. Ce travail, basé sur des estimations de risque, contribue à améliorer la surveillance des maladies à transmission vectorielle chez les chevaux et facilite la prise de décision. Les principales perspectives de ce travail sont d'améliorer la collecte et le partage de données, de mettre en oeuvre une évaluation complète des performances des systèmes de surveillance multivariés, et de favoriser l'adoption de ce genre d'approche par les décideurs en utilisant une interface conviviale et en mettant en place un transfert de connaissance.

Mots clefs : surveillance syndromique, West Nile, analyse de risques quantitative, peste équine, encéphalose équine, maladies à transmission vectorielle, surveillance basée sur le risque

Figure 1 :

 1 Figure 1: Estimated geographical distribution of horses population (ICFE-SIRE) ............................................

Figure 2 :

 2 Figure 2: Geographic distribution of the French sentinel veterinarians involved in RESPE. .........................

Figure 3 :

 3 Figure 3 : National median probability of EE and AHS viruses entry to France. ............................................

Figure 4 :

 4 Figure 4 : Median probabilities of viruses entry via an infectious host. Example of the year 2012. .............

Figure 5 :

 5 Figure 5 : Median probabilities of viruses entry via an infectious vector. Example of the year 2012. ..........

Figure 6 :

 6 Figure 6 : At risk areas for viruses entry when entry via an infectious host and via an infectious vector are considered together. .....................................................................................................................................

Figure 7 :

 7 Figure 7 : Correlation of the model input parameters with the probability of entry of AHS and EE via an infectious host ...............................................................................................................................................

Figure 8 :

 8 Figure 8 : Correlation of the model input parameters with the probability of entry of AHS and EE via an infectious vector ............................................................................................................................................

Figure 9 :

 9 Figure 9 : Overall method to implement syndromic surveillance. ................................................................

Figure 10 :

 10 Figure 10 : Number of nervous symptoms cases declared to RESPE from 2006 to 2013..............................

Figure 11 :

 11 Figure 11 : Four time series used ..................................................................................................................

Figure 12 :

 12 Figure 12 : West Nile virus outbreaks ............................................................................................................

Figure 13 :

 13 Figure 13 : Two examples of simulated outbreaks inserted in TS0. Positions of outbreaks identified with dotted lines above the peak. .........................................................................................................................

Figure 14 :

 14 Figure 14 : Decomposition of time series ......................................................................................................

Figure 15 :

 15 Figure 15: Combining syndromic surveillance and probability of disease introduction to obtain a posterior probability that there is an ongoing outbreak. ...........................................................................................

Figure 16 :

 16 Figure 16: EE simulated outbreak in Aquitaine ...........................................................................................

Figure 17 :

 17 Figure 17: Value of evidence in France at week 31 in year 2012 from the simulated outbreak in Aquitaine, using a detection radius of 50 km ...............................................................................................................

Figure 18 :

 18 Figure 18: Posterior probability of EE outbreak in France in year 2012 during the simulated outbreak in Aquitaine from week 29 to week 32 ...........................................................................................................

  .................................................................................. Table 2: Mandatory notifiable diseases to the French ministry.. .................................................................. Table 3 : import procedure for African horse sickness and equine encephalosis ......................................... Table 4 : Parameters specific of diseases and used for African horse sickness and Equine encephalosis in the model of viruses entry. ............................................................................................................................ Table 5 : Description of scenario tested. Scenarios 1 to 5 changed the existing legislation, scenarios 6 to 7 changes imports from third countries. .......................................................................................................... Table 6 : Change (in %) on median probabilities of viruses entry to France compared to the default scenario. ........................................................................................................................................................ Table 7 : Summary of the advantages and limitations of the main detection algorithms in the time series analysis. ......................................................................................................................................................... Table 8 : Metrics used for evaluation of outbreak detection algorithms ...................................................... Table 9 : Advantages and disadvantages of types of test data (Buckeridge et al. 2005) .............................. Table 10 : Smoothing and forecasting performance of GLMs.. ..................................................................... Table 11 : Smoothing and forecasting performance of Holt-Winters models.. ............................................. Table 12 : System's detection performances ................................................................................................ Table 13 : system's detection performances for time series fitted with generalized linear models............. Table 14: system's detection performances for time series fitted with Holt-Winters ..................................

-

  interprofessionnelle du cheval de sport, loisir travail': Cross-sector organization; promotes horse-related activities -'Fédération nationale de cheval': Breeders' association -'Association syndicale des étalonniers particuliers': Stallion raisers' association -'Chambre syndicale du commerce des chevaux de France': Professional traders' association -'Groupement hippique nationale': Riding centers' association -'Syndicat National des Exploitants d'établissements Professionnels Enseignant l'équitation': Riding centers' association -'Société hippique francaise': Coordinates genetic selection; riders' association -'Fédération française d'équitation': Issues required licenses and complementary certificates; develops regulations for competitions -'Acteurs et cavaliers de sauts d'obstacles en France': Riders' association -'Haras nationaux': Confirms the origins of horses; promotes horse industry development Butchery industry -'Interbev equin': Promotes horse meat, develops marketing and production rules -'France trait': Union of nine French associations of draft horses; coordinates genetic selection Breeding industry Different breed-specific stud books: coordinate horse selection and genetic improvement;

