Samuel Alizon
email: samuel.alizon@cnrs.fr

MIVEGEC Mircea T Sofonea

SARS-CoV-2 virulence evolution: avirulence theory, immunity, and trade-offs

Keywords: virus, trade-off, immunopathology, genomics, epidemiology, immune escape, maladaptation

The COVID-19 pandemic has led to a resurgence of the debate on whether host-parasite interactions should evolve towards avirulence. In this review, we first show that SARS-CoV-2 virulence is evolving, before explaining why some expect the mortality caused by the epidemic to converge towards that of human seasonal alphacoronaviruses. Leaning on existing theory, we then include viral evolution into the picture and discuss hypotheses explaining why the virulence has increased since the beginning of the pandemic. Finally, we mention some potential scenarios for the future.

Introduction

The year 2019 witnessed the emergence of one of the largest and fastest-spreading pandemics ever, which had caused more than 80 million infections and claimed more than 1.8 million human lives throughout the world by the end of 2020 (World Health Organisation, 2021b). In April 2021, the pandemic was still out of control in many countries all over the world. The causative agent was rapidly identified as a novel coronavirus and named SARS-CoV-2 [START_REF] Gorbalenya | The species Severe acute respiratory syndrome-related coronavirus : classifying 2019-nCoV and naming it SARS-CoV-2[END_REF]. Its most likely origin is believed to be from viruses currently circulating in bat populations (World Health Organisation, 2021c).

Many reviews have been written on the evolutionary origin of the virus [START_REF] Andersen | The proximal origin of SARS-CoV-2[END_REF][START_REF] Boni | Evolutionary origins of the SARS-CoV-2 sarbecovirus lineage responsible for the COVID-19 pandemic[END_REF] and on its genetic evolution since then (van Dorp et al., 2020a;[START_REF] Worobey | The emergence of SARS-CoV-2 in Europe and North America[END_REF]. Here, we focus on the phenotypic evolution of infection life-history traits and, in particular, on virulence.

When it comes to the negative effects of infectious diseases on their hosts, a set of related but distinct notions can be found in the literature: mortality, lethality, pathogenicity, and virulence. Among the four, mortality is the only aspect that refers to the population [START_REF] Bonita | Basic epidemiology[END_REF]. The others are defined at the level of an individual. Lethality, or fatality ratio, is the probability for an infected host to die in a given context. For SARS-CoV-2, lethality was rapidly shown to be 10 times that of seasonal influenza and also to strongly depend on age [START_REF] Verity | Estimates of the severity of coronavirus disease 2019: a model-based analysis[END_REF]. However, it is important to stress that this trait varies depending on access to healthcare infrastructure or treatments availability. Pathogenicity can be defined at the cellular level and characterises some of the harmful interactions between the virus and host cells [START_REF] Isenberg | Pathogenicity and virulence: another view[END_REF]. Finally, virulence is defined as the decrease in host fitness due to the infection [START_REF] Read | The evolution of virulence[END_REF]. Contrarily to the other definitions, it has an evolutionary dimension because it involves the notion of fitness, which is notoriously difficult to measure. Overall, the choice of the most appropriate trait to measure to study virulence evolution should maximise measurement practicality and public health importance, but also, most importantly, trait values should affect infection fitness [START_REF] Alizon | Adaptive virulence evolution: the good old fitness-based approach[END_REF].

In the following, unless stated otherwise and to simplify the reasoning, we will consider the infection fatality ratio (IFR), which is the proportion of infected hosts that dies from the infection, to be a proxy of virulence. At the individual level, it is the metric that has the most direct meaning to a wide audience, however, care must be taken at the population level because IFR strongly varies with age [START_REF] Verity | Estimates of the severity of coronavirus disease 2019: a model-based analysis[END_REF][START_REF] O'driscoll | Age-specific mortality and immunity patterns of SARS-CoV-2[END_REF] (Figure 1A). This implies that the age pyramid of a country shapes the IFR, even if the latter is assumed not to depend on non-demographic conditions, e.g. health care (Figure 1B). Furthermore, host immunity introduces another dimension of variation that needs to be accounted for when estimating the IFR.

We first present the evidence for the evolution of SARS-CoV-2 virulence. We then explain why some predict the virus population will evolve towards avirulence, before explaining why current trends do not follow this expectation. Finally, we present some hypotheses for future evolutionary dynamics.

From neutral mutants to 'variants'

For nearly a year, there was little clear evidence of phenotypic variations that could be linked to virus genetics. Of course, as shown by in vitro experiments of deep mutational scanning [START_REF] Starr | Deep Mutational Scanning of SARS-CoV-2 Receptor Binding Domain Reveals Constraints on Folding and ACE2 Binding[END_REF], some mutations have strong effects and many decrease the affinity of the Receptor Binding Domain (BBD) of the virus Spike protein to the human ACE2 receptor so much that they are likely detrimental. An exception that proves the rule is the D614G substitution in the Spike protein, which occurred independently in different lineages throughout the world and was shown to increase the affinity of the virus for the ACE2 receptor on human cells [START_REF] Korber | Tracking Changes in SARS-CoV-2 Spike: Evidence that D614G Increases Infectivity of the COVID-19 Virus[END_REF]. This was associated with an increased transmission rate in some regions, although teasing apart this effect from genetic drift was difficult in some locations [START_REF] Volz | Evaluating the effects of SARS-CoV-2 Spike mutation D614G on transmissibility and pathogenicity[END_REF].

The picture completely shifted at the end of 2020 with the emergence of what are now referred to as 'variants of concern' (VOC). To avoid confusion, unless stated otherwise, we will only use the term 'variant' to refer to virus strains that cause phenotypically different infections compared to a reference, 'wild type', strains. For some strains, this phenotypic effect may be suspected, for instance, if several epidemiological clustered cases are caused by virus lineages bearing some mutations suspected to have strong phenotypic effects. The potential VOCs are referred to as variants of interest (VOI) and closely monitored by health authorities. Less preoccupying variants are referred to as variants under investigation (VUI). We also use the term lineage to refer to all viruses that have a different genotype than the ancestral reference.

As mentioned above, the D614G mutation is associated with an increased transmission rate [START_REF] Volz | Evaluating the effects of SARS-CoV-2 Spike mutation D614G on transmissibility and pathogenicity[END_REF] and, therefore, can be considered as a VOC. A second VOC (see Table 1 for a summary) was detected in September 2020 in Kent (UK) because a high proportion of ThermoFisher RT-PCR screening tests were exhibiting an unusual pattern. Indeed, this assay contains probes targeting three areas of the SARS-CoV-2 genome (in ORF1, S, and N). Although in a small proportion of tests, one of the probes sometimes failed to detect its target, laboratories were seeing rapidly increasing numbers of RT-PCR tests that seemed positive but where the S gene was not detected. This phenomenon was referred to as S-gene target failure (SGTF). The analysis of sequencing data confirmed that infections with SGTF were caused by viruses belonging to the same lineage (B.1.1.7). The striking surprise was that these bore much more mutations in their genome than expected given the substitution rate estimated so far, with several of them, such as the N501Y mutation and ∆69-70 deletion in the Spike protein, being already under scrutiny [START_REF] Rambaut | Preliminary genomic characterisation of an emergent SARS-CoV-2 lineage in the UK defined by a novel set of spike mutations[END_REF]. The dense epidemiological survey in the UK was used to track the SGTF in positive RT-PCR tests and the statistical analyses identified a significant transmission advantage of what is now known as the α variant over the other lineages (Davies et al., 2021a;[START_REF] Volz | Transmission of SARS-CoV-2 Lineage B.1.1.7 in England: Insights from linking epidemiological and genetic data[END_REF]. The analysis of in contact-tracing data also identified a higher per-contact transmission risk (Variant Technical group, 2021). Variant α spread all over the world, and similar transmission advantages were estimated in countries such as Denmark, Switzerland (Davies et al., 2021a), or France [START_REF] Haim-Boukobza | Detection of Rapid SARS-CoV-2 Variant Spread[END_REF].

