# The time of infection matters: seasonal interplay between host and pathogen drives epidemic dynamics

Rémi Fay, Marlène Gamelon, Eric Baubet, Thibaud Porphyre

► To cite this version:

Rémi Fay, Marlène Gamelon, Eric Baubet, Thibaud Porphyre. The time of infection matters: seasonal interplay between host and pathogen drives epidemic dynamics. Oikos, 2025, 2025 (3), pp.e10750. 10.1111/oik.10750. hal-04841051

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Research article

# The time of infection matters: seasonal interplay between host and pathogen drives epidemic dynamics

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Rémi Fay ID, Marlène Gamelon ID, Eric Baubet<fnref n="2" /> and Thibaud Porphyre ID

Correspondence: Rémi Fay (fay.remi@gmail.com)

Oikos

2025: e10750

doi: 10.1111/oik.10750

Subject Editor: Pedro Peres-Neto

Editor-in-Chief: Pedro Peres-Neto

Accepted 5 November 2024

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Host and pathogen dynamics are driven by seasonal variation, leading to complex epidemic patterns which are not well understood. Here, we linked demography and epidemiology in a single framework to reach a mechanistic understanding of disease dynamics in natural populations characterized by seasonality. We applied this approach to depict the interplay between a host, the wild boar, and a viral disease, African swine fever. This virus spreads in wild boar by direct-contact among living individuals or though contacts with infected carcasses. In this system, both host and pathogen show seasonal patterns: survival and reproduction probabilities vary across the year in the wild boar, and virus persistence in the environment is affected by temperature which influences the speed of carcasses degradation. Using a stochastic individual-based model, we showed that virus invasion success strongly varies according to the time of introduction due to the seasonal specific interaction between the virus and host. Furthermore, the shape of the following epidemic varies across seasons, with variation in speed and magnitude of the outbreak. Consequently, the host population response was also season-specific, both regarding the speed of the decline and the change in population structure. Overall, our study highlights the inextricable connections between host, pathogen and the environmental dynamics, and the importance to consider each component to understand disease dynamics.

Keywords: African swine fever, disease ecology, infectious disease, population dynamics, wild boar

## Synthesis

Despite the increasing risk of epidemics, little is known about how host demography influences pathogen dynamics and vice versa. We investigated how seasonality in both host population dynamics and pathogen prevalence drives epidemic dynamics, and well as how the timing of pathogen introduction affects invasion risk and spread within the host population. Our results show that the timing of virus introduction plays a critical role in epidemic dynamics, influencing the likelihood of invasion, the speed and magnitude of subsequent outbreaks, and the demographic responses of the host population. By bridging the gap between demography and epidemiology, our transdisciplinary study highlights key interactions among hosts, pathogens, and environmental dynamics, advocating for a holistic approach that embraces the complexity of ecological systems.

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<footnote n="1">¹Laboratoire de Biométrie et Biologie Évolutives, UMR 5558, Université Claude Bernard Lyon 1, CNRS, VetAgro Sup, Villeurbanne, France</footnote>

<footnote n="2">²Office National de la Chasse et de la Faune sauvage, DRE-Unité Ongulés Sauvages, Monfort, Birieux, France</footnote>
Introduction

Modern world has increased the risk of infectious disease outbreaks for both wildlife and humans (Jones et al. 2008). The increase in human population, its aggregation in dense and connected urban areas, the intensification of animal husbandry and the globalization with intensive international trade, facilitate the emergence and spread of pathogens (Baker et al. 2022). Furthermore, changes in climate and land use lead to shift in species distribution, creating new opportunities for pathogens to expand geographically, and to infect and evolve in new hosts (El-Sayed and Kamel 2020, Carlson et al. 2022). Materializing this increasing risk, 60% of human infectious diseases which emerged between 1940 and 2004 were zoonotic diseases of animal origin, with a majority from wildlife (Jones et al. 2008). This illustrates the strong connection between wildlife and human health, and the need to develop research in disease ecology (Cunningham et al. 2017).

Currently, host–pathogen dynamics remain poorly understood due to the complexity of their ecological relationships (Lisovski et al. 2017, Sweeny et al. 2021). Host–pathogen dynamics result from the interplay among pathogens, hosts and their environment (Altizer et al. 2006, Begon et al. 2009, Martinez-Bakker and Helm 2015), with pathogens affecting host vital rates (e.g. survival), and host ecology modulating pathogen spread, while environmental conditions influence both (Altizer et al. 2006). Environmental conditions often vary cyclically, generating seasonality, which plays a critical role on host–pathogen dynamics (Altizer et al. 2006, Sweeny et al. 2021, Wilber et al. 2022). Seasonality often shapes within-year variation in host population size and age structure, with most births occurring over a short period of time when food availability peaks, and mortality rising during the less favorable period, in winter in the Northern Hemisphere. This in turn shapes infection risk and pathogen spread (Davis et al. 2004, Wilson et al. 2004, Begon et al. 2009, Mariën et al. 2020). Likewise, seasonality in environmental conditions such as temperature and humidity affect pathogen persistence in local environments (Marcus et al. 2023).