Figure 3 :

 3 Figure 3 : National median probability of EE and AHS viruses entry to France.

Figure 4 :

 4 Figure 4 : Median probabilities of viruses entry via an infectious host. Example of the year 2012.

Figure 5 :Figure 6 :

 56 Figure 5 : Median probabilities of viruses entry via an infectious vector. Example of the year 2012.

Figure 7 :

 7 Figure 8.

Figure 10 :

 10 Figure 10 : Number of nervous symptoms cases declared to RESPE from 2006 to 2013.

Figure 11 :

 11 Figure 11 : Four time series used with datapreprocessing used from 2006 to 2010 and raw data used from 2011 to 2014. TS0 = raw data, TS1 = only the cases with no positive laboratory results, TS2 = outbreaks removed based on historical data, TS3 = extreme values above the 95% confidence interval deleted.

Figure 12 :

 12 Figure 12 : West Nile virus outbreaks. solid line = outbreak Italy 1998 (Autorino et al. 2002), dotted line = outbreak in France 2004 (Leblond et al. 2007), dashed line = outbreak in France 2000 (Murgue et al. 2001).

Figure 13 :

 13 Figure 13 : Two examples of simulated outbreaks inserted in TS0. Positions of outbreaks identified with dotted lines above the peak.

Figure 14 :

 14 Figure 14 : Decomposition of time series. For each decomposition, the upper graph represents the observed data, the second graph shows the trend identified in the data, the third graph indicates the seasonal pattern found in the data and the fourth graph shows the residuals after deletion of trend and seasonal components.

French

  network for the surveillance of equine diseases (http://www.respe.net/) collects standardized declarations from veterinary practitioners registered as sentinels. All the samples sent for laboratory diagnosis are systematically tested for WNV and equine herpes virus, and results are registered in the RESPE database. To obtain an outbreak-free baseline dataset, we used data from 2006 to 2013 that included only the 44 declarations without positive laboratory test results from the region of the French Mediterranean coast. The time series of nervous syndromes in horses is designated NervSy in subsequent sections.

DeadBird.

  These extreme values were removed based on a method adapted from Tsui et al.[START_REF] Tsui | Value of ICD-9 coded chief complaints for detection of epidemics[END_REF]: the entire dataset was first fitted to a Poisson distribution and then values above the 95% confidence interval were deleted and replaced with the average value of the four previous weeks. To calibrate the models, we used NervSy data from 2006 to 2010, DeadHorse data from 2011 to 2013, and DeadBird data from 2007 to 2011. Instead, to validate the quality of predictions, we used NervSy data from 2011 to 2013, DeadHorse data from 2014, and DeadBird data from 2012 to 2013. To define the background noise of the time series without outbreaks, we fitted alternative regression models based on Poisson and negative binomial (NB) distributions. Models were implemented in R x64 version 3.0.2.

  detecting WNV outbreaks without considering any a priori values for disease status (O pri =1). Examples of simulated baselines with inserted outbreaks and associated variations in log10(V) are presented in Appendix I.The best results for univariate outbreak detection were obtained for NervSy, which outperformed analyses using DeadHorse and DeadBird (figure3 and table 2). DeadBird models yielded intermediary

Figure 1 :

 1 Figure 1: three time series considered. NervSy: number of declaration of nervous syndrome in horses without positive lab result. DeadHorse: number of dead adult horses collected by French fallen stock companies. DeadBird: number of dead wild birds autopsied with values above the 95% confidence interval deleted. Dotted lines = training data, solid black lines = test data, solid blue lines = predicted value, solid red lines = 95% Confidence interval

Figure 2 :

 2 Figure 2: Value of evidence and probabilities of observing n cases during a non-outbreak (Base) and an outbreak (Out) situation. Base= distribution of distribution into the baseline, Out = distribution of cases related to a WNV outbreak, Tot= distribution of cases during an outbreak (Base + Out), Log(V)= log 10 (p(n|outbreak)/p(n|baseline)). Out was based for NervSy on NB(mu= 3.12, theta =1.150), for DeadHorse on NB(mu= 3, theta =2.005), and for DeadBird on NB(mean= 2.23, theta=3.34).

