Unravelling key drivers of Ostreid herpesvirus type 1 (OsHV- 1) transmission dynamics in Pacific oysters through a data-driven epidemiological modeling approach

Unravelling key drivers of Ostreid herpesvirus type 1 (OsHV- 1) transmission dynamics in Pacific oysters through a data-driven epidemiological modeling approach | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Unravelling key drivers of Ostreid herpesvirus type 1 (OsHV- 1) transmission dynamics in Pacific oysters through a data-driven epidemiological modeling approach Jules Trillaud, Coralie Lupo, Benjamin Morga, Nicole Faury, Bruno Petton, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9246047/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Over the past few years, methodological advances have driven major progress in epidemiological modelling tools, improving our ability to understand pathogen dynamics and inform management strategies. However, these powerful approaches remain underused in marine mollusc health, despite their well-recognized potential to assess the impact of pathogens that threaten the long-term viability of the industry. This is notably the case for Ostreid herpesvirus type 1 (OsHV-1), a virus associated with recurrent mass mortalities of Pacific oyster spat worldwide. These recurring outbreaks underscore important gaps in our understanding of its transmission dynamics and the strategies required to mitigate epizootic events. To bridge this gap, we developed a stochastic compartmental epidemiological model that extends the classical SEIR framework by incorporating an environmental viral compartment and distinguishing between oysters that survive infection and those that succumb to it. Model parameters were estimated using targeted experimental data and integrated into stochastic simulations, enabling the model to reproduce the overall dynamics of the observed mortality kinetics and thereby supporting its validity. Remaining discrepancies were then addressed using an Approximate Bayesian Computation approach to refine parameter estimates and improve model accuracy. Additionally, sensitivity analysis identified viral shedding rates as the main drivers of epidemic dynamics. Through this integrative framework, we provide new insights into OsHV-1 transmission patterns and establish a foundation for future spatial modelling aimed at supporting disease management in oyster farming. OsHV-1 Herpesvirus Magallana gigas Epidemiological modelling Aquaculture Mollusk diseases Oyster mortality Approximate Bayesian Computation Sensitivity analysis Figures Figure 1 Figure 2 Figure 3 Figure 4 INTRODUCTION In 2022, the global production of farmed aquatic animals reached 94 million tonnes (FAO, 2024 ). Mollusk accounted for 20% of this production, led by the Pacific oyster, Magallana gigas (formerly Crassostrea gigas ), generating revenues exceeding 1.5 billion US dollars in the same year (FAO, 2024 ). However, despite overall growth, this production has decreased in certain countries. In France, for example, it has steadily declined at an average rate of 0.05% per year since 1950 (Botta et al., 2020 ). Although influenced by multiple factors, this decline mainly reflects historical and ongoing health challenges faced by the oyster industry, inducing substantial economic losses and concerns for producers and coastal activities (Girard & Pérez Agúndez, 2014 ). Among these, the Ostreid HerpesVirus type 1 (OsHV-1) (Davison et al., 2005 ; Renault, 2024 ) stands out as a central issue, causing reccurrent annual mortality in Pacific oyster spat, leading to losses ranging from 40% to 100% in affected regions (Garcia et al., 2011 ; Renault, Cochennec, et al., 1994 ; Renault, Le Deuff, et al., 1994 ; Segarra, 2014 ). OsHV-1 was first identified in France in the early 1990s following unexpected mortality events among Pacific oyster spat (Renault et al., 1995 ; Renault, Le Deuff, et al., 1994 ). These outbreaks rapidly extended beyond France, and the virus, along with several of its variants, was subsequently detected in Pacific oyster farming areas worldwide (Hwang et al., 2013 ; Jenkins et al., 2013 ; S. E. Keeling et al., 2014 ; Renault et al., 2012 ). In 2008, a marked shift in viral infection distribution was observed in France, with nearly all production sites reporting spat mortality rates ranging from 80 to 100% within a few days (EFSA, 2010 ). This unprecedented increase in mortality was associated with the emergence of an OsHV-1 variant designated as OsHV-1 µVar (Segarra et al., 2010 ). Since then, this variant has remained highly virulent, causing recurrent outbreaks when seawater temperatures exceed approximately 16°C (Alfaro et al., 2019 ; Renault et al., 2014 ). OsHV-1 is transmitted throught waterborne pathways