A few months later, two analyses conducted in the UK detected a possible increase in the virulence of the infections caused by the α variant [START_REF] Challen | Risk of mortality in patients infected with SARS-CoV-2 variant of concern 202012/1: matched cohort study[END_REF]Davies et al., 2021b). Care must be taken to interpret these results because many SARS-CoV-2 infections are asymptomatic, meaning that the case fatality ratio (CFR) can differ from the infection fatality ratio (IFR) [START_REF] Verity | Estimates of the severity of coronavirus disease 2019: a model-based analysis[END_REF]. Indeed, the former quantifies the fraction of deaths among detected COVID-19 cases (usually because they are symptomatic), whereas the latter estimates the fraction of deaths among all infected hosts. Logically, CFRs are greater than IFRs. However, as reported by both studies, the fraction of infections caused by 501.V1 is not higher when analysing data from a random sample of the population instead of symptom and contactoriented tests. This rules out the possibility that the variant might be causing an increased proportion of asymptomatic infections, which would bias the IFR estimate.

In summary, there is reasonable evidence that variant α, according to the World Health Organisation's (WHO) terminology (World Health Organisation, 2021a), has an increased transmission rate and an increased virulence compared to the wild type strains.

Also at the end of 2020, another lineage (B.1.351) was reported to spread rapidly in South Africa. Sequencing quickly revealed that it too bore a higher number of mutations than expected based on the mean molecular clock value [START_REF] Tegally | Emergence and rapid spread of a new severe acute respiratory syndrome-related coronavirus 2 (SARS-CoV-2) lineage with multiple spike mutations in South Africa[END_REF]. Among these mutations, there was the N501Y substitution found in variant α, but also the E484K mutation, which is associated with immune escape [START_REF] Cele | Escape of SARS-CoV-2 501Y.V2 variants from neutralization by convalescent plasma[END_REF]. Evidence from other countries confirmed that what is now known as the β variant also has a transmission advantage over wild type strains. Its virulence remains less known but its ability to evade natural host immunity and even some vaccine immunity is very likely [START_REF] Hoffmann | SARS-CoV-2 variants B.1.351 and P.1 escape from neutralizing antibodies[END_REF].

Table 1 -Taxonomy and properties of the main SARS-CoV-2 variants detected to date.

Only variants with demonstrated phenotypic differences are shown. 'Detection' indicates the first country to report the variant and 'date' indicates the date of the earliest sample known. 'WHO' (World Health Organisation, 2021a), 'pango' [START_REF] Rambaut | A dynamic nomenclature proposal for SARS-CoV-2 lineages to assist genomic epidemiology[END_REF], 'GISAID' [START_REF] Elbe | Data, disease and diplomacy: GISAID's innovative contribution to global health[END_REF], and 'nextstrain' [START_REF] Hadfield | Nextstrain: real-time tracking of pathogen evolution[END_REF] refer to the main nomenclatures. Mutations and deletions (∆) in the Spike protein compared to the first sequence from Wuhan (China) were obtained from outbreak.info [START_REF] Latif | the Center for Viral Systems Biology[END_REF]. Mutations of concern are highlighted in italic. A third major epidemic took place at the end of 2020 that suggested involvement in virus evolution. This epidemic was unexpected because it took place in Brazil and especially in the region of Manaus, where serological data suggested that, after a major health catastrophe, the cumulative incidence reached the theoretical herd immunity threshold [START_REF] Buss | Three-quarters attack rate of SARS-CoV-2 in the Brazilian Amazon during a largely unmitigated epidemic[END_REF]. As for the other variants, genomic analyses again showed that the new epidemic was associated with a specific lineage bearing several mutations (P.1), including the N501Y and E484K substitutions [START_REF] Faria | Genomics and epidemiology of a novel SARS-CoV-2 lineage in Manaus, Brazil[END_REF]. In this case, the analysis was able to detect a significant transmission advantage of what is now known as the γ variant, as well as an ability to reinfect hosts with natural immunity [START_REF] Hoffmann | SARS-CoV-2 variants B.1.351 and P.1 escape from neutralizing antibodies[END_REF].

The last WHO VOC, now known as the δ variant, corresponds to the B.1.617.2 lineage. The oldest known sample dates from the end of 2020 and was collected in India, where the variant was associated with a major outbreak in spring 2021. Early analyses in United Kingdom, where it reached the majority of new contaminations early in 2021, suggest that the δ variant is associated with an increased transmissibility and, potentially, an increased risk of hospitalisation, compared to the α variant (Scientific Pandemic Influenza Group on Modelling, Operational sub-group, 2021; Public Health England, 2021). Early epidemiological results also suggest that this new variant may partially evade immunity [START_REF] Bernal | Effectiveness of COVID-19 vaccines against the B.1.617.2 variant[END_REF], especially in people with only a single vaccine dose [START_REF] Bernal | Effectiveness of COVID-19 vaccines against the B.1.617.2 variant[END_REF]. Furthermore, the fact that the δ variant does not bear the N501Y and E484K mutations found in respectively in all three and two previous VOCs, illustrates the limits of SARS-CoV-2 convergent evolution [START_REF] Martin | The emergence and ongoing convergent evolution of the N501Y lineages coincides with a major global shift in the SARS-CoV-2 selective landscape[END_REF] and challenges the current existence of strong genomic bottlenecks.

Many VOIs have been reported worldwide World Health Organisation (2021a) but, by definition, their phenotypic effect on infection life-history traits remains limited, if not unknown. Note that one of these VOI, CAL.20C (pango lineages B.1.427 and B.1.429), which was first detected in California (USA), was shown to have a slight transmission advantage [START_REF] Zhang | Emergence of a Novel SARS-CoV-2 Variant in Southern California[END_REF]. In France, variant 20C/H655Y (pango lineage B.1.616) appears to have a pronounced tropism for lower respiratory tracts and seemed difficult to detect using classical nasopharyngeal swabs [START_REF] Fillatre | A new SARS-CoV-2 variant poorly detected by RT-PCR on nasopharyngeal samples, with high lethality[END_REF].

In the context of the 'test, trace, and isolate' strategy implemented by many countries, this latter VOI raises speculations about a potential transmission-detection trade-off. Indeed, specialising in colonising the epithelium of the upper airways is expected to yield a transmission gain for the virus [START_REF] Wölfel | Virological assessment of hospitalized patients with COVID[END_REF][START_REF] Harrison | Mechanisms of SARS-CoV-2 Transmission and Pathogenesis[END_REF] but it also increases the probability of detection using nasopharyngeal swabs. If case isolation measures are strong [START_REF] Grassly | Comparison of molecular testing strategies for covid-19 control: a mathematical modelling study[END_REF], such a tropism can greatly affect further virus transmission. Therefore, if the selection pressure exerted by nasopharyngeal mass testing measures is significant enough, the evolution of a virus tropism towards the lower respiratory tract and, hence, an increased virulence, could be favoured if the decrease in detection probability compensates the decrease in transmission rate.

What is likely is the replacement of the ancestral lineages by variants with a significantly different genetic background is likely going to set a new stage for the SARS-CoV-2 fitness landscape [START_REF] Martin | The emergence and ongoing convergent evolution of the N501Y lineages coincides with a major global shift in the SARS-CoV-2 selective landscape[END_REF]. In other words, mutations that had little effect or were deleterious in the ancestral genome may prove to be adaptive. Furthermore, the immunisation of the population is introducing a coevolutionary dimension, which makes the effect of specific mutations difficult to anticipate.