Figure 3 :

 3 Figure 3: ROC curves for univariate and multivariate outbreak detection using NervSy, DeadHorse and DeadBird.

Figure

  Figure 16: EE simulated outbreak in Aquitaine. The outbreak starts mid July 2012 and lengths 6 weeks (from week 29 to

Figure 17 :

 17 Figure 17: Value of evidence in France at week 31 in year 2012 from the simulated outbreak in Aquitaine, using a detection radius of 50 km. Map on the left = respiratory symptoms, middle map = nervous symptoms, map on the right = multivariate syndromic surveillance (Andersson et al. 2015)

Figure 18 :

 18 Figure 18: Posterior probability of EE outbreak in France in year 2012 during the simulated outbreak in Aquitaine from week 29 to week 32. Radius for detection is 50 km (Andersson et al. 2015)



  a. No quarantine and CF test are required Entire period of being at risk of infection is the high risk period (HRP). Probability that the imported host is infected before clin If HRP < e = PO jm × CI m If HRP > e If HRP < 30 + e m × e + CI m-1 × 30 + CI m-2 × (HRP -30 -e)]  Probability that the imported host is infected after clin = PO jm × CI m b. Quarantine and CF tests required Probability that the imported host is infected before q If q m-2 × (60 -q + e) + CI m-3 × (Inf time -60 + q -e)]

  Les valeurs de O post pour lesquelles il sera utile d'agir plutôt que de ne rien faire, sont les valeurs situées au-dessus du seuil O post * défini pour U(A1) = U(A0).

Figure 1

 1 Figure 1 Rapport de vraisemblance (V) et probabilités d'observer n cas de syndromes nerveux chez les chevaux lorsque la maladie est présente (p(n|M+)) et lorsque la maladie est absente (p(n|M-))

Figure 2

 2 Figure 2 Données de syndromes nerveux des chevaux et calcul du rapport de vraissemblance pour chaque semaine. Trois épizooties fictives insérées : A. insertion entre les semaines 36 et 39 ;B. insersion entre les semaines 1 et 4 ; C. insersion entre les semaines 24 et 28.

Table 1 :

 1 Main players in the French equine industry

All of these sub-industries are further subdivided into several sectors, each with its own specific regulations and organizations as presented in Erreur ! Source du renvoi introuvable.. The 'Institut français du cheval et de l'équitation' (IFCE) is a central institute which manages the SIRE database ('système d'identification des équidés') which collects all the data available on French microchipped equids.

Table 3 : import procedure for African horse sickness and equine encephalosis African horse sickness Equine encephalosis High risk

 3

		Quarantine: 40 days	Quarantine: 40 days
		2 ELISA tests with minimum 21 days and maximum 30	2 ELISA tests with minimum 21 days and maximum 30
		days between them (Sensitivity: Beta(60, 4),	days between them (Sensitivity: 1, Specificity: 1)
		Specificity: Beta(62, 2))	Vectors protection (efficacy Uniform(0.5,0.9))
		Vectors protection (efficacy Uniform(0.5,0.9))	Time to clinical inspection: day of embarkation
		Time to clinical inspection: day of embarkation
			Israel:
			Quarantine: 40 days
			No ELISA test.
			Vectors protection (efficacy Uniform(0.5,0.9))
			Time to clinical inspection: day of embarkation
		Quarantine: 40 days	Quarantine: 40 days
	Low risk countries) (non EU	2 ELISA tests with minimum 21 days and maximum 30 No Vectors protection Specificity: Beta(62, 2)) days between them (Sensitivity: Beta(60, 4)	No laboratory test. No vector protection Time to clinical inspection: day of embarkation
		Time to clinical inspection: day of embarkation
	Very low risk (non EU countries)	No quarantine, No laboratory test, No vector protection Time to clinical inspection: at least 48h before embarkation	No quarantine, No laboratory test, No vector protection Time to clinical inspection: at least 48h before embarkation

Table 4 :

 4 Parameters specific of diseases and used for African horse sickness and Equine encephalosis in the model of viruses entry. The parameters used for African horse sickness come from

horse sickness Equine encephalosis Mortality rate for hosts

			Horse: 70%, Donkey: 10%, Zebra: 1%	All equidae: 5%
			When animal died:
			Horse: Gamma(20.25, 0.22)
			Donkey: 12
			Zebra: 28
	Length of viraemia (days)		All equidae: Pert(7, 30) Mean 19
			When animal survived:
			Horse: Gamma(29.75, 0.20)
			Donkey: 28
			Zebra: 40
	Incubation period (days)	Pert(2, 10) Mean 6	Pert(2, 6) Mean 4
	Time between infection and seroconversion (days)	Uniform(10, 14)	Uniform(length of incubation, length of viraemia)
		High risk	Sub-Saharan countries	Sub-Saharan countries + Israel
	Definition of at risk area	Low risk	Regions that have experienced AHS outbreaks in the past and/or where the main vector, C. imicola, is present	Regions that have experienced AHS outbreaks in the past and/or where the main vector, C. imicola, is present
		Very low risk	All the other countries	All the other countries
	Rate of Culicoides	High risk	0.014	Uniform(0.0005,0.23)
	infected
	during an	Low risk	0.00014	Uniform(0.0005,0.23)/100
	outbreak
	High risk	Low risk	2*Incubation period for AHS + time till next infectious blood meal based on 18°C	70 days
	period (days)	Very low risk	2*Incubation period for AHS + time till next infectious blood meal based on 12°C	70 days
	Probability of	Low risk	Gamma(AHS High risk period in Low risk region*15, 1/(365*60)) Mean: 0.016	Gamma(7*365, 1/(365*47)) Mean: 0.14
	disease
	occurrence	Very low risk	Gamma(AHS High risk period in Very Low risk region, 1/(365*61)) Mean: 0.0027	Gamma(EE High risk period in Very Low risk region ,1/(365*48)) Mean: 0.0033