Challenges in investigating disease ecology are linked to the fundamental interdisciplinarity of the research field, including the difficulty in joining epidemiology and population ecology. Indeed, the processes associated with these areas are usually apprehended on different spatial and temporal scales. For instance, while population dynamics studies are generally conducted locally due to the considerable field effort required to collect demographic information (individual monitoring, regular counts) (Clutton-Brock and Sheldon 2010), epidemiological studies based on prevalence data are conducted on larger scales (continental or even global, Xie et al. 2023). Similarly, while demographic parameters are classically estimated on a long time-scale, generally annual, epidemic dynamics are monitored on a much shorter time-scale: on a daily, weekly or monthly basis. Most of earlier studies have overcome these empirical challenges by adopting

a theoretical approach (Ireland et al. 2004, Peel et al. 2014, Brandell et al. 2021). The notable exceptions are based on extensively studied host–pathogen systems (Vicente et al. 2007, Eisinger and Thulke 2008, McCallum et al. 2009, Paniw et al. 2022), but remain limited in accounting for the role of key seasonal processes (e.g. birth pulse, pathogen survival) on pathogen dynamics.

While seasonality clearly has a critical role in wildlife disease dynamics (Altizer et al. 2006), few studies have provided detailed information on the interplay between host and pathogen dynamics generating these seasonal patterns (Sweeny et al. 2021). In a seasonal environment, the invasion success of a pathogen is expected to vary across time according to the demographic state of the host population (population density, age structure, recruitment) (Begon et al. 2009, Peel et al. 2014, Wells et al. 2015, Paniw et al. 2022), and to the environmental conditions influencing pathogen survival and development (Wilber et al. 2022). Theoretical studies have shown that the influence of seasonality on epidemic dynamics depends on the degree of host demographic variation within a year, and on the direct effect of seasonality on pathogen persistence (Ireland et al. 2004). To understand epidemic dynamics, it is thus important to assess the level of seasonal forcing in real systems. Seasonal forcing also determines the importance of the timing of pathogen introduction on subsequent epidemic dynamics (Paull and Johnson 2014, Wells et al. 2015). While understanding the role of the timing of pathogen introduction could be critical for epidemic outbreak, it is surprisingly rarely considered in epidemic studies (Peel et al. 2014).

Here, we investigate the seasonal interplay between pathogen and host dynamics in a unified framework. We assess how seasonality in both host and pathogen dynamics drives epidemic outbreak, and how the timing of pathogen introduction within the host population influences its invasion risk and spread. We illustrate our approach by studying the interplay between the wild boar *Sus scrofa* and African swine fever (ASF), a swine viral disease that is currently spreading worldwide, with impacts on economy and food security due to massive losses in pig production (Sauter-Louis et al. 2021). This virus spreads through direct contacts among living wild boars and via infected carcasses, when susceptible individuals feed on surrounding contaminated soil, touch the carcasses or eventually feed on it (Probst et al. 2017, Pepin et al. 2020). Although the wild boar plays a key role in the spread and persistence of ASF (Palencia et al. 2023), little is known about the seasonal disease dynamics in this reservoir species.

Taking advantage of long-term (40 years) individual monitoring of a hunted wild boar population, we built a stochastic individual based model (IBM) informed with age- and sex-specific demographic rates. Daily-breeding probability shows a peak during the spring, and mortality rate is the highest during the hunting season, illustrating a clear seasonal pattern in both reproduction and survival for the host population. Likewise, carcasses, which constitute a main factor for the ASF persistence in the environment (Pepin et al. 2020), degrade at varying rates depending on temperatures, illustrating a clear
seasonal pattern for the pathogen. We then simulated dif-
ferent timing of virus introduction into the population by
adding one infected individual, and assessed the resulting
effects on the host–pathogen dynamics. Because both host
demography and pathogen persistence are highly seasonal
(ASF survives longer in winter due to cold temperatures and
low carcasses degradation rate, Mazur-Panasiuk et al. 2019,
Pepin et al. 2020), we anticipate that the pathogen probabil-
ity to invade a population will vary according to its time of
appearance within a year. In case of invasion, we also predict
that the outbreak dynamics will be different according to the
season of pathogen arrival (probability of invasion, R₀, maxi-
mal daily incidence rate, duration of the outbreak). As a con-
sequence, the wild boar demographic response (population
size, age structure, extinction risk) should also vary according
to the time of virus introduction.