On the road to avirulence?

Theory stemming from Theobald Smith's law of declining virulence more than a century ago [START_REF] Méthot | Why do Parasites Harm Their Host? On the Origin and Legacy of Theobald Smith's 'Law of Declining Virulence' -1900-1980[END_REF] postulates that we should expect SARS-CoV-2 to evolve to cause avirulent infections in humans. Although this reasoning is frequently invoked for many infectious diseases, in the current case it is reinforced by the fact that the most common, and seasonal, coronaviruses we know cause little mortality [START_REF] Gorbalenya | The species Severe acute respiratory syndrome-related coronavirus : classifying 2019-nCoV and naming it SARS-CoV-2[END_REF].

A model by [START_REF] Lavine | Immunological characteristics govern the transition of COVID-19 to endemicity[END_REF] elegantly explains why SARS-CoV-2 could become a seasonal virus causing little mortality at the population level. The essential ingredients of their reasoning are that i) the IFR strongly depends on age, and ii) the immunity that prevents severe disease (i.e. anti-virulence immunity) is long-lasting. What they show is that such an age-structured system can converge in a matter of years towards a steady state where individuals are infected as children, which allows them to build an immune response with very low mortality. This immunity prevents severe symptoms (i.e. COVID-19) when infected as adults. The time to converge towards this state depends on how fast the virus spreads, which itself depends on the transmission rate of the virus and the intensity of transmission-blocking immunity. The authors also find that this trend is not expected for coronaviruses such as Severe Acute Respiratory Syndrome (SARS) and Middle-East Respiratory Syndrome (MERS) because their virulence in children is so high that it would lead to massive mortality at the population level. Importantly, this reasoning focuses on mortality (i.e. a population-level variable) and that it does not require any virulence evolution per se (the IFR remains unchanged for a given age).

When virus evolution is allowed, the existence of multiple SARS-CoV-2 infection sites can be used to build scenarios consistent with the avirulence hypothesis [START_REF] Smith | Parasitic bacteria and their relation to saprophytes[END_REF]. To simplify, when this virus infects lower respiratory tracts (LRT), it faces a strong immune response, it causes more damage to host tissues, and its transmission to new hosts is limited. Conversely, in the upper respiratory tract (URT), infections face a weak immune response, cause minor damage to the host, and achieve high transmission rates [START_REF] Harrison | Mechanisms of SARS-CoV-2 Transmission and Pathogenesis[END_REF]. The virus can also infect cells in the intestinal tracts [START_REF] Xiao | Evidence for gastrointestinal infection of sars-cov-2[END_REF]. This is thought to be associated with diarrhoea but the transmission potential is unknown [START_REF] Guo | Potential intestinal infection and faecal-oral transmission of SARS-CoV-2[END_REF]. Therefore, one expects natural selection to favour SARS-CoV-2 mutants that specialise in infecting URT because it maximises transmission and, more importantly, because immunity will build up in the LRT, either through recovery from natural infection or from vaccination.

Given that the ACE2 receptor, which is SARS-CoV-2's entry point into the cells, is more expressed in the URT than in the LRT, and given that many mutations in the Spike protein increase its affinity for ACE2 [START_REF] Ziegler | SARS-CoV-2 Receptor ACE2 Is an Interferon-Stimulated Gene in Human Airway Epithelial Cells and Is Detected in Specific Cell Subsets across Tissues[END_REF], the fixation of the D614G mutation could be interpreted as an evolutionary trend towards avirulence. However, another interpretation is that this increased affinity for the receptor might not be traded-off for a lower ability to exploit the LRT, therefore combining increased transmission rate and virulence. The latter seems more likely given that variant α represents the majority of the genomes uploaded on the GISAID platform since February 2021, meaning that, so far, the average virulence of the world population of SARS-CoV-2 has increased.

Why is SARS-CoV-2 virulent?

When a parasite spills into a new host population, it is often maladapted because there are known tradeoffs relating to host exploitation. This host specialisation was actually used to create live-attenuated vaccines by performing serial passages of a parasite through cell cultures, or chicken eggs, or another host, to generate less virulent strains that could be used for vaccination [START_REF] Ebert | Experimental evolution of parasites[END_REF]. As we will see later, when it comes to virulence, there is no rule for maladaptation: the virus can be nearly avirulent if it fails to exploit human cells, but it can also be extremely virulent if it causes massive immunopathology, e.g. via the activation of cytokine storms. Illustrating these differences in maladaptation is difficult because, ideally, it would require finding different strains of the same parasite species that are maladapted in different ways. In the case of coronaviruses, two extreme examples could be MERS, which is extremely virulent in humans [START_REF] Lessler | Estimating the Severity and Subclinical Burden of Middle East Respiratory Syndrome Coronavirus Infection in the Kingdom of Saudi Arabia[END_REF], and feline coronavirus, which cannot infect humans [START_REF] Sykes | Feline Coronavirus Infection[END_REF]. In the case of SARS-CoV-2, evidence point more towards maladaptation with high virulence given the physiopathology of the infection [START_REF] Tay | The trinity of COVID-19: immunity, inflammation and intervention[END_REF].

Maladaptation to a novel host can account for SARS-CoV-2's initially large virulence but it does not explain why it is not decreasing rapidly. A first possibility is that natural selection cannot act on SARS-CoV-2 virulence, for instance, because of a lack of genetic variability [START_REF] Dearlove | A SARS-CoV-2 vaccine candidate would likely match all currently circulating variants[END_REF]van Dorp et al., 2020b). RNA viruses have to balance large mutation rates and strong genomic constraints and it could be that there is no viable way for the virus to decrease the immunopathology it causes (Belshaw The clinical timeline shows the distribution function of the incubation period (time from infection to onset of symptoms), the vertical bar representing the median value [START_REF] Mcaloon | Incubation period of covid-19: a rapid systematic review and meta-analysis of observational research[END_REF]. The breakdowns into clinical phases are exposed is presented with respect to the median symptom onset date [START_REF] Bouadma | Severe sars-cov-2 infections: practical considerations and management strategy for intensivists[END_REF][START_REF] Polak | A systematic review of pathological findings in covid-19: a pathophysiological timeline and possible mechanisms of disease progression[END_REF][START_REF] Nalbandian | Post-acute covid-19 syndrome[END_REF]. The asymptomatic fraction on the top is that estimated by [START_REF] Byambasuren | Estimating the extent of asymptomatic covid-19 and its potential for community transmission: systematic review and meta-analysis[END_REF]. The epidemiological timeline represents the probability density of the generation time estimated by [START_REF] Ferretti | The timing of covid-19 transmission[END_REF], with the vertical bar showing the median. The latency is the time between infection and the onset of contagiousness. The diagnosis timeline indicates the positivity kinetics of nasopharyngeal RT-qPCR tests. Following the estimates from [START_REF] Hellewell | Estimating the effectiveness of routine asymptomatic pcr testing at different frequencies for the detection of sars-cov-2 infections[END_REF], more than 50% of cases are positive in the central green band and more than 5% in the peripheral light green bands. Antigenic and serological (immunoglobulin (Ig) M and G) test positivities are shown for qualitative purposes following the estimates from [START_REF] Mercer | Testing at scale during the covid-19 pandemic[END_REF]Salit (2021). et al., 2008). Note that, as pointed out earlier, these constraints could be changing and the fixation of many mutations in the variant lineages could have reshaped the fitness landscape [START_REF] Martin | The emergence and ongoing convergent evolution of the N501Y lineages coincides with a major global shift in the SARS-CoV-2 selective landscape[END_REF].