Table 5

 5

	: Description of scenario tested. Scenarios 1 to 5 changed the existing legislation, scenarios 6 to 7
		changes imports from third countries.
	Scenario 1	Quarantine period of 60 days instead of 40
	Scenario 2	Quarantine period of 20 days instead of 40
		Same regulation implemented in Low risk EU state than in low risk non-
		EU state
		1.
	Scenario 3

AHS: Quarantine of 40 days, 2 ELISA tests with minimum 21 days and maximum 30 days between them (Sensitivity: Beta(60, 4) Specificity: Beta(62, 2)), no Vectors protection, and clinical inspection the day of embarkation. 2. EE: Quarantine of 40 days, no laboratory test, no vector protection, and clinical inspection the day of embarkation.

Table 6 :

 6 Change (in %) on median probabilities of viruses entry to France compared to the default scenario.

		African horse sickness	Equine encephalosis
		Infectious	Infectious	Overall	Infectious	Infectious	Overall
		host	vector	risk	host	vector	risk
	Quarantine period of 60 days instead of 40	-1.74	0	-0.17	-0.3	0	-0.10
	Quarantine period of 20 days instead of 40	+2.69	0	+0.27	+0.08	0	+0.03
	Same regulation
	implemented in Low risk EU state than in low risk non-EU	-49.31	0	-4.90	-46.26	0	-15.36
	state
	No serological test implemented	+0.20	0	+0.02	+0.03	0	0.00
	Vector protection
	implemented on all animals	-2.87	-51.07	-46.13	-0.35	-57.26	-2.07
	coming from low risk area
	No importation from high risk region	-3.53	-31.67	-28.78	-0.03	-3.40	-0.12
	No importation from low risk region and non-EU states	-2.88	-0.45	-0.69	-0.29	-0.70	-0.12

Table 7 :

 7 Summary of the advantages and limitations of the main detection algorithms in the time series analysis.

	Detection algorithm	Advantages	Limitations
	Regression
	ARMA		Needs long historical baseline; requires
			preconditioning to remove seasonality, trends,
			and other variations
	ARIMA Trends taken into account	Needs long historical baseline
	SARIMA Seasons taken into account	Needs long historical baseline
	HW Needs short historical baseline; easily	Only one type of seasonality allowed
		automatable; adaptable to local changes
	lm and glm Explanatory variables present; several type of	Needs long historical baseline
		seasons possible
	Historical	Easy to implement	Needs long historical baseline; no adjustment
	limits		possible for trends, disease clusters, or
			aberrations; no consideration of reporting
			delays; inconsistent case inclusion criteria
	Control chart
	Shewhart	Needs short historical baseline; peak-shaped	Requires preconditioning to remove
	chart	outbreak	seasonality, trends, and other variations;
			detection only based on the last previous value
	EWMA Needs short historical baseline; outbreak in	Requires preconditioning to remove
		the form of a slow increase	seasonality, trends, and other variations
	CUSUM Needs short historical baseline; outbreak in	Requires preconditioning to remove
		the form of an increase longer than one time	seasonality, trends, and other variations
		unit

Table 8 :

 8 Metrics used for evaluation of outbreak detection algorithms[START_REF] Buckeridge | Algorithms for rapid outbreak detection: a research synthesis[END_REF][START_REF] Choi | Comparison of Various Statistical Methods for Detecting Disease Outbreaks[END_REF]

	Parameters	Definition
	Sensitivity	Probability of alarm given that an outbreak is occurring. Can be based on overall
		outbreak detection or on the outbreak day number (each day considered a separate
		and independent case)
	Specificity	Probability of no alarm given that an outbreak is not occurring
	Predictive	Probability that an alarm signals a true outbreak
	positive value

Table 9 :

 9 Advantages and disadvantages of types of test data[START_REF] Buckeridge | Algorithms for rapid outbreak detection: a research synthesis[END_REF]

	Type of set	Advantages	Disadvantages
	Wholly authentic	Face validity;	Sufficient resources required to define
		authentic background and outbreak	outbreaks; validity and reliability of outbreak
		signals	indications may be poor and difficult to assess;
			limited number and variety of outbreaks
	Wholly simulated	Exact specification of outbreak signal;	Complexity of simulating baseline and outbreak
		large number of test data possible;	signal;
		can be simple to develop;	validity may be poor and difficult to assess;
		enables sensitivity analyses	can require many parameter values
	Simulated	Greater face validity than wholly	Complexity of simulating outbreak signal;
	outbreaks	simulated test sets;	validity may be poor and difficult to assess;
	superimposed onto	exact specification of outbreak signal;	can require many parameter values
	authentic data	large number of test sets possible;
		enables sensitivity analyses

  passive French surveillance system 'RESPE' (introduced in Chapter I.C.1.3) has collected data on nervous symptoms observed in French horses since 2006. Although the sentinel veterinarians involved in this system are present in most French regions (92 of 96), the nervous symptoms collected are mainly reported from areas with high horse densities (see Figure10). Diagnostic tests for West Nile virus (WNV),

equine herpes virus serotype 1 (EHV-1), and consensus equine herpes virus (EHV-sp)

[START_REF] Léon | Detection of equine herpesviruses in aborted foetuses by consensus PCR[END_REF]

) are systematically implemented for each declaration.