**Material and methods**

Study system

The wild boar is a large omnivorous, polygynous and sexu-
ally dimorphic ungulate widespread in Eurasia (Massei et al.
2015). The pace of life of this species is remarkably fast for its
size (Focardi et al. 2008), its demography being characterized
by a high fecundity (litter size between 1 to 13 piglets) and a
short generation time (2–4 years, Gamelon et al. 2011). The
study focuses on a hunted population monitored since 1982
in the forest of Châteauvillain-Arc-en-Barrois (48°02N,
04°56E), north-eastern France. Births could occur through-
out the year, but the rut usually begins in mid-December
(Cachelou et al. 2022) leading to a marked birth peak in
April-May (Gamelon et al. 2011). Mortality is mostly due
to hunting that takes place each year between October and
February (Gamelon et al. 2012). A capture–mark–recapture
program is running and data on reproduction are collected
through the analysis of females shot during the hunting sea-
sons (cf. Servanty et al. 2009 and Gamelon et al. 2012 for a
full description of the protocols). This population is not yet
infected by the ASF.

The ASF virus is a DNA-virus of the Asfarviridae family which infect suids species only. ASF originates from Africa, where the warthog *Phacochoerus* sp. is believed to be the natural host. In 2007, the disease was introduced in Europe and rapidly spread both westward and eastward, and is now covering most of Europe and Asia (Sauter-Louis et al. 2021). With a case-fatality rate approaching 100%, and no vaccine available, ASF represents a major socio-economic burden and a threat to food security and biodiversity (Sauter-Louis et al. 2021).

Modelling framework

We developed a stochastic IBM to describe the daily inter-
play between wild boar population dynamics and ASF trans-
mission dynamics. Below, we describe our model concisely.

An extended presentation following the overview, design concepts, and details (ODD) protocol (Grimm et al. 2010) is given in the Supporting information.

Briefly, the model is composed of two major components,
representing 1) the demographic dynamics of the host popu-
lation and 2) the transmission dynamics of the virus within
the population. Our model assumed a closed wild boar popu-
lation, corresponding to situations where a population has
been isolated following disease detection, as has been done in
Europe (Sauter-Louis et al. 2021). Hosts were modeled indi-
vidually and characterized by sex, age and health status. Each
day, individuals may successively survive or die, breed or not,
and change health status (Fig. 1A). The infection dynamics
in the population was modelled considering an SEIR epide-
miological process, in which individuals are either susceptible
(S), exposed but not infectious (E), infectious (I) or recovered
(R). We further considered that individuals that died over-
time, either from natural causes or from the disease, remain
as carcasses in the environment for a time that depends on
temperature (Fig. 1C). As such, susceptible individuals can
be infected through direct contacts with infectious individu-
als or with infected carcasses that remain in the environment.
All animals killed during the hunting season were removed
from the population and thus do not participate in the dis-
ease transmission dynamics.

Wild boar population dynamics

Demographic parameter values

We estimated age-specific litter size based on the analysis of reproductive tracts of pregnant females shot. All other demographic parameters were obtained from previous studies conducted in the studied population (Supporting information for values and associated references). Because wild boar demographic parameters are strongly affected by body size, previous estimations were size-specific (Gamelon et al. 2012). Yet, age-specific demographic parameters are required to inform our IBM. Thus, age-specific demographic parameters were derived from size-specific estimates using sex-specific growth trajectories fitted in the studied population linking body mass to age (Veylit et al. 2021, Supporting information).

Survival process

Individual survival was modelled using a Bernoulli sampling
process, and was dependent on age, sex, health status as well
as the period of the year, survival being lower during the
hunting season (15 October – 5 February, 241 days) than
during the non-hunting season (16 February – 14 October,
124 days). Piglets less than 1-month old depend on maternal
care and thus would die if their mother die.

Reproduction process

Reproduction was decomposed in three successive steps:
breeding probability, litter size and sex-ratio. We modelled
the breeding probability using a Bernoulli distribution, the
litter size using a multinomial distribution, and the sex-
ratio using a binomial distribution assuming a balanced sex-
ratio at birth (Servanty et al. 2007, Gamelon et al. 2012).
<figure><img src="image_6.png" /><figcaption>Figure 1. Schematic overview of the individual-based model. (A) Demographic processes and infection dynamics. Gray arrows figure host demographic processes (solid = reproduction, dashed = mortality), black arrows figure disease course and red arrows figure infection risk. The color of frames indicates the sanitary state: blue = no virus, naïve individuals, orange = virus present currently or formerly but individuals not contagious, red: virus present, contagious individuals. (B) Seasonality in demographic processes. (C) Example of temperatures- and mass-dependent carcass degradation as a driver of seasonality in virus persistence.</figcaption></figure>

Both breeding probability and litter size vary with females age. Finally, reproduction was constraint by male presence: female reproduction was not possible if all sexually mature males (>2-year-old) disappeared.