following the release of viral particles by infectious oysters in seawater (Schikorski, Faury, et al., 2011 ; Schikorski, Renault, et al., 2011a ). The virus primarily affects larvae, spat (< 6 months old), and juvenile oysters (6–12 months old), which experience substantially higher mortality rates than adults (Green et al., 2016 ; P. M. Hick et al., 2018 ; Segarra, Baillon, et al., 2014 ). Studies investigating interactions between OsHV-1 and its host have highlighted inter-individual variability in resistance to infection, with some oysters able to limit viral replication and survive infection (Dégremont, 2011 ; Dégremont et al., 2010 ). Among the factors involved, host genetics has emerged as a major determinant of this resistance (Azéma et al., 2017 ; Dégremont, Lamy, et al., 2015 ; Dégremont, Nourry, et al., 2015). However, the high costs associated with research and genetic selection constrain both the large-scale implementation and evaluation of breeding programs (Delomas et al., 2023 ). In addition, the oyster production cycle, which lasts approximately three years and relies on both wild-caught and hatchery-produced spat, is characterized by a diversity of zootechnical practices and numerous transfers between sites at different growing stages. This structural complexity, together with the range of stakeholders involved, makes the development of effective and sustainable OsHV-1 mitigation strategies particularly challenging. Given these issues, epidemiological modelling stands out as a particularly suitable and adapted approach, enabling a deeper understanding of infection dynamics, evaluating risks, and assessing the effectiveness of potential management strategies to guide decision-making (M. J. Keeling & Rohani, 2008 ; Pernet et al., 2016 ; Renault, 2024 ). Modeling approaches are widely used to study pathogen dynamics, not only in human health (Marques et al., 2021 ; Tang et al., 2020 ), but also in livestock species (Doeschl-Wilson, 2011 ; Siettos & Russo, 2013 ). In aquatic production systems, adaptations of the Susceptible, Exposed, Infectious, Recovered (SEIR) framework (Kermack & Mckendrick, 1927 ) have been applied to both wild fish populations (Giménez-Romero et al., 2021 ; Murray et al., 2001 ) and aquacultured fish species (Murray, 2013 ; Salama & Murray, 2013 ). In the context of marine mollusk diseases, the availability of epidemiological models remains relatively scarce. Nevertheless, specific models have been developed to examine the dynamics of pathogens such as the parasite Perkinsus marinus in Crassostrea virginica (Bidegain et al., 2017 ) and the bacterium Vibrio aestuarianus in M. gigas (Lupo et al., 2019 ). Similary, only a few studies have explored modeling approaches for OsHV-1, both within populations of M. gigas (Ferreira et al., 2021 ) and in co-culture systems involving M. gigas and Crassostrea virginica (Adekunle et al., 2025 ). These studies provide a basis for exploring the epidemiological dynamics of OsHV-1 by calibrating, respectively, a Susceptible, Exposed, Infectious, Dead (SEID) and a Susceptible, Infectious, Dead (SID) model. However, none of the existing models account for host survival following infection, a key factor influencing OsHV-1 dynamics that exhibits considerable variation across oyster populations (Dégremont et al., 2016 ). Accounting for this biological trait is essential for realistic epidemiological modeling and supports the inclusion of a R compartment, as in SEIR models, to represent indiviuals surviving infection and their effect on transmission dynamics. Furthermore, parameters estimates used in the existing models derived from diverse literature sources and therefore may reflect OsHV-1 µVar of different origins, likely corresponding to different microvariants. This is particulary important because such variants have been shown to induce distinct responses within the same oyster population (Agnew-Camiener et al., 2026 ; Friedman et al., 2020 ). Consequently, model calibration should be performed specifically for the microvariant under study in order to improve predictive accuracy and capture specific epidemiological patterns of a geographic region. In this context, we developed a compartmental model to simulate the dynamics of OsHV-1 µVar in M. gigas populations and calibrated its parameters using OsHV-1 µVar viruses isolated from the Marennes-Oléron Bay in 2014. Our objectives were to i) adapt the SEIR model structure by introducing two distinct pathways to differentiate between oysters that survive or succumb to infection, ii) estimate model parameter values using dedicated experimental data in combination with Approximate Bayesian Computation (ABC) inference techniques and iii) conduct a sensitivity analysis to identify the