Table 11 :

 11 Smoothing and forecasting performance of Holt-Winters models. ACF and PACF are, respectively, the autocorrelation and partial autocorrelation functions of the residuals. Residuals are theoretically assumed to have an ACF and PACF that have no correlation for all lags. RMSE c and RMSE v are measures of root-mean-squared error within the calibration period and the validation period, respectively.In both cases, lower values are better.

	AIC	RMSE c	RMSE v

Table 14 :

 14 system's detection performances for time series fitted with Holt-Winters. K = constant multiple of the standard error of the model prediction, Se_wk = sensitivity based on detection of each week which is a part of an epidemic period, Se_out = sensitivity based on the number of outbreaks detected, Sp = specificity based on the number of true negative and false positive alarms, Average time of detection = Average number of weeks needed to produce the first alarm within an outbreak.

			Se_wk	Se_out	Sp	Average time of detection (weeks)
		TS0	0.68	0.96	0.71	1.83
	0.5	TS1 TS2	0.76 0.76	0.96 0.96	0.57 0.57	1.56 1.57
		TS3	0.76	0.96	0.57	1.56
		TS0	0.48	0.96	0.94	3.13
	1	TS1 TS2	0.60 0.62	0.96 0.96	0.80 0.80	2.36 2.16
		TS3	0.56	0.96	0.86	2.75
		TS0	0.33	0.96	0.99	3.68
	1.5	TS1 TS2	0.44 0.44	0.96 0.96	0.98 0.97	3.27 3.25
		TS3	0.41	0.96	0.97	3.33
		TS0	0.22	0.88	1	4.10
	2	TS1 TS2	0.37 0.39	0.96 0.96	0.99 0.99	3.38 3.34
		TS3	0.31	0.94	0.99	3.73
		TS0	0.11	0.74	1	4.72
	2.5	TS1 TS2	0.26 0.27	0.92 0.93	1 1	3.85 3.77
		TS3	0.20	0.84	1	4.21
		TS0	0.07	0.60	1	4.38
	3	TS1 TS2	0.21 0.22	0.89 0.89	1 1	4.23 4.01
		TS3	0.15	0.80	1	4.69

Table 1 : Models and models parameters obtained for the three time series.

 1

		NervSy	DeadHorse	DeadBird	NervSy & DeadBird	NervSy & DeadHorse	DeadHorse & DeadBird	Total
	AUC	0.80	0.50	0.75	0.87	0.80	0.75	0.87
	Standard error	0.0082	0.0097	0.0089	0.0068	0.0081	0.0089	0.0068

Table 2 : Area under the ROC curve (AUC) and standard error for univariate and multivariate outbreak detection using NervSy, DeadHorse and DeadBird.

 2

  [START_REF] De Vos | Risk of introducing African horse sickness virus into the Netherlands by international equine movements[END_REF]. For high risk region, CI ijm was estimated for horses as a Pert distribution based on data from WAHID and FAO used by de Vos et al. (de Vos et al. 2012): Pert(4x10

	-6 , 5.02x10	-4 , 1x10	-3

  . Développer des méthodes innovantes pour améliorer la détection d'émergences de WN s'avère ainsi particulièrement intéressant.Appliquée au cas de la surveillance syndromique, on peut définir M+ comme le fait que la maladie soit présente, M-comme le fait que la maladie soit absente et n comme le nombre de syndromes observés à un moment t. est un odds qui correspond aux connaissances a priori qu'on a du statut présence vs absence de la maladie dans un territoire à un moment t. Il tient notamment compte des facteurs de risque connus tels que la saison ou la circulation du pathogène dans une région voisine. Il sera noté O pri dans les paragraphes suivants.

							II -MÉTHODE : CADRE THÉORIQUE
	1.	CADRE STATISTIQUE BAYÉSIEN
	La formule de Bayes se définit initialement comme suit :	La combinaison des connaissances a priori sur la
							maladie avec les informations obtenues à partir
		𝑃(𝑀+) 𝑃(𝑀-)	X	P(𝑛|𝑀+) P(𝑛|𝑀-)	=	𝑃(𝑀+| 𝑛) 𝑃(𝑀-| 𝑛)	des observations de terrain permet d'obtenir le 𝑃(𝑀+| 𝑛) troisième terme 𝑃(𝑀-| 𝑛)
	Le premier terme	𝑃(𝑀+) 𝑃(𝑀-)
	Le second terme	P(𝑛|𝑀+) P(𝑛|𝑀-)	représente le rapport de
	deux probabilités. p(n|M+) est la probabilité

d'observer n cas de syndromes lorsque la maladie est présente et p(n|M-) correspond à la probabilité d'observer le même nombre de syndromes lorsque la maladie est absente. Ce second terme correspond au rapport de vraisemblance noté V dans les paragraphes suivants.