### Disease transmission and dynamics

#### Infection risk

Transition between susceptible to the exposed state occurs as a function of three components: 1) the number of daily contacts an individual has with other individuals (direct contact, DC) or with carcasses (indirect contact, IC); 2) the proportion of those contacts that were infectious; and 3) the probability that an infectious contact would result in an infection event.

#### Direct contact

While wild boar social behavior is well studied, quantitative measurements of contact rates are, to our knowledge, inexistent in the literature. Therefore, to parametrize our model, we used values compatible with wild boar behavior and then conducted a sensitivity analysis to check the influence of the parameters on the results. The daily number of direct contacts was considered both age- and sex-dependent to mimic the social structure of the wild boar that is based around matriarchal groups composed of a few subadult and adult females and their offspring (Kaminski et al. 2005). The number of contacts of solitary adult males with conspecifics varied seasonally and peaked during the mating season (Maselli et al. 2014). Furthermore, because contact rate increases typically nonlinearly with population density (Hopkins et al. 2020),

we simulated the density-dependent direct contact numbers DC₀ using a generalized logistic model, such as:

$$DC_{0} = A + \frac{K - A}{(1 + e^{-rN})^{1/v}}$$

Where N is the total population size, A and K are the lower and higher asymptotes respectively, r is a growth rate, and v influences the population size near which asymptote maximum growth occurs. Parameter values were chosen to simulate realistic daily contact numbers (Supporting information). Especially, we used A=0.01 so that, although rare, daily contacts are still possible when the population size is small, because we are simulating a localized population. Similarly, we used K=10 so that the maximum number of daily contacts correspond to the size of a large group (Maselli et al. 2014). Daily number of contacts were then corrected by modulating DC₀ as a function of age and sex as well as time to account for the seasonal change in contacts of sexually mature males during rut (Maselli et al. 2014) such as:

$$DC_{i,t} = \frac{DC_{0}}{\gamma_{age_{i}} + \gamma_{sex_{i}}} \times f_{t,sex_{i}}$$

where i and t are indices for individuals and days respectively, γ<sub>age</sub> have three levels corresponding to juvenile individuals (< 6 months), sub-adults (6 months to 2 years) and adults (> 2 years), and γ<sub>sex</sub> has two levels, one per sex. We assumed no differences between males and females when individuals
were < 6 month-old since both sexes live together within social groups at this early age (Maselli et al. 2014). $f_{t,sex}$ is a function which modulates the number of contacts according to the day $t$ of the year, and applies for old males only (> 2 years). This function, with the same shape than the birth distribution (Supporting information), allows modelling males behavior change during the rut from a solitary to a harem mode of life (Maselli et al. 2014).

### Contact with carcass

We assumed that the number of contacts with carcasses was frequency-dependent. The daily number of contacts with carcasses per individual IC was modelled using the following linear model:

$$IC = C \times \delta$$

where $C$ is the total number of wild boar carcasses remaining in the environment, and $\delta$ the rate of increase of indirect contact per unit of carcasses available in the environment. No previous studies have estimated contact rates of wild boars with carcasses of conspecific. Here, we used $\delta=0.01$ to ensure IC remains low, hence reflecting the limited attractivity of carcasses as observed in natural populations (Probst et al. 2017, Cukor et al. 2020). The influence of the value of this parameter on epidemic dynamic was investigated using sensitivity analyses.

### Disease course

Once infected, individuals become infectious after an incubation period of four days, and remain infectious for an average of five days (Gallardo et al. 2017). Most infection events (95%) are fatal, regardless of age, sex and the period of the year (Gallardo et al. 2017). However, if an infected individual survives the disease course, we assumed that it becomes immune for life and cannot be infected again, nor can it be infectious. We further assumed no maternal immunity transfer from immunized sows to newborn piglets because no study has yet reported such transfer for virulent strains.