parameters that most influence disease dynamics and model outcomes. MATERIAL AND METHODS Adaptation of the SEIR compartmental model We developed a Susceptible, Water, Exposed, Infectious, Recovered and Dead (SWEIRD) model extending the classical SEIR framework, by explicitly incorporating OsHV-1 concentration ( W ) and by distinguishing oysters that survive or succumb to the infection, through separate pathways leading to the Recovered ( R ) or Dead ( D ) compartment, respectively ( Fig. 1 ) . As virus transmission occurs through direct waterborne exposure, the infection rate of susceptible oysters ( S ) is defined as the infection probability β (1). $$\:\left(1\right)\:\:\:\:\:\beta\:=\frac{W}{W+K}$$ This probability is modeled with a logistic dose-response function, capturing the non-linear relationship between the viral concentration in seawater ( W ) and the infection probability to better represent transmission dynamics. This function is derived from the well-established Hill equation (Hill et al., 1910 ) where K refers to the 50% infectious concentration, defined as the concentration resulting in a 50% probability of infection. The infected oysters are distributed between the two distinct pathways based on Φ , the probability of an oyster to survive the infection. Oysters that will survive progress from the exposed (infected not yet infectious) stage ( E 1 ) to the infectious stage ( I 1 ) before ultimately transitioning to the recovered compartment ( R ). In contrast, oysters that will succumb to infection progress from the exposed compartment ( E 2 ) to the infectious compartment ( I 2 ) and then enter a transient compartment of recently deceased oysters ( D w ) that continue to shed viral particles, before reaching the final dead compartment ( D ) which no longer contributes to the evolution of viral concentration in seawater. All inter-compartmental transition rates in the model are governed by parameters estimated from experimental approaches. Experimental data acquisition for model parameter calibration and validation Several experimental infection approaches were implemented to estimate the model parameters, either as value distributions or as single-point values (Table 1 ). Moreover, these parameters were estimated using a viral suspension prepared from dead oysters collected in Marennes-Oléron Bay in 2014, according to a previously published protocol (Schikorski, Renault, et al., 2011a ). Table 1 Estimation and implementation of SWEIRD model parameters Symbol Meaning Estimation approach Estimation used Sample size Stochasticity Φ Probability of an oyster to survive infection Mean survival rate of the validation experimental data Single estimation NA Multinomial draw β Probability of a susceptible oyster to become infected Logistic dose-response function Estimation at each step NA Binomial draw K Concentration of virus that yields a 50% chance of becoming infected Regression between infection rate and log-transformed injected dose Single estimation 1 No ρ 1 Latent period of oysters that survive infection Time between virus injection and detection in the tank for oyster that survive infection Density function 11 Density + Binomial draw ρ 2 Latent period of alive oysters that succumb to infection Time between virus injection and detection in the tank for oysters that succumb to infection Density function 39 Density + Binomial draw γ Infectious period of oysters that survive infection Virus detection period for oysters that survive infection Density function 11 Density + Binomial draw δ 1 Infectious period of alive oysters that succumb to infection Virus detection period till death for oysters that succumb to infection Density function 39 Density + Binomial draw δ 2 Infectious period of dead oysters Delay before removing dead oysters in the validation experimental setup Single estimation NA Binomial draw ω 1 Virus shedding rate of infectious oysters that survive infection Experimental volume × concentration of virus for infectious oysters that survive infection / time spent in tank Density function 15 Density + Poisson draw ω 2 Virus shedding rate of alive oysters that succumb to infection Experimental volume × concentration of virus for infectious alive oyster that succumb to infection / time spent in tank Density function 45 Density + Poisson draw ω 3 Virus shedding rate of infectious dead oysters Experimental volume × concentration of virus for infectious dead oysters / time spent in tank Density function 7 Density + Poisson draw ε Rate of viral particles inactivation Proportion of viral particles that become non-infectious within one hour Single estimation 1 Poisson draw V Volume of the simulation environment Volume of the validation experimental setup Single estimation NA No The first experimental approach was designed to estimate, latent periods, i.e. the time required for infected oysters to become infectious ( ρ 1 and ρ 2 ), infectious periods ( γ and δ 1 ), and viral shedding rates ( ω 1 and ω 2 ) (Supplementary Fig. 1A) . To this end, a group of 63 specific pathogen-free Pacific oyster spats produced in Ifremer hatcheries (mean weight of 3.39 g) were injected with 100 µL of a viral suspension, at a concentration of 2.2 x 10 5 copies of DNA per µL⁻¹ (cp.