  . La difficulté ici vient du fait que le résultat de l'option choisie est déterminé par l'élément incertain qui ne peut être connu (et ce parfois même après que la décision ait été prise). Pour prendre une décision, il est donc nécessaire d'évaluer les conséquences de chaque action (en termes d'utilité ou de pertes) et leur probabilité de se produire. Le choix rationnel est celui pour lequel l'utilité est maximale c'est-à-dire, celui comportant les pertes attendues les plus faibles.Ainsi, l'utilité d'une action A (noté U(A)) se définit comme la somme des utilités de l'action A dans la situation i (noté chacune U(A i )), multipliée par la probabilité estimée d'être effectivement dans la situation i (noté p(A i )) :Nous avons appliqué ce raisonnement au cas de la prise de décision en surveillance syndromique. Ici seuls deux types d'action sont possibles : A1, mise en oeuvre de mesures de contrôle de la maladie et A0, pas d'action de contrôle. Leurs utilités respectives sont évaluées en fonction du contexte épidémiologique : soit M1 la maladie est présente, soit M0 la maladie est absente. Les pertes relatives à chaque couple U(A i ,M j ) sont fondées sur des évaluations socio-économiques. Les connaissances a priori sur le contexte sont fournies par O post .

	𝑛
	U(A) = ∑ 𝑈(𝐴 𝑖	) × 𝑝(𝐴 𝑖 )
	𝑖=0

des épizooties fictives insérées et valeurs seuils pour le déclenchement d'une action en fonction du nombre de syndromes observés et de la saison

  Un détail des cas observés par épizootie et des rapports de vraisemablance associés est présenté dans le tableau 2. Combiné avec les connaissances a priori sur la saisonnalité de la maladie (O pri ) défini précédement, nos connaissances a posteriori (O post ) sur la maladie sont déduites. Combinée avec le seuil d'action défini à partir des couts estimés, la valeur seuil du nombre de cas à partir de laquelle il est utile d'intervenir est déduite. Ainsi, en automne/été, quatre cas de syndromes nerveux suffisent à déclencher une action alors qu'en hiver, sept cas de syndromes nerveux observés ne déclenchent toujours pas d'action vis-à-vis d'une alerte WN.Dans ce travail, nous avons montré comment le cadre statistique bayésien peut être incorporé dans un système d'aide à la décision en surveillance syndromique et comment il peut être utilisé pour l'évaluation des risques et la prise de décision éclairée. L'approche proposée est en accord avec le guide d'analyse de risque (OIE 2010) puisqu'elle permet une séparation explicite des hypothèses (O pri ), des preuves scientifiques (V) et des critères pour la prise de décision (U(A0) et U(A1)). Par ailleurs, la manière dont les preuves scientifiques sont évaluées est également transparente et quantitative, ce qui limite les interprétations subjectives. Les critères utilisés pour la prise de décision sont également en accord avec ce qui est préconisé par l'OIE. En effet, le code sanitaire pour les animaux terrestres recommande de fonder la décision de mise en place de mesures de contrôle sur l'équilibre entre le coût des activités de lutte et les conséquences économiques et sociales d'une réponse retardée.L'approche utilisée permet de combiner facilement les données de surveillance syndromique avec d'autres sources d'information épidémiologiques. Dans l'exemple développé ici, la prise en compte des données de saisonnalité dans l'interprétation des résultats de la surveillance syndromique permet ainsi de déclencher des alertes pour la fièvre de WN préférentiellement dans les périodes à haut risque. La détection des émergences est ainsi plus sensible en période à haut risque et plus spécifique en période à faible risque. Par exemple, en automne/été, quatre cas de syndromes nerveux suffisent à déclencher une alerte pour WN alors qu'en hiver sept cas de syndromes nerveux observés ne déclenchent pas d'alerte pour WN. Notre approche permet donc de rendre l'interprétation des résultats de la surveillance syndromique plus spécifique sans pour autant diminuer la sensibilité. Ceci est particulièrement intéressant lorsqu'il faut détecter des maladies connues.Dans l'exemple développé ici, seules les connaissances sur la saisonnalité de la circulation du virus WN ont été intégrées. Cependant, des données quantitatives beaucoup plus complexes peuvent être utilisées comme par exemple les résultats de modèles de risque d'introduction ou de risque de diffusion. De même, nous avons travaillé uniquement à une échelle temporelle mais le modèle pourrait être adapté pour détecter des agrégats spatio-temporels de cas. Cette approche offre ainsi des perspectives d'utilisation et de développement ultérieurs intéressants en

	permettant	de	passer	d'informations
	épidémiologiques morcelées à une vision plus
	synthétique et intégrée.
				Tableau 2
	Détails A. Automne/Été	B. Printemps	B. Hiver
	Log 10 (O pri )		-0,99		-1,78		-3,03
	Nombre de cas observés	3	4	5	7	5	7
	Log 10 (V)		0,26	0,74	1,54	3,11	1,24	2,6
	Log 10 (O post )		-0,73	-0,25	-0,24	1,33	-1,77	-0,43
	Seuil d'Action Log 10 (O post *)	-0,38		-0,88		-0,38
	Alerte? O post > O post *	Non	Oui	Oui	Oui	Non	Non
				IV -DISCUSSION

Paper 2

Appendix 6: Poster presented at the 7th EPIZONE meeting in Brussel, 2013.