### Carcass degradation

Infected carcasses were potential source of infection as long as they remained in the environment. The rate at which individual carcasses are decaying was considered varying as a function of their size and the air temperature (Fig. 1C). Carcass degradation was modeled as a cumulative process. We defined a degradation coefficient that varied from 0 (no degradation corresponding to the day of death) to 1 (full degradation). Each day, the degradation coefficient of a carcass was updated adding the degradation occurring since the previous day. The daily degradation $DD_{i,t}$ of the carcass $i$ on day $t$ was computed such as:

$$DD_{i,t} = \frac{1}{(-4.076 \times T_i + 92.75) \times (-0.0143 \times M_i + 1.572)}$$

where $T_i$ is the daily mean air temperature (°C) and $M_i$ is the carcass mass at the time of death (kg). We parametrized this model to mimic boar carcass degradation speed observed empirically (Matuszewski et al. 2014, Probst et al. 2017). Under this model, the full degradation of a 40 kg carcass takes around two to three weeks in summer and three months in winter, and these durations increase with carcass size being roughly increase by 33% for carcass of 80 kg. The average daily air temperature variation across the year was computed from daily temperature data collected from 2003 to 2022 on six Météo France weather stations surrounding our study area (< 50 km).

### Sensitivity analyses

Empirical data for contact rates in wild boar is very limited, for both alive individuals and carcasses. Thus, we used a sensitivity analysis to check the influence of the parameters used in the model on the epidemic dynamics. We defined a range of values for each parameter (Supporting information) and created 300 set of randomly-generated parameters values using a random latin hypercube sampling method. Then, we re-ran the model for all these alternative parametrizations, and conducted a sensitivity analysis of the model outputs to parameter inputs based on standardized regression coefficients (Saltelli et al. 2000). We also assessed the raw relationship between the epidemic output and the parameter used for inputs by fitting generalized additive models (GAM) using the 'mgcv' R package (Wood 2011). This approach provided a more visual assessment of sensitivity, and allowed the assessment of the linear assumption required for the regression-based sensitivity analyses.

### Model implementation and outputs

Each simulation run was started assuming a population of 100 individuals. We simulated a modest population size because our model is appropriate to describe a localized, but not a large-scale, wild boar population. Initial age and sex distributions were attributed according to the stable age and sex distribution. All individuals were immunologically naïve (susceptible). Host population was projected one year prior to the introduction of the virus to insure independence from the initial conditions. The virus was introduced in the population by adding one infected sub-adult male (age = 1.5 years), mimicking the immigration of an infected individual within the population. To assess the influence of the timing of virus introduction on epidemic dynamics, we considered 12 scenarios where the virus was introduced on the first day of each month. Following virus introduction, the population was projected for three additional years. Each scenario was run 1000 times to describe the wild boar-virus interplay, accounting for stochasticity in model output. The model was built and run using R statistical software ver. 4.2.2 (www.r-project.org).

Model outputs include the wild boar population dynamics estimated at a daily time step, i.e. survival, reproduction,
population size and structure (age, sex). To describe the epi-
demic dynamics, we computed the basic reproduction num-
ber (R₀), that is the number of secondary infections generated
by a single infected individual. Values of R₀ above one indi-
cate that pathogen will grow and generate outbreaks, while
values of R₀ below one suggest that a pathogen is likely to
die out. We also estimated the introduction success, defined
as the probability that the first infected individual generates
at least one secondary case, and the invasion success, here
defined as the probability that at least five individuals were
infected. Then, given invasion success, we computed the
maximum daily incidence rate (i.e. maximum number of
new cases observed in a single day), the delay between virus
introduction and this maximum, the daily virus extinction
risk and epidemic duration. Because we ran a large number
of simulations, average epidemic values are obtained without
uncertainty so that there is no confidence interval in the fig-
ures presenting them.

**Results**

Host population dynamics

In absence of disease, the wild boar demographic model indi-
cated a slightly increasing population size (annual population
growth rate = 1.04), in accordance with previous studies in
this population (Gamelon et al. 2012, 2021). Both popu-
lation size and age structure fluctuated over time, whereas
sex-ratio (all ages) remained constantly slightly female biased
(female proportion: 53%, Fig. 2). From the end of the hunt-
ing season (February) to early summer (June), the population

increased on average by 220% and strongly rejuvenated, with
the proportion of juveniles varying from 7 to 62 % of the
total population. Afterwards, the population size remained
high until early autumn (October), and then declined con-
tinuously until the end of the hunting season.