Even if we assume that mutants with a comparable transmission ability and a lower virulence than the wild type strains could emerge, it is still possible that they would not have a clear advantage in terms of natural selection. Indeed, it is essential to account for the life-history of the infection (Figure 2). Although the IFR is approximately 10 times that of seasonal influenza, severe symptoms and hospital admission are a minority and, when they occur, take place on average 14 days after infection [START_REF] Sofonea | Epidemiological monitoring and control perspectives: application of a parsimonious modelling framework to the COVID-19 dynamics in France[END_REF]. By that time, contagiousness is virtually negligible since 95% of the transmission events seem to occur between 2 to 11 days after infection [START_REF] He | Temporal dynamics in viral shedding and transmissibility of COVID-19[END_REF]. More generally, the symptoms of an index case appear on average 1.3 days after the mean transmission time to her/his 'infectee' [START_REF] Alene | Serial interval and incubation period of covid-19: a systematic review and meta-analysis[END_REF]. Therefore, from the virus' perspective, harming the host is not very costly as it will have little effect on its epidemiological fitness, which, if we leave aside host immunity, can be approximated through the basic reproduction number (R 0 ), i.e. the average number of secondary infections caused by an infected person during her infectious period. As explained by [START_REF] Day | Virulence evolution and the timing of disease life-history events[END_REF], this idea echoes classical results from life-history theory, especially the evolution of ageing, where traits that have deleterious late in life tend not to be selected against.

Since the early 1980s, an explanation for the maintenance of virulence is that the latter can be correlated with traits that are adaptive for the parasite [START_REF] Levin | Selection of intermediate rates of increase in parasite-host systems[END_REF][START_REF] Anderson | Coevolution of hosts and parasites[END_REF][START_REF] Ewald | Host-parasite relations, vectors, and the evolution of disease severity[END_REF][START_REF] Bremermann | A game-theoretical model of parasite virulence[END_REF]. For instance, as shown in the case of HIV, strains that cause the most virulent infections tend to be the more transmissible, and the correlation between the two traits could be mediated by the virus load [START_REF] Fraser | Virulence and pathogenesis of HIV-1 infection: an evolutionary perspective[END_REF]. According to such a transmission-virulence trade-off hypothesis, the exact shape of the relationship between the two traits determines the level of virulence that maximises the epidemiological fitness of the virus [START_REF] Alizon | Virulence evolution and the trade-off hypothesis: history, current state of affairs and the future[END_REF]. The latter can be seen, in the simplest setting, as the number of secondary infections caused by an infected host. Note that the transmission-virulence trade-off is restrictive and that other infection life-history traits should be taken into account to capture the whole life-cycle of the virus [START_REF] Alizon | Adaptive virulence evolution: the good old fitness-based approach[END_REF]. In the case of SARS-CoV-2, it may be relevant to investigate virulence-recovery trade-offs (i.e. more virulent strains would have longer infectious periods, [START_REF] Anderson | Coevolution of hosts and parasites[END_REF]) or transmissionrecovery trade-offs (if strains that cause shorter infections have higher transmission rates, [START_REF] Alizon | Transmission-recovery trade-offs to study parasite evolution[END_REF]). Another life-history trait that could matter is the time until symptom onset because infectiousness of asymptomatic hosts is a key driver of epidemic spread [START_REF] Fraser | Factors that make an infectious disease outbreak controllable[END_REF]. Trade-offs involving this trait have been less studied but Saad-Roy et al. ( 2020) investigated the evolutionary consequence of a trade-off between the duration of the asymptomatic period and the transmission rate and, more generally, [START_REF] Sorrell | The evolution of covert, silent infection as a parasite strategy[END_REF] studied the evolution of asymptomatic infections, which could have implications for SARS-CoV-2 given that some individuals appear never to exhibit any symptoms.

In the case of SARS-CoV-2, some (limited) evidence suggests that increased virulence can be associated with variations in other life-history traits that are adaptive for the virus. For instance, a contacttracing study showed that individuals with higher viral loads tend to infect a larger proportion of their contacts [START_REF] Marks | Transmission of COVID-19 in 282 clusters in Catalonia, Spain: a cohort study[END_REF]. Furthermore, longitudinal follow-ups show that patients who develop more severe infections tend to have higher virus loads (estimated via the cycle threshold values of RT-qPCR tests) for a longer time [START_REF] Néant | Modeling SARS-CoV-2 viral kinetics and association with mortality in hospitalized patients from the French COVID cohort[END_REF]. Therefore, it could be envisaged that an increased virus load could lead to both increased virulence and contagiousness. Finally, there is data suggesting that the α variant is causing longer infections [START_REF] Cosentino | SARS-CoV-2 viral dynamics in infections with variants of concern in the French community[END_REF][START_REF] Elie | Inferring SARS-CoV-2 variant within-host kinetics[END_REF].

The adaptive virulence hypothesis is illustrated in Figure 3B, which assumes a transmission-virulence trade-off. If the virus population is sitting on the trade-off curve and if the virulence is below the level that maximises the viral fitness, any increase in transmission rate requires an increase in virulence. However, the trade-off curve only indicates a constraint and, as we saw above, the virus population could very well be located far from the optimum (Figure 3C). In this case, short-term evolutionary dynamics are more difficult to anticipate because first, we do not know how far the virus population is from the trade-off curve (there are many ways to be maladapted) and second, what matters in the short term is the shape of the local fitness landscape. To take a verbal example, one could imagine that a mutant with a virulence and transmission rate could have higher epidemiological fitness (or R 0 ) than its strain of origin, even if the virulence of this strain is already larger than that of the evolutionary stable strategy (the black dot in Figure 3C). In the other scenarios, such a mutant would most likely have a small R 0 than its strain of origin (Figure 3A) or be a biological aberration (i.e. fall into the non-viable area in Figure 3B).

More generally, non-equilibrium dynamics can explain the persistence of virulent strains, at least transiently. As clearly shown using the Price equation formalism, in the short term, and under the assumption of a correlation between virulence and transmission, more virulent strains tend to be favoured early in an epidemic [START_REF] Day | A general theory for the evolutionary dynamics of virulence[END_REF]). The underlying process, which has been shown experimentally using bacteria and phages [START_REF] Berngruber | Evolution of virulence in emerging epidemics[END_REF], is that in an expanding population, an increase in birth rate (or, in the case of an epidemic, transmission) bring more benefits than the same increase in longevity (or infection duration). When the population shrinks, which is the case after an epidemic peak, longevity then becomes more important than birth rates. The Essay by [START_REF] Day | On the evolutionary epidemiology of SARS-CoV-2[END_REF] discusses these non-equilibrium dynamics in the context of the COVID-19 pandemic showing, for instance, that the strongest selective pressure in the initial stage of the epidemic is for increased transmission rate. They also expect selection to favour viruses that tend to be less virulent and cause less symptomatic infections. Virulence and transmission rate are correlated and strains are well-adapted (i.e. they sit on the trade-off curve), and C) same as B but strains are currently maladapted (far from the trade-off curve). Dashed blue lines show hypothetical transmission-virulence relationships, shaded blue areas the inaccessible state space, and black dots the trait combinations maximising invasion fitness in a naive population (R 0 ). Dashed arrows show potential evolutionary trajectories. Virulence and transmission rates are in arbitrary units. The virulence and transmission rate of the β and γ variants are currently largely unknown. For the γ variant, the transmission rate appears to be higher [START_REF] Buss | Three-quarters attack rate of SARS-CoV-2 in the Brazilian Amazon during a largely unmitigated epidemic[END_REF]. Viruses can emerge anywhere in the white area, even if they cause virulent and poorly transmissible infections as B.1.616 [START_REF] Fillatre | A new SARS-CoV-2 variant poorly detected by RT-PCR on nasopharyngeal samples, with high lethality[END_REF]. For further details about the variants, see Table 1.