Appendix 8: Poster presentation at the Journées de l'Ecole doctorale SVSAE inClermont-Ferrand, 2015.

ACKNOWLEDGEMENTS

First of all, I would like to thank the members of the jury, Katharina Stärk, Matthew Baylis and David Biron, for having accepted the invitation to the defense of my doctoral thesis and for reading and commenting this document.

ACKNOWLEDGMENTS

Data on mortality in horses were provided by the French Ministry of Agriculture. Data on mortality in wild birds were provided by the event-based surveillance system "SAGIR", the French surveillance network for wild birds and mammals. Data on nervous symptoms in horses were provided by 'RESPE' (Réseau d'Epidémio-Surveillance en Pathologie Equine). The authors wish to thank all persons involved in these networks (hunters, technicians of FDC and environmental inspectors of ONCFS, local veterinary laboratories, veterinarians, and fallen stock companies) for collecting these data and all these institutes for providing them.

This research was carried out as part of the VICE project funded under the FP7 EMIDA ERA-NET initiative.

National funding within ERA-Net was provided by the Dutch Ministry of Economic Affairs (Project nr. BO-20-009-009) and by the Swedish research council Formas. This work was also partially financially supported by IFCE (Institut Français du Cheval et de l'Equitation) and Vetagro Sup (National Veterinary School of Lyon).

This research was carried out as part of the VICE project funded under the FP7 EMIDA ERA-NET initiative.

National funding within ERA-Net was provided by the Dutch Ministry of Economic Affairs (Project nr. BO-20-009-009). This work was also partially financially supported by IFCE and VetAgro Sup. I would like to thank all these institutes for having made this work possible.

List of Appendices

CORRESPONDENCE ADDRESS

FAVERJON Céline, celine.faverjon@vetagro-sup.fr, INRA UR0346 Animal Epidemiology, VetagroSup, F-ABSTRACT Background: Various methods are currently used for the early detection of West Nile virus (WNV) but their output is either not quantitative or does not take into account all available information. Our study aimed to test a multivariate syndromic surveillance system in order to improve early detection of WNV.

Method: Weekly time series data on nervous syndromes in horses and mortality in both horses and wild birds were used. Baselines were fitted to the three time series and used to simulate 100 years of surveillance data. WNV outbreaks were simulated and inserted into the baselines based on historical data and expert opinion. Univariate and multivariate syndromic surveillance systems were tested in order to gauge how well they detected the outbreaks; detection was based on an empirical Bayesian approach.

The systems' performances were compared using measures of sensitivity, specificity, and area-under-ROCcurve (AUC).

Result: When data sources were considered separately (i.e. univariate systems), the best detection performance was obtained using the dataset of nervous symptoms in horses compared to those of bird and horse mortality (AUCs respectively equal to 0.80, 0.75, and 0.50). A multivariate outbreak detection system that used nervous symptoms in horses and bird mortality generated the best performance (AUC = 0.87).

Conclusion:

The proposed approach is suitable for performing multivariate syndromic surveillance of WNV outbreaks. This is particularly relevant given that a multivariate surveillance system performed better than a univariate approach. Such a surveillance system could be especially useful in serving as an alert for the possibility of human viral infections. This approach can be also used for other diseases for which multiple sources of evidence are available.

KEY WORDS:

West Nile, syndromic surveillance, Bayes, horses, multivariate detection Supplementary figure 1: Examples of simulated baseline with inserted outbreak and corresponding variation of the value of evidence (V). solid black line = simulated data, solid blue line = predicted value, solid red line = 95% confidence interval, Dotted lines = log10(V)

In + Vir -q -t AB Inf time

 When infected between q and cf1

If

 When infected between cf1 and cf2

ii. 𝑃(𝐶𝐹2 𝑖𝑧 ) = Probability for an infected host to be detected by cf2 Assumption: cf1 and cf2 are independent

iii. P(clin) = Probability for an infected host to be detected by clinical inspection  When infected before q If In + Vir < q -clin or

 When infected between q and cf1

If In + Vir < cf1 -clin or In > q -clin = 0

 When infected between cf1 and cF2

 When infected between q and cf1

If In + Vir < cf1 + t AB or In > q + t AB = 0

5. 𝐏(𝐬𝐮𝐫𝐯 𝐤𝐦 ) = Probability that the vector survives to the EIP and can have a blood meal during the month m P(surv km ) = 𝑒 -(𝑁 𝑘𝑚 ×𝐺𝐶 𝑘𝑚 ×𝑀𝑅 𝑘𝑚 )

Appendix 2: Model calculation for PW-vector. Details of calculation regarding the AHSV introduction via the import of an infectious vector.