Seasonal epidemic dynamics

Epidemic dynamics varied strongly according to seasonality (Fig. 3). The probability that the virus invaded the population successfully was the lowest when it was introduced in winter (February–March, ~ 60%), and the highest when it was introduced in late spring or early autumn (May or September, ~ 80%) (Fig. 3B). The basic reproduction number (R₀) varies overtime with a clear seasonal effect, being twice higher in case of virus appearance during the autumn than when the virus is introduced in the winter (Fig. 3B). In case of successful invasion, the outbreak generated by virus spreading into the population was also influenced by the timing of the virus introduction. Maximum daily incidence rate was 56% larger and was reached three time faster for outbreaks generated by virus incursions in summer compared to those generated by virus incursions in winter (Fig. 3C, D, 4). Finally, outbreaks lasted for longer duration when the virus was introduced at the end of the summer (July–August), about 375 days, compared to when it is introduced in spring (April–May), about 280 days. The epidemic duration distribution was strongly bimodal due to the seasonality of the host-pathogen interactions, leading most virus extinction to occur during the summer, either from the first year (first peak) or the second year (second peak) of epidemic (Fig. 4).

<figure><img src="image_7.png" /><figcaption>Figure 2. Seasonal wild boar population dynamics emerging from the IBM, in absence of virus (reference scenario). Results present the average changes occurring within a year in (A) population size, (B) age structure and (C) sex structure. On (A), the bold black line shows the average seasonal population variation and the gray lines show the individual stochastic simulations.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 3. Epidemic dynamics as a function of time of virus introduction in the population. Results include (A) the introduction success probability defined as the probability that the first infected individual generates at least one secondary case, (B) the invasion success probability defined as the probability that there were at least five secondary cases, (C) the basic reproduction number ($R_0$) and the number of secondary cases generated by direct contacts and contacts with carcasses, (D) the maximum daily incidence rate, (E) the time between the introduction of the virus and the maximum daily incidence rate and (F) the epidemic duration, that is the persistence time of the virus in the population, conditional on successful virus invasion.</figcaption></figure>

## Host population response to virus introduction

The wild boar population response to virus introduction strongly varied according to the timing of virus appearance. Two timescales could be distinguished for population size response: the short-term (within four months) and the long-term (> six months). Over the short-term, in case of summer virus introduction, the host population size strongly decreased, on average by 60%, compared to the reference situation (scenario without virus introduction). In contrast, in case of winter or early spring virus introduction, population size was similar to the reference situation (Supporting information). Over the long-term, host-population size fluctuated at a low level, 40-20% of the reference population size, regardless of the date of virus introduction. The outbreak also impacted the population age structure which became biased towards older age classes. The proportion of juveniles was up to two times lower compared to the age structure observed for

the same month when no virus was introduced. The maximum decrease in the proportion of juveniles tended to be stronger (decrease by 50 versus 40%), and faster (four versus height months), in case of summer virus introduction, as opposed to winter introduction (Fig. 5). Finally, compared to the reference situation, population sex-ratio shift from female to male bias (male proportion: from 47 to 52%) in response to virus introduction, this shift being again stronger and faster in case of summer virus introduction (Fig. 5).

## Sensitivity analysis

The sensitivity analysis showed that most patterns described above were robust to parameter uncertainty regarding wild boar contact rates (Fig. 6, Supporting information). One exception was the $R_0$, and the closely related introduction success probability, for which seasonality varies according to the contact rate with carcasses. When the contact rate with
<figure><img src="image_9.png" /><figcaption>Figure 4. Comparison of epidemic dynamics according to two dates of virus introduction: 1 January (blue) and 1 June (red). Results include (A) the daily change in the incidence rate, (B) the daily change in virus extinction risk and (C–D) the distribution of epidemic duration (in days), that is the time between virus appearance (time 0) and virus extinction. In (C) and (D), the dashed lines show the average epidemic duration over all simulations.</figcaption></figure>

carcasses was low ($\delta < 0.015$ daily contact per carcass), $R_0$ and the introduction success were both higher in case of summer virus appearance (Fig. 6). In contrast, when $\delta > 0.015$ daily contact per carcass, a greater $R_0$ value was observed when ASF was introduced during the winter, whereas the risk of onward transmission remained constant across seasons. The maximum number of contacts per day (K) also influenced outbreaks seasonality. Summer outbreaks were larger than winter outbreaks only when $K > 9$ (Supporting information). Overall, the sensitivity analysis showed that seasonality in ASF epidemic dynamics is very likely, but that the exact pattern will depend on the relative importance of the direct (live individuals) versus indirect (carcasses) source of infections.

## Discussion

Modelling the interplay between a host and a pathogen, we showed that considering the seasonality of both host and pathogen, as well as the timing of pathogen introduction, is critical for the understanding of epidemic dynamics. In the wild boar-ASF system, epidemic risk and the shape of the outbreak result from the complex interaction between the seasonal virus persistence in carcasses and host demographic seasonality. As a result of this, ASF summer introduction caused higher epidemic risk, with faster and larger outbreaks, which also last for longer and generate a stronger

host population decrease over the short term. During summer, increased population density with a larger proportion of young individuals enhances direct transmission rates and disease spread, despite the accelerated decomposition of carcasses in warmer temperatures.