The future

The evolution of variants has changed the nature of the SARS-CoV-2 pandemic by showing that strong phenotypic evolution is possible for this virus. Interestingly, the difficulty to label these variants is a direct illustration of the ongoing evolutionary dynamics. With the emergence of the D614G mutation in many lineages around the world [START_REF] Volz | Evaluating the effects of SARS-CoV-2 Spike mutation D614G on transmissibility and pathogenicity[END_REF], it was tempting to define VOCs through 'mutations of concern'. This was further supported by the parallel evolution of the N501Y mutation in the α, β, and γ variants or of the E484Y mutation in the β and γ variants. However, it is also troubling that VOC all appear to bear a higher number of mutations in their genome than other lineages (Table 1). Furthermore, except for D614G, mutations of concern such as N501Y or E484K seem to be advantageous only in some generic backgrounds. For instance, in the UK, the B.1.1.7 lineage (i.e. the α variant) bearing the E484K mutation appears to have a smaller epidemiological fitness than the β or γ variants. Current trends suggest that epistatic interactions may now dominate SARS-CoV-2 evolution and that mutations with effects similar to D614G could be rare. However, it may be hazardous to use past evolutionary trends to anticipate SARS-CoV-2 evolution since the fitness landscape that viruses can explore changes as the virus population evolves. For instance, the fixation of the N501Y mutation in the genome has been suggested to deeply affect the fitness landscape compared to that inferred from the original strain detected in Wuhan, China [START_REF] Martin | The emergence and ongoing convergent evolution of the N501Y lineages coincides with a major global shift in the SARS-CoV-2 selective landscape[END_REF].

The epidemiological scenario by [START_REF] Lavine | Immunological characteristics govern the transition of COVID-19 to endemicity[END_REF], which does not include virus evolution, relies on the assumption that host immunity against symptoms is robust. Unfortunately, field epidemiological data suggests that this might not be the case for the β and γ variants (Abdool Karim and de Oliveira, 2021), and, perhaps, for the δ variant [START_REF] Bernal | Effectiveness of COVID-19 vaccines against the B.1.617.2 variant[END_REF]. For some vaccines, this immunity appears to be more robust but will this still be the case for future variants? Currently, the greatest unknown appears to reside in immune escape, which can jeopardize the avirulence scenarios. Indeed, with immune escape, absolute fitness (i.e. R 0 ) should be abandoned in favour or relative fitness measures since the ability of a strain to spread will depend on the immunity of the population, that is on the nature of the strains that are and that have circulated in the past [START_REF] Lion | Beyond R0 Maximisation: On Pathogen Evolution and Environmental Dimensions[END_REF].

With the diversification of SARS-CoV-2, the role of multiple infections will likely increase, and these are known to affect virulence evolution [START_REF] Alizon | Multiple infections and the evolution of virulence[END_REF]. Even for short respiratory infections, some infection patterns, in the sense of [START_REF] Sofonea | Exposing the diversity of multiple infection patterns[END_REF], such as ambinfection, where genotypes are always co-transmitted, could matter [START_REF] Lythgoe | SARS-CoV-2 within-host diversity and transmission[END_REF]. Furthermore, the alleviation of non-pharmaceutical interventions implemented to control the pandemic will allow other respiratory infections to spread again. This is particularly true for influenza virus. Here, the evolutionary dynamics are even more difficult to foresee because these involve coevolution between different parasite species and heavily rely on the nature of within-host interactions [START_REF] Choisy | Mixed infections and the evolution of virulence: effects of resource competition, parasite plasticity and impaired host immunity[END_REF][START_REF] Kamiya | Coevolution of virulence and immunosuppression in multiple infections[END_REF].

In the long run, immune escape strategies may not be viable for coronaviruses because they impose too many constraints on their genomes [START_REF] Belshaw | Pacing a small cage: mutation and RNA viruses[END_REF]. Such reasoning largely rests on our knowledge of the current seasonal coronaviruses, for which large pandemics of immune escape mutants have not been recorded. However, recent results from a time shift experiment conducted using human serum collected from 1985 and 1990 and synthesised spike proteins of the seasonal alphacoronavirus 229E from 1984 to 2016 found that our immune system appears to be less efficient at recognising 'future' coronaviruses [START_REF] Eguia | A human coronavirus evolves antigenically to escape antibody immunity[END_REF]. This would mean that regular reinfections by seasonal coronaviruses may not just be related to their ability to infect URT, where the immune response is limited, but could also depend on antigenic evolution of the viral spike. Furthermore, an important lesson from this pandemic is that extreme care should be taken before comparing SARS-CoV-2 to other viruses, even human coronaviruses. Indeed, this has led to underestimating the transmission before symptoms onset, the airborne transmission, and even the magnitude of the pandemic. One of the most recent seasonal coronaviruses is thought to have emerged in the 1950s [START_REF] Forni | Molecular Evolution of Human Coronavirus Genomes[END_REF]. As suggested by Figure 1B, even though half a century ago the age pyramids were different in many countries, the IFR of a coronavirus with a virulence pattern similar to SARS-CoV-2 would not have gone unnoticed, although the baseline immunity in the population to viral infections could have been higher at the time due to higher exposition to infectious diseases. This suggests that the virulence of the new virus, which is lower than SARS-CoV and MERS, with increased transmission before symptoms, but higher than the seasonal coronaviruses, is the worst in terms of population mortality. Again, basing our strategies on immune escape patterns from known coronaviruses can be extremely hazardous.

The high virulence of SARS-CoV-2 and its evolution make it essential to closely monitor this trait. Beyond the definition issues raised in the introduction, a major difficulty for this resides in the proportion of asymptomatic or paucisymptomatic infections, meaning that the IFR is much more difficult to measure than the CFR. To minimise the biases in virulence estimation, the random testing strategy implemented in countries such as the UK seems ideal because it allows controlling for the proportion of variants [START_REF] Challen | Risk of mortality in patients infected with SARS-CoV-2 variant of concern 202012/1: matched cohort study[END_REF]Davies et al., 2021b). International coordination for such random testing appears to be particularly urgent, especially in the context of vaccination [START_REF] Kennedy | Monitor for COVID-19 vaccine resistance evolution during clinical trials[END_REF].

On a more positive note, the successful implementation of RNA vaccines does change the dark picture painted by immune escape risk. Indeed, these vaccines theoretically have the potential to follow the coevolutionary race with the virus, at least while its genetic diversity remains limited [START_REF] Dearlove | A SARS-CoV-2 vaccine candidate would likely match all currently circulating variants[END_REF], and this could prove decisive, given the evolutionary rates observed so far. However, we also know that virulence-blocking vaccines tend to select for strains that are more virulent in non-vaccinated hosts [START_REF] Gandon | Imperfect vaccines and the evolution of pathogen virulence[END_REF]. More than ever, we need to monitor virus evolution to avoid an arms race between SARS-CoV-2 and public health policies [START_REF] Van Baalen | Coevolution of recovery ability and virulence[END_REF][START_REF] Kennedy | Monitor for COVID-19 vaccine resistance evolution during clinical trials[END_REF].

Figure 1 -

 1 Figure 1 -Individual SARS-CoV-2 infection fatality ratio (IFR) as a function of age (A) and population average IFRs in 8 countries according to their demography since 1950 (B). In panel B, counterfactual mean IFRs were obtained by weighting the age-stratified IFR data from O'Driscoll et al. (2020) by the relative frequencies of age classes from annual age pyramid data compiled by United Nations (2019). Dots show the median values and shaded areas the 95% confidence intervals.