µL⁻¹) in the adductor muscle and placed individually in 1 L tanks containing UV-filtered seawater at 22°C. The water was renewed at an average interval of 24 hours, with a 1.5 mL water sample being collected and undergoing quantitative polymerase chain reaction (qPCR) analysis at each renewal in order to assess viral DNA concentration (see above for more details). Monitoring was conducted for a maximum of 13 days post-injection (dpi), stopping upon the death of the oyster. A second, similar experimental approach was implemented to obtain data for estimating the shedding rates of dead oysters ( ω 3 ) (Supplementary Fig. 1B) . A total of 10 specific pathogen-free Pacific oyster spats produced in Ifremer hatcheries (mean size of 4 cm) were injected with 100 µL of a 2.5 × 10 7 cp.µL⁻¹ viral suspension in the adductor muscle and subsequently maintained individually in 1 L tanks containing UV-filtered seawater at 22°C. Upon their death, oysters were maintained in the tank, and daily 1 mL water samples were collected for up to 7 dpi. The samples were then analyzed using qPCR to quantify the viral DNA concentration in the tank on each sampling day. A third experimental approach was implemented to estimate the concentration required to infect 50% of oysters ( K ) (Supplementary Fig. 1C) . In this experiment, 80 specific pathogen-free Pacific oyster spats produced in Ifremer hatcheries (mean size of 4 cm) were injected with 100 µL of a viral suspension at 8 different concentrations, i.e. 8 different doses of virus, with 10 oysters per concentration level. These suspensions were obtained through serial dilutions of viral solutions, and the concentrations were quantified using propidium monoazide (PMA) qPCR (see above). Oysters were then injected with suspensions ranging from 6.14 × 10 2 to 1.00 × 10 − 1 cp.µL⁻¹ and placed in clean tanks containing 0.5 L of UV-treated, filtered seawater maintained at 22°C. Seawater samples of 1 mL were collected daily from each tank for 7 dpi to monitor infection rate using PMA qPCR. A fourth experimental approach was implemented to estimate the inactivation rate of viral particles in seawater ( ε ) (Supplementary Fig. 1D) . To this end, seawater enriched with viral particles was prepared by injecting Pacific oysters with 100 µL of a 3.23 × 10 5 cp.µL⁻¹ viral suspension. After being left to rest for different durations (0, 2, 4, 8, 12, 16, and 20 hours), this contaminated water was then used to expose groups of 10 specific pathogen-free Pacific oyster spats produced in Ifremer hatcheries (mean size of 2.5 cm) at 20°C for 10 days. Mortality was monitored daily for each group and the oyster survival rate at the end was used to provide an estimation of the viral concentration at the begining of the exposure using the Hill equation and the estimated K value. These estimated concentrations were then regressed against resting time using a linear model to determine the slope coefficient, which was subsequently used to estimate the viral particle inactivation rate in seawater under constant and controlled conditions. Finally, a complementary experimental setup was employed to generate data for model validation. Five 3 L tanks of seawater were prepared, each maintained at 22°C and containing 10 oysters (including one injected with with 100 µL of OsHV-1 suspension) originating from Ifremer hatcheries (mean size of 3 cm). Over a 7-day period, oyster survival was monitored daily, and any dead oysters were removed from the tanks on a daily basis. DNA extraction, OsHV-1 quantification and data processing Total DNA was extracted from seawater samples according to a previously described protocol (Pepin et al., 2008 ) using virus-specific primers pairs targeting a region of the OsHV-1 µVar genome predicted to encode a DNA polymerase catalytic subunit (Webb et al., 2007 ). Amplification specificity was verified by melting curve analysis, and absolute viral quantification was determined by comparing Ct values with a standard curve generated from an amplicon cloned into the pCR4-TOPO vector for OsHV-1 µVar. Additionally, except for the estimation of K , PMA treatment, which allows the selective quantification of DNA copies associated with intact viral capsids only, was not applied prior to amplification. Consequently, the parameters were estimated from qPCR measurements reflecting viral DNA concentrations rather than concentrations of infectious viral particles (Renault et al., 2024 ). Despite the biases introduced by these approximations, viral DNA quantification results were considered throughout this study as proxies for the number of infectious particles in order to simplify model formulation and facilitate interpretation. Moreover, to reduce bias associated with qPCR measurement uncertainty, a detection threshold of 4 cp.