## Host-pathogen interplay

While many epidemiological studies accounted for pathogen or host seasonal variation, few have investigated both simultaneously (Kronfeld-Schor et al. 2021, Paniw et al. 2022). Because seasonality in host and pathogen are dependent, considering only one component would inevitably lead to bias epidemic projections (Altizer et al. 2006, Paull and Johnson 2014). For instance, in the wild boar-ASF system, considering only the seasonality of pathogen persistence in the environment would wrongly lead to the conclusion that $R_0$ is the highest during winter months, overestimating the importance of the indirect pathway through carcasses. Indeed, ASF epidemic outbreaks emerge from the tradeoff between higher pathogen persistence in carcasses during the cold season and higher pathogen spread among individuals during the warm season, when both population size and the proportion of young individuals peak. Most ecological studies using SIR-type models ignore host demographic seasonality, assuming constant host population density and age structure (Hopkins et al. 2020). The within-year variation in host population size and age structure we found is likely to be ubiquitous in host populations and is a key factor shaping pathogen dynamics (Davis et al. 2004, Begon et al. 2009, Mariën et al. 2020). Overall, higher population density lead to higher contact rates among individuals, resulting in greater transmission of pathogens, while younger population could be more susceptible to pathogens due to the immaturity and naïve state of the immune system of young individuals, putting aside cases of maternal immune transfer (Nussey et al. 2012, Clerc et al. 2019). Our study highlights the key role of host demography, suggesting that the implementation of realistic host demographic dynamics component in epidemiological models is critical for our understanding of disease ecology (Sweeny et al. 2021).

## Importance of the timing of virus introduction

In a seasonal system, the timing of virus introduction is critical for the subsequent epidemic dynamics, an aspect which has been overlooked in previous studies that often consider a virus introduction at a fixed date (Hayes et al. 2021). In accordance with previous studies showing that the timing of pathogen introduction influences post-epidemic fade-outs probability (Peel et al. 2014), we found that the timing of virus introduction strongly influences $R_0$ and the invasion success probability. The importance of timing of introduction has previously been emphasized in the theory on invasive species, where the fluctuating resource hypothesis suggests that fluctuations in resources availability modulate competition intensity, promoting invasion success probability of
<figure><img src="image_10.png" /><figcaption>Figure 5. Wild boar population response to virus introduction according to two dates of virus appearance: 1 January and 1 June. (A) and (B) show the population size response to virus introduction: the bold colored lines show the mean population trajectory, the thin light-colored lines show the individual simulations, the bold colored dotted-dashed lines show the average population trajectory for simulations with successful virus invasion (at least five secondary cases), and the dashed gray lines show the average population trajectory in the absence of virus for comparison. (C) and (D) show the population age structure change on a monthly basis following virus introduction (dark colored bars). Gray colored bars show, for each corresponding month, the age structure observed in the absence of virus for comparison. (E) and (F) show the population sex-ratio change on a monthly basis following virus introduction (dark colored bars). Gray colored bars show, for each corresponding month, the sex-ratio observed in the absence of virus for comparison.</figcaption></figure>

non-native species when resources are plentiful (Davis et al. 2000). In such systems, the success of the invader is thus closely linked to the timing of propagule introduction relatively to the availability of the fluctuating resources (Li and Stevens 2012), analogously to our epidemiological context, where available resources are the number of susceptible individuals.

The timing of pathogen introduction has also long-lasting consequences on the following outbreak, and thus on the host population response. In the case of winter introduction, ASF spreads slowly leading to a smaller outbreak with a smaller and delayed peak of incidence, as compared to summer introduction. Consequently, virus introduction in that season has negligible effects on population size and structure during the first months of the epidemic, which contrasts with the sharp population decline and a biased toward males and older age classes observed from the first months, in case of summer virus introduction. The critical role of timing of introduction brings challenges for outbreak prediction because pathogen introduction is typically a stochastic event, and thus date of introduction could be not predictable. However, recognizing the importance of the timing effect could also be useful, as for instance for the design of surveillance, by adopting time-varying monitoring (Duke-Sylvester et al. 2011). In the case of the ASF, while a wild boar demographic monitoring could

provide relevant clues for an early detection of an outbreak in summer, it could be less relevant for detecting winter virus incursion. More generally, prevention and mitigation measures could be more or less restrictive according to the seasonal pathogen outbreak risk.