Figure 2 -

 2 Figure 2 -Semi-quantitative clinical, epidemiological, and diagnostic individual history of COVID-19 infections.The clinical timeline shows the distribution function of the incubation period (time from infection to onset of symptoms), the vertical bar representing the median value[START_REF] Mcaloon | Incubation period of covid-19: a rapid systematic review and meta-analysis of observational research[END_REF]. The breakdowns into clinical phases are exposed is presented with respect to the median symptom onset date[START_REF] Bouadma | Severe sars-cov-2 infections: practical considerations and management strategy for intensivists[END_REF][START_REF] Polak | A systematic review of pathological findings in covid-19: a pathophysiological timeline and possible mechanisms of disease progression[END_REF][START_REF] Nalbandian | Post-acute covid-19 syndrome[END_REF]. The asymptomatic fraction on the top is that estimated by[START_REF] Byambasuren | Estimating the extent of asymptomatic covid-19 and its potential for community transmission: systematic review and meta-analysis[END_REF]. The epidemiological timeline represents the probability density of the generation time estimated by[START_REF] Ferretti | The timing of covid-19 transmission[END_REF], with the vertical bar showing the median. The latency is the time between infection and the onset of contagiousness. The diagnosis timeline indicates the positivity kinetics of nasopharyngeal RT-qPCR tests. Following the estimates from[START_REF] Hellewell | Estimating the effectiveness of routine asymptomatic pcr testing at different frequencies for the detection of sars-cov-2 infections[END_REF], more than 50% of cases are positive in the central green band and more than 5% in the peripheral light green bands. Antigenic and serological (immunoglobulin (Ig) M and G) test positivities are shown for qualitative purposes following the estimates from[START_REF] Mercer | Testing at scale during the covid-19 pandemic[END_REF].

Figure 3 -

 3 Figure 3 -SARS-CoV-2 virulence evolution scenarios. A) More virulent strains are always less fit, B)Virulence and transmission rate are correlated and strains are well-adapted (i.e. they sit on the trade-off curve), and C) same as B but strains are currently maladapted (far from the trade-off curve). Dashed blue lines show hypothetical transmission-virulence relationships, shaded blue areas the inaccessible state space, and black dots the trait combinations maximising invasion fitness in a naive population (R 0 ). Dashed arrows show potential evolutionary trajectories. Virulence and transmission rates are in arbitrary units. The virulence and transmission rate of the β and γ variants are currently largely unknown. For the γ variant, the transmission rate appears to be higher[START_REF] Buss | Three-quarters attack rate of SARS-CoV-2 in the Brazilian Amazon during a largely unmitigated epidemic[END_REF]. Viruses can emerge anywhere in the white area, even if they cause virulent and poorly transmissible infections as B.1.616[START_REF] Fillatre | A new SARS-CoV-2 variant poorly detected by RT-PCR on nasopharyngeal samples, with high lethality[END_REF]. For further details about the variants, see Table1.

Acknowledgements

We thank Yannis Mickalakis and the ETE team for discussion.

Conflict of interest

The authors declare that there is no conflict of interest.


Bastien Reyné

Christian Selinger

Mircea T Sofonea

Stéphanie Miot

Amandine Pisoni

Edouard Tuaillon

Jean Bousquet

Hubert Blain

Dr Samuel Alizon
email: samuel.alizon@cnrs.fr

Analysing different exposures identifies that wearing masks and establishing COVID-19 areas reduce secondary attack risk in aged care facilities

Keywords: COVID-19, aged care facilities, mask wearing, Generalised Linear Mixed Models, secondary attack risk

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

COVID-19 spreads rapidly within aged care facilities (ACFs) [START_REF] Mcmichael | Epidemiology of Covid-19 in a Long-Term Care Facility in King County, Washington[END_REF][START_REF] Blain | Efficacy of a Test-Retest Strategy in Residents and Health Care Personnel of a Nursing Home Facing a COVID-19 Outbreak[END_REF][START_REF] Bouza | Outbreak of COVID-19 in a nursing home in Madrid[END_REF], and recommendations have been issued to reduce new cases once an outbreak has been identified [START_REF]Preparing for COVID-19 in Nursing Homes[END_REF]. Guidelines from the European Geriatric Medicine Society (EuGMS) mention a variety of interventions based on testing, mask wearing, or isolation of people with established or suspected infection (as well as their contacts) [START_REF] Blain | August 2020 Interim EuGMS guidance to prepare European Long-Term Care Facilities for COVID-19[END_REF]. The relative impact of the different interventions on the magnitude of potential COVID-19 outbreaks in ACFs remains unclear and requires testing.

In France, the first COVID-19 epidemic wave is estimated to have started mid-January 2020 [START_REF] Sofonea | Epidemiological monitoring and control perspectives: application of a parsimonious modelling framework to the COVID-19 dynamics in France[END_REF]. The first COVID-19 cases in a French ACF were detected in the Hérault department (France) on March 10. This first outbreak triggered an immediate response from the Regional Health Authority (ARS Occitanie). Infection prevention and control (IPC) guidelines were implemented and included (i) mask wearing, (ii) establishment of "COVID-19 units" to isolate exposed or infected residents (Table 1), and (iii) repeated testing for SARS-CoV-2 [START_REF] Blain | Efficacy of a Test-Retest Strategy in Residents and Health Care Personnel of a Nursing Home Facing a COVID-19 Outbreak[END_REF]. Several studies have assessed the secondary attack risk of SARS-CoV-2, showing, for instance, that mask wearing reduces virus transmission in households [START_REF] Liu | Secondary attack rate and superspreading events for SARS-CoV-2[END_REF][START_REF] Jing | Household secondary attack rate of COVID-19 and associated determinants in Guangzhou, China: a retrospective cohort study[END_REF][START_REF] Wang | Reduction of secondary transmission of SARS-CoV-2 in households by face mask use, disinfection and social distancing: a cohort study in Beijing, China[END_REF]. However, we are not aware of similar studies in ACFs. These are all the more necessary, given (i) that ACFs have very specific features regarding the average infection fatality ratio [START_REF] Verity | Estimates of the severity of coronavirus disease 2019: a model-based analysis[END_REF], (ii) the variety of SARS-CoV-2 symptoms exhibited by the residents [START_REF] Blain | Atypical clinical presentation of COVID-19 infection in residents of a long-term care facility[END_REF], and (iii) the difficulty to implement certain IPC measures such as mask wearing [START_REF]Preparing for COVID-19 in Nursing Homes[END_REF]. Furthermore, in France, during the early stages of the epidemic, the wearing of surgical masks was still associated with clinical settings. Since ACF management and staff insist on not being seen as a hospital setting, this may have limited the implementation of mask wearing in these facilities, despite its strong potential to decrease epidemic spread [START_REF] Mitze | Face masks considerably reduce COVID-19 cases in Germany[END_REF][START_REF] Martinez | Patient Questions Surrounding Mask Use for Prevention of COVID-19 and Physician Answers from an Evidence-Based Perspective: a Narrative Review[END_REF]. The need for more data is also illustrated by a recent review on the clinical practice guidelines of various agencies, associations, and organisations to control COVID-19 epidemics in ACFs. These guidelines do not include mask wearing [START_REF] Rios | Preventing the transmission of COVID-19 and other coronaviruses in older adults aged 60 years and above living in long-term care: a rapid review[END_REF].

The goal of this study was to investigate the efficiency of the IPC measures implemented in the Hérault department (Occitanie region, France) in reducing the spread of SARS-CoV-2 in ACFs when a patient was tested positive. We first estimated the secondary attack risk, defined as the proportion of residents infected (positive Reverse Transcription-Polymerase Chain Reaction, RT-PCR) in an ACF after an outbreak [15, 1 6 ]. We further analysed the data using maximum likelihood and generalised linear models to better understand the relative role of specific exposures among ACF residents on the total outbreak size.