All the parameters used are detailed in the Appendice 3.

The probability to introduce a single vector from j to k during the month m which is able to induce an entire transmission cycle in which at least one local host is infected by a local vector is defined as: 𝑃(𝑖𝑛𝑡𝑟𝑜𝐵 𝑗𝑘𝑚 ) = 𝑃(𝑟𝑒𝑙𝐵 𝑗𝑘𝑚 ) × 𝑃(𝑒𝑠𝑡𝐵 𝑗𝑘𝑚 )

Where P(relB jkm ) = P (trans culi jm ) × P (surv trans jkm ) × P(inf _culi jm ) × n trans jkm

And P(estB jkm

With culi km the number of vector feeding on an infected viraemic imported host calculated as: culi km = BR km x Vir x C km 1. 𝐏(𝐢𝐧𝐟 _𝐜𝐮𝐥𝐢 𝐣𝐦 ) = Probability for a vector to be infected the month m in area j P(inf _culi jm ) = PO jm × r jm 2. 𝐏 (𝐭𝐫𝐚𝐧𝐬 𝐜𝐮𝐥𝐢 𝐣𝐦 ) = Probability for a vector to be transported after infection from area j

Only a vector which is infected and transported poses a risk, therefore we only consider those vectors that are infected and transported during their life time. We assume that an infected vector will be infected at a uniformly distributed time during its life, D inf . Additionally, we assume that a vector is transported at a uniformly distributed moment during its life time, which is exponentially distributed with mean 1/MR jm .

The probability that the moment of transportation occurs after the infection event is equal to the part of the total lifetime of the vector that it is infected. Thus P (trans culi jm ) is estimated, as made by Napp et al. [START_REF] Napp | Assessment of the risk of a bluetongue outbreak in Europe caused by Culicoides midges introduced through intracontinental transport and trade networks[END_REF]), as:

NB: Temperature in departure area j was assumed to be constant over months and thus MR jm is here also constant over months.

3. 𝐏 (𝐬𝐮𝐫𝐯 𝐭𝐫𝐚𝐧𝐬 𝐣𝐤𝐦 ) = Probability for a vector to stay alive from j until the arrival in area k during the month m The conditions during travel (e.g. temperature) are assumed to not affect the viability of culicoides except when pest control is applied (worst case scenario). There is no data available on survival rate of culicoides in an unfavorable context as assumed to occur during transport. Moreover the conditions during transports have a high variability and information are impossible to collect. The probability to stay alive until the arrival is the probability to survive until transport and during the time of transport. If t jk < GC jm we assume that the last GC m is spent half in the departure area j and half in the arrival area k.

P (surv trans

= e -MR km × GC jm -𝑡 𝑗𝑘 2 NB : if T k < T_min (9.5°C), where T_min is the minimal temperature for formulae for MR and GC (if T k is lower, the formulae are not valid), we will use the T_min in our calculus (worst case scenario). C km is the number of competent vectors feeding on one equine in area k during the month m (details of the estimation available in the main text) -ρ k is the ratio of the number bovines to the number of equines per area k (details of the estimation available in the main text) -e is defined as the day of embarkation (set the 12 th of each month) -q is the length of quarantine ( 40

𝐏(𝐬𝐮𝐫𝐯

Dernières nouvelles du monde : cas de l'Afrique du Sud

En Afrique du Sud 8 des 9 sérotypes circulent de façon enzootique. Un dispositif spécifique à ce pays avait été mis en place par les autorités vétérinaires sud-africaines en collaboration avec l'Union Européenne. Ainsi, l'UE avait demandé qu'une zone de surveillance sans vaccination autour de Cap Town et qu'une zone de protection avec vaccination autour de cette dernière ait été mise en place. Les chevaux qui devaient être exportés vers l'UE devaient subir une quarantaine (40 jours) en station confinée à Cape Town. En 2011, un foyer dans la zone de surveillance avait entraîné l'arrêt des exportations vers l'UE. En mai 2013, soit 2 ans après cet épisode, une visite de contrôle a été effectuée par les représentants de l'UE. Cependant, les conditions ne semblent pas encore réunies pour que les échanges directs de chevaux vers l'UE puissent reprendre dans des conditions satisfaisantes.

Risque d'introduction en France

Les principaux vecteurs du virus, les Culicoides, sont présents sur l'ensemble du territoire français.

ABSTRACT

In this work we propose the adoption of a statistical framework to be used in the evaluation of forensic evidence as a tool for evaluating and presenting circumstantial "evidence" of a disease outbreak from syndromic surveillance. The basic idea is to exploit the predicted distributions of reported cases to calculate the ratio of the likelihood of observing n cases given an ongoing outbreak over the likelihood of observing n cases given no outbreak. The likelihood ratio defines the Value of Evidence. Using Bayes´ rule, the prior odds for an ongoing outbreak are multiplied with V to obtain the posterior odds.