## Seasonality in the ASF system

Our model brings new lights on the seasonality of the ASF–wild boar system. Outbreaks seem more likely to peak in summer or early autumn, which is supported by empirical studies reporting more frequent ASF outbreaks during warm seasons (Bergmann et al. 2021). However, this seasonal pattern is not pervasive as numerous exceptions have been reported (Bergmann et al. 2021, Palencia et al. 2023), showing that epidemic outbreaks could also occur during cold season. Such discrepancy between our theoretical expectations and empirical observations could be due to the spatial variation in environmental seasonality (Duke-Sylvester et al. 2011), modulating the tradeoff between the indirect (through carcasses) and direct pathway (live individuals), generating region specific ASF dynamics. Alternatively, inconsistency in ASF seasonality could be due to variation in the wild boar ecology across space, modulating the relative
<figure><img src="image_11.png" /><figcaption>Figure 6. Sensitivity of the epidemic dynamic to parameters determining host contact rates with relative and carcasses, according to two dates of virus introduction: 1 January (blue) and 1 June (red). Epidemic metrics include the introduction success, defined as the probability that the first infected individual generates at least one secondary case, the invasion success, defined as the probability that at least five individuals were infected, and the basic reproduction number R₀, that is the number of secondary infections generated by the first infected individual. Parameter A, K, r, Age, Sex and Rut modulate wild boar daily contact rate with relative, and Carcass, which corresponds to the parameter δ, modulates the daily contact rate with carcasses (submodels description in section ‘Disease transmission and dynamics’).</figcaption></figure>

importance of each pathway. For instance, contacts with
carcasses may vary across space and time according to the
populations and environmental conditions (e.g. winter food
availability) (Cukor et al. 2020), influencing the frequency
of the indirect transmissions. Similarly, wild boar population
density strongly varies across space, from less than one to ten
individuals km⁻² (Melis et al. 2006), which may influence
the contact rate among individuals and thus the strength
of the direct pathway. Although our model generates ASF

outbreaks matching those reported from empirical obser-
vation (i.e. peak of incidence a few months after the virus
apparition, about 90% decrease of the wild boar popula-
tion followed by a stabilization at low density (Palencia et al.
2023)), we note that virus get extinct from all simulations,
while empirical evidences show that ASF circulates endemi-
cally in the wild boar (Palencia et al. 2023). This suggests
that other factors important in viral persistence are absent
from our model. Relaxing the assumption of a small and
closed population using a spatially explicit model would
allow modelling epidemic outbreak at a larger scale. This
would allow to account for the spatial shift of adult males
among different matriarchal groups during the rut, and
more generally for metapopulation dynamics, implying new
disease spread and persistence opportunities (Scherer et al.
2019). Our model is thus better suited to understand the
occurrence and course of ASF outbreaks, than their long-
term persistence.

Conclusion

To conclude, this study contributes to fill the gap between
demography and epidemiology to gain a better mechanistic
understanding of infectious diseases within natural popula-
tions in a seasonal environment. In line with previous studies,
we emphasis the key role of the seasonal interplay between
host and pathogen dynamics (Begon et al. 2009, Wells et al.
2015, Wilber et al. 2022), and the critical role of timing
of virus introduction (Paull and Johnson 2014, Wells et al.
2015). Our results have broad implication for our under-
standing of disease ecology. They suggest that predicting
future epidemic outbreak would require to account for the
effect of environmental change on both hosts, pathogens and
their interaction (Paull and Johnson 2014). This is definitely
challenging but is essential to obtain realistic epidemiological
model in order to anticipate changes in pathogens dynamics.
In this perspective, it is critical to pursue data collection on
host's phenology and demography, as well as on pathogens in
natural conditions.

***Acknowledgements*** – We thank the Office Français de la Biodiversité (OFB) and all the people involved in data collection. This study is part of the long-term Studies in Ecology and Evolution (SEE-Life) program of the CNRS. This work was performed using the computing facilities of the CC LBBE/PRABI.

***Funding***– This work was funded by the French National Research Agency and Boehringer Ingelheim Animal Health France through the IDEXLYON project (ANR-16-IDEX-0005) and the Industrial Chair in Veterinary Public Health, as part of the VPH Hub in Lyon.

Author contributions

**Rémi Fay:** Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal); Writing – review and editing (equal). **Marlène Gamelon:** Conceptualization (equal); Investigation (equal); Methodology (equal); Supervision (equal); Writing – review and editing (equal). **Eric Baubet:** Conceptualization (equal); Investigation (equal); Writing – review and editing (equal). **Thibaud Porphyre:** Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Writing – review and editing (equal).

Data availability statement

Data are available from Zenodo: https://doi.org/10.5281/zenodo.8337377 (Fay et al. 2024).

**Supporting information**

The Supporting information associated with this article is
available with the online version.

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