Methods

Survey

In the Hérault department (France), an observational retrospective longitudinal study was carried out in 12 public and private ACFs which experienced a COVID-19 outbreak between March and May 2020. The exposure period lasted from early March to the end of April. Epidemic spread was monitored in each ACF by RT-PCR testing on a weekly basis. The follow-up of an ACF ended when there was a full week without any of the residents testing positive for SARS-CoV-2, which was interpreted as the end of the outbreak. The primary endpoint was the number of infected residents in the ACF at the end of an outbreak.

After the clinical identification of a COVID-19 case in any ACF, all residents and staff were tested weekly via RT-PCR on nasopharyngeal swabs. COVID-19 IPC measures were applied to all residents who were clinically followed up for 6 weeks, and who underwent repeated RT-PCR testing. Contact patients were treated as positive patients but were not moved to COVID units.

Positive or contact patients were considered as uninfected only after a full week of negative testing.

After the end of the last infection in an ACF, serum antibodies were assessed by two clinical laboratories that performed the analyses. Blood testing for IgG antibodies directed against the SARS-CoV-2 nucleocapsid protein used an enzyme-linked immunosorbent assay CE-IVD marked kit (ID screen SARS-CoV-2-N IgG indirect from IDVet, Montpellier, France). In the following analyses, positivity was based on RT-PCR tests. As reported earlier, there was a 95% match between RT-PCR and the serological result [START_REF] Blain | Efficacy of a Test-Retest Strategy in Residents and Health Care Personnel of a Nursing Home Facing a COVID-19 Outbreak[END_REF].

When a COVID-19 outbreak was detected in an aged care facility, all residents and/or their relatives were informed that the residents' anonymised clinical and biological data would be used for research purposes. None of them disagreed. In the present analysis, the data were further anonymised by being aggregated at the facility floor level. This observational study was approved by the Institutional Review Board of the Montpellier University Hospital (IRB-MTP_2020_06_202000534).

Seven main exposures associated with each ACF were extracted from a survey carried out among the directors of the 12 ACFs:

 number of floors,  number of days between the first COVID-19 case and the generalisation of mask wearing,  number of medical staff per resident,  presence or not of a "COVID unit", i.e. isolation of infected patients,  ACF director reporting sufficient or lack of mask availability after the detection of the first case,  proportion of single rooms,  presence or not of temporary agency workers before the detection of the first case.

The masks used were all surgical facial masks (NF EN 14683 norm) and were worn by all people entering the ACF (residents, staff, and potential visitors). Floors refer to the actual physical floor in the facility, which may overlap with the "COVID unit" exposure in some of the establishments. The medical staff includes nurses, nursing assistants, and hospital service agents (Table 1). All exposures were defined at the facility level, and were reported by ACF directors. The data were aggregated by ACF floor and are provided in Supplementary data file, along with the Supplementary R-code file.

Statistical analyses

The response variable in our analyses was the number of residents infected during each outbreak. We first estimated the Secondary Attack Risk of the selected outcomes using a model-based approach described by Bailey [START_REF] Bailey | The mathematical theory of infectious diseases and its applications[END_REF]. Formally, the probability that j persons have been infected among n susceptible persons, knowing there were a introduction events in the household during the outbreak, is given by the formula:

π jn a = ( n -a j -a ) π jj a (1-SAR) (n-j ) j ,if a ⩽ j< n π nn a =1 -∑ j -a n -A π jn a (Equation 1)
Here, the "household" is assumed to be the floor of an ACF. The value of the secondary attack risk

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was estimated using a maximum likelihood approach. By treating the proportion of infected residents in each ACF after the outbreak (f) as a final epidemic size, we estimated the basic reproduction number (denoted R0) in these ACFs by solving the following classical equation [START_REF] Hethcote | The mathematics of infectious diseases[END_REF]:

R 0 = -log (1-f ) f (Equation 2)
To study the effect of the 7 main exposures on the proportion of infected residents, we used generalised linear models (GLMs) with a binomial distribution for the response variable weighted by the total number of residents. In these models, the unit of analysis (the "household" in the secondary attack risk model) is the ACF.

To avoid arbitrary selecting some of the exposures or using only univariate models, we performed GLMs with all possible combinations of our 7 covariates (i.e. 2 7 = 128 models), and performed model selection using the Akaike Information Criterion (AIC). An AIC difference of 2 between models was considered to be significant following classical statistical practice [START_REF] Burnham | A practical information-theoretic approach. Model selection and multimodel inference[END_REF]. This means that the models eventually selected may only include some of the exposures.

To improve statistical power, we also performed the analysis at the level of the ACF floors. The rationale for accounting for such structure within ACFs is that activities between groups of residents were cancelled and that French national guidelines incited ACFs to separate different structures and staff. To partly correct for non-independence issues, we used a nested structure with the floors being associated to an ACF, which was itself treated as a random effect in the model. This was done using Generalised Linear Mixed Models (GLMMs) with a binomial distribution for the response variable and a normal distribution for the random effect [1 9 ]. As for GLMs, the model comparison was performed using the AIC. Analyses were performed using the lme4 package (glmer function) [START_REF] Bolker | Generalized linear mixed models: a practical guide for ecology and evolution[END_REF] in R version 4.0.2.

Results

The study involved 930 residents and 360 medical staff spread over 40 floors from 12 aged care facilities (ACFs), with an average of 3.3 floors per ACF. Details regarding the ACF and the number of infected residents can be found in Table 1. The first RT-PCR-positive cases were detected on March 10, 2020, while the last ACF of the area to be affected by the first wave reported its first case on April 21, 2020.

Assuming a single virus introduction per ACF floor, and independence between floors, we estimated a secondary attack risk of 0.041 (95% CI: [0.036,0.047]) among the residents. Assuming two virus introductions instead of one per ACF floor decreased the estimate to 0.033 (95% CI: [0.028,0.038]). Based on the final outbreak size, i.e. the total number of residents infected per ACF floor, we found that the estimate for the basic reproduction number (R0), assuming a single introduction per ACF, was 1.021 (95% CI: [1.018,1.024]).

We then used GLMMs to identify the covariates associated with ACF outbreak size. The GLMM with the lowest Akaike Information Criterion (AIC), shown in Supplementary Table S1, contained two covariates: the delay in mask wearing (in days) and the reported mask availability. These exposures were both significantly associated with larger outbreaks, as shown in Figure 1. When analysing the 11 GLMMs that were comparable from a statistical point of view (their difference in AIC with the best model was smaller than 2), we found consistent results. Table 2 shows that the two covariates identified in the best model were often the most significant in the 11 models.

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Another significant covariate was the presence of a "COVID unit", which decreases outbreak size. Finally, in some of the models, the presence of temporary agency workers before the first case was associated with larger outbreaks. In terms of associations between covariates, we have identified two classes of models. In the first class, the significant covariates are the two related to mask wearing. In the second class, the significant covariates are the presence of a COVID unit and the presence of temporary agency workers.

When assuming a less detailed model without any structure at floor level, we identified 11 generalised GLMs that performed comparatively well from a statistical point of view (their AIC difference with the best model was smaller than 2). The presence of a COVID unit had a significant effect in all 11 models. The next significant effects were (i) the presence of temporary agency workers before the first case (10 models out of 11), (ii) the delay in mask wearing (6 models out of 11), and, for two of the models, (iii) the number of floors in the ACF. The effect of the covariates on outbreak size was the same as for the GLMMs.