µL⁻¹ was applied to all water samples, and values below this threshold were set to zero (Pepin et al., 2008 ). Then, only data from oysters that exhibited detectable viral shedding and subsequently either recovered (remained alive with no further detectable shedding) or died during the experiment were retained for the analysis, allowing individuals to be classified as surviving or succumbing following infection. Finally, for the experimental approach without daily water renewal, viral shedding rates were estimated from daily variations in viral DNA concentrations. Differences in viral copy numbers between consecutive water samples collected at times t and t–1 were calculated, and positive differences were interpreted as net viral release into the water. These values were converted into total viral DNA copies using the experimental volume and subsequently expressed as hourly excretion rates based on the sampling interval. Accounting for experimental variability into a stochastic framework Introducing stochasticity into the modeling framework is essential to account for intrinsic random fluctuations and biological variability among individuals. Moreover, this is particularly important in small populations, where individual-level fluctuations do not average out and can substantially affect the overall system dynamics. Because our study focuses on small sample-sizes, stochasticity was incorporated into model transitions to better reflect the inherent variability of the system. The distributions of the latent periods ( ρ 1 and ρ 2 ), the infectious periods ( γ and δ 1 ) and viral shedding rates ( ω 1 , ω 2 and ω 3 ) were compared to normal, log-normal and gamma distributions using the Akaike Information Criterion (Akaike, 1974 ) to identify the best fitting density function. The resulting probability density functions were then incorporated into the model to randomly assign parameter values at the beginning of each simulation, thus introducing a stochastic component that captures inter-individual variability ( Table 1 ) . Moreover, to introduce a second stochastic layer accounting for intra-individual variability, a counterpart of the model’s ordinary differential equation system was implemented in discrete-time with a 1-hour time step. The transition rates ( r ij ) between oyster compartments i and j were converted into transition probabilities ( p ij ) using the expression p ij = 1 − exp(− r ij ) . The number of individuals transitioning from compartment i to compartment j ( N ij ) was then drawn from a Binomial distribution: N ij ∼ Binomial (C i , p ij ) , where C i represents the number of individuals in compartment i . For rates associated with virus shedding ( rs i ), the number of OsHV-1 particles shed from compartment i at each time step ( S i ) was drawn from a Poisson distribution: S i ∼ Poisson (C i × rs i ) , where C i is still the number of individuals in compartment i . The number of viral particles from oysters of each compartement is then divided by the simulation volume ( V ) to determine its specific contribution to the overall viral concentration. Moreover, since all compartment contributions are expressed relative to the same volume ( V ), they can be directly summed to the global viral concentration from the previous time step. The result is then corrected for the proportion of inactivated particles to obtain the updated viral concentration in W . Parameters not associated with a distribution ( Φ, K , δ₂ , and ε ) were fixed to single values derived from experimental estimation. However, stochasticity was still introduced for the decay rate of viral particles ( ε ) and the infectious period of dead oysters ( δ₂ ), using a Poisson and a Binomial draw, respectively. Stochasticity was also incorporated into the infection process by applying a Binomial draw using β to determine the number of individuals moving from the susceptible compartment ( S ) at each time step ( Table 1 ) . Initial settings for model simulation and comparison with validation data In this study, all simulations were initialized identically to replicate the conditions under which the model validation data were obtained, allowing direct comparison between model outputs and observed oyster mortality kinetics. Each simulation began with nine susceptible oysters and one infected individual. Several key parameters were fixed: the probability of an oyster surviving infection ( Φ ) was set to 0.375 (reflecting the 37.5% survival rate observed in validation data), the infectious period of dead oysters ( δ₂ ) was set to 24 hours (corresponding to the daily removal of dead individuals in the experimental setup) and the simulation volume ( V ) was fixed at 3 L to reproduce the conditions of the validation experiment ( Table 1 ). Using this standardized initialization, we first conducted 1,000 simulations and aggregated the outputs to perform an initial comparison with the validation data. This allowed us to assess the model’s ability to reproduce observed patterns before refining parameter estimates through an Approximate Bayesian Computation (ABC) approach. The model was implemented in R (R Core Team, 2023 ), using the dplyr (Wickham et al., 2014 ) and tidyr (Wickham, Vaughan, et al., 2025) packages for data manipulation and ggplot2 (Wickham, Chang, et al., 2025 ) and reshape2 (Wickham, 2025 ) packages for visualization. Model validation following ABC parameter adjustment An ABC framework was then employed to refine model parameter distributions by comparing simulated outputs with observed data (Beaumont et al., 2002 ; Csilléry et al., 2010 ). To reduce the computational cost and time typically associated with this type of approach, we adopted the adaptive ABC iterative algorithm (Lenormand et al., 2013 ), which estimates the posterior distribution of each parameter by progressively sampling from a series of intermediate distributions, thereby refining parameter estimates according to the observed data. At each iteration, parameter sets are sampled from the previous iteration’s distributions, and simulation errors are computed by comparing the aggregated mortality kinetics from 10 simulations per parameter set with the observed data. Only sets below a dynamically updated threshold (the 20th percentile of previously accepted errors) are retained. This process continues until 1,000 accepted sets are collected, forming updated parameter distributions progressively focusing on sets producing simulations that better fit the observed data. The algorithm terminates when the proportion of accepted simulations falls below 1%, indicating that further iterations are unlikely to significantly improve the model’s accuracy. For the initialization of this approach, we used densities derived from the experimental data as prior distributions. However, for parameters estimated as point values, we calculated confidence intervals using a bootstrap procedure with 1,000 iterations (Efron & Tibshirani, 1994) for K and using the delta method (Oehlert, 1992 ) implemented in the car package in R (Fox et al., 2024 ) for ε . These confidence intervals ( CI = [CI₁, CI₂] ) were then used to define normal prior distributions for each parameter, setting the mean equal to the point estimate and the standard deviation as σ = (CI₂ − CI₁) / (2 × 1.96). The factor 1.96 corresponds to the 97.5th percentile of the standard normal distribution, ensuring that the resulting normal distribution matches the 95% confidence interval. The final parameter distributions obtained from the ABC approach were used to perform 1,000 new simulations, which were then aggregated to validate the model and the parameter calibration by comparing the simulated mortality with the observed data. This approach and the resulting final model was also implemented in R (R Core Team, 2023 ), using the same packages for data manipulation and visualization as previously presented. Exploring parameter influence through sensitivity analysis A sensitivity analysis using the Morris method (Morris, 1991 ) and the sensitivity package (Iooss et al., 2025 ) was performed to assess the effect of individual parameter variations on model dynamics while keeping the computational cost low (Wu et al., 2013 ). The method was applied generating 100 random trajectories across the parameter space (10 discrete levels, grid jump = 2), varying one parameter at a time, and performing 100 simulations per parameter set to estimate the effect of individual parameter variations on model outputs. We used the 95% confidence intervals of the posterior distributions obtained from the ABC approach to define the lower and upper bounds for each parameter and parameters not experimentally estimated ( δ₂ and Φ ), were included using bounds relative to values derived from validation data ( Table 2 ). Table 2 SWEIRD model calibrated parameters and their sampling ranges for sensitivity analysis Symbol Unit Mean Lower bounds Upper bounds Φ NA NA 0.1 0.9 K cp·µL − 1 67.0 3.7 × 10 − 1 2.4 × 10 2 ρ 1 h 38 