Discussion

First, we estimated the secondary attack risk of COVID-19 outbreaks in ACFs. We found values lower than 5%, which is much lower than the earlier estimates that ranged from 13.8% to 19.3% [START_REF] Jing | Household secondary attack rate of COVID-19 and associated determinants in Guangzhou, China: a retrospective cohort study[END_REF], 23% [START_REF] Wang | Reduction of secondary transmission of SARS-CoV-2 in households by face mask use, disinfection and social distancing: a cohort study in Beijing, China[END_REF], or even 35% [START_REF] Liu | Secondary attack rate and superspreading events for SARS-CoV-2[END_REF]. This is consistent with the strict IPC measures implemented after the first outbreak that was detected on March 10, 2020. These were also most likely helped by the implementation of the national lockdown in France, which began March 17, 2020. However, by the end of June 2020, less than 34,370 of the 726,410 residents in French ACFs had been infected by SARS-CoV-2 [START_REF]COVID-19 : point épidémiologique du 2 juillet 2020[END_REF], i.e. less than 4.8%. Since our secondary attack risk by definition only includes facilities that suffered an outbreak, its magnitude is low compared to the national average. This is consistent with other analyses that underline the importance of virus testing and cooperation from all stakeholders [START_REF] Blain | Atypical symptoms, SARS-CoV-2 test results, and immunization rates in 456 residents from eight nursing homes facing a COVID-19 outbreak[END_REF].

Second, we conducted statistical modelling analyses to identify the relevant exposures that best explain the observed heterogeneity in COVID-19 transmission. Generalised Linear Models (GLMs) were used because the response variable was not continuous (number of infected residents per ACF), making classic linear regression -such as ANOVA or ANCOVA -inadequate. The structure of the data allowed us to gain even more insight by working at the floor level. However, this raises non-independence issues between the same floor of an ACF. To address this, we used Generalised Linear Mixed Models (GLMMs), also known as hierarchical generalised linear models, which are commonly used in clinical research [ 1 9 ]. In these models, the ACF had a 'random' effect, thereby partly corrected for the non-independence issue. However, care had to be taken in model interpretation [START_REF] Bolker | Generalized linear mixed models: a practical guide for ecology and evolution[END_REF].

Our main approach was to analyse epidemics at the level of an ACF floor using GLMMs. This was motivated by the fact that early guidelines led to limiting contacts in ACFs (e.g. cancelling group events, or assigning staff members to specific floors). We found that two exposures affected the epidemic spread within the ACFs: the delay in mask wearing and the reported mask availability. The earlier the mask wearing was generalised in the ACF, the smaller the outbreak. Unexpectedly, models where this covariate was significant also found that reporting a lower mask availability was associated with fewer outbreaks. While this effect should be handled with care -due to the subjective dimension of the covariate -an explanation could be that a (reported) shortage of masks

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occurred in the ACFs that were using more masks. Indeed, there was a national shortage of mask availability in France, and regional health authorities (the ARS) constituted a stock of masks in order to ensure a fair distribution between facilities. Therefore, it is possible that variations in adherence to the ARS guidelines (which are known to occur given the variations in the date of generalisation of mask wearing) could have affected mask availability in the facility, especially since masks were supposed to be worn by residents, staff, and potential visitors. Another hypothesis to explain the lower secondary attack risk of ACFs reporting insufficient masks could be that the shortage of masks led to the local implementation of stricter guidelines that help control the outbreaks.

It is important to stress that ACFs differ from hospitals, especially in the context of an epidemic. For instance, training on how to use personal protective equipment is important, and studies have shown that in hospitals, the workers who were not assigned to the care of COVID-19 patients were those most affected by the virus [START_REF] Thibon | Healthcare associated coronavirus disease 2019 among health care workers in Normandy, France: a multi-center study[END_REF]. Furthermore, residents may display a variety of symptoms in response to SARS-CoV-2 infection [START_REF] Blain | Atypical clinical presentation of COVID-19 infection in residents of a long-term care facility[END_REF] and can also refuse to wear masks.

Interestingly, when using less detailed statistical models that ignored the floor structure (i.e. GLMs), therefore assuming that cases occurred homogeneously within the ACF, the main effect we found was the setting up of a "COVID unit", which was associated with smaller outbreaks. This further strengthens our choice to use a detailed GLMM model to analyse the data. The presence of temporary agency workers before the first case was also associated with larger outbreaks in some of the GLMs.

Although this study includes 12 aged care facilities, which makes it one of the largest conducted to date, the statistical power is still limited. However, increasing the number of facilities could introduce additional biases, especially if they depend on different regional health authorities that may implement different guidelines.

From a statistical standpoint, the potential presence of over-dispersion in the data deserves further investigation. When correcting for this potential bias, only 9 of the 127 potential GLMMs had a significant covariate: the presence of a COVID unit in the ACF. Unfortunately, correcting for overdispersion requires the use of quasi-likelihoods, therefore precluding AIC-based model comparison.

Another major limitation of this study is that it was conducted retrospectively, which constrained the design and variable choices. In particular, some of the exposures are subjective, which can generate unexpected correlations. However, this work can be considered as a pilot and will help to design further prospective studies with improved statistical power and the possibility to potentially include additional covariates in the analysis. For instance, understanding the origin of the introduction of the virus in the facilities as well as the potential superspreading events could help prevent such outbreaks [START_REF] Lemieux | Phylogenetic analysis of SARS-CoV-2 in Boston highlights the impact of superspreading events[END_REF].

Overall, these results confirm the efficiency of the measures implemented in the South of France to prevent SARS-CoV-2 epidemics in aged care facilities. They reveal the importance of within-ACF structure. They also show that delays in the generalisation of mask wearing before the first case are strongly associated with the magnitude of the outbreaks. Finally, they support the United States' Centers for Disease Control and European guidelines, which both recommend that ACFs facing a COVID-19 outbreak should dedicate an area of the facility -with specific staffing and ICP measures -for the care of residents with suspected or confirmed COVID-19 infection [START_REF] Blain | Efficacy of a Test-Retest Strategy in Residents and Health Care Personnel of a Nursing Home Facing a COVID-19 Outbreak[END_REF][START_REF]Preparing for COVID-19 in Nursing Homes[END_REF].

  Analysing different exposures identifies that wearing masks and establishing COVID-19 areas reduce secondary-attack risk in aged-care facilities Bastien Reyné, Christian Selinger, Mircea T Sofonea, Stéphanie Miot, Amandine Pisoni, Edouard Tuaillon, Jean Bousquet, Hubert Blain, Samuel Alizon To cite this version: Bastien Reyné, Christian Selinger, Mircea T Sofonea, Stéphanie Miot, Amandine Pisoni, et al.. Analysing different exposures identifies that wearing masks and establishing COVID-19 areas reduce secondary-attack risk in aged-care facilities. International Journal of Epidemiology, 2021, 50 (6), pp.1788-1794. 10.1093/ije/dyab121. hal-03289625

Acknowledgements:

The authors would like to thank (i) the residents and their families for participating in the study, (ii) all of the ACF staff who found time to answer a survey, whilst helping their residents during the crisis, (iii) IdVet for providing serological tests, and (iv) Anna Bedbrook for her help in improving the writing.

Funding:

The authors acknowledge support from the CNRS, the IRD, the University of Montpellier.

Ethics approval. This observational study was approved by the Institutional Review Board of the Montpellier University Hospital (IRB-MTP_2020_06_202000534).

Author contributions: SA, MTS, CS, HB, and JB conceived the study, HB and SM collected the data from the ACFs, ET and AP performed the biological analyses, BR performed the statistical analyses, SA wrote the first version of the manuscript, which was greatly improved by JB's edits, all authors contributed to the final version of the manuscript. Data availability: The data used for the analysis is available in Appendix.

Supplementary data: Supplementary Table S1, Supplementary data file and Supplementary R script file.

Conflict of interest: None declared. S1. B) Predicted proportion of infected residents in aged care facilities that reported an adequate supply of masks are in blue and the others are in green based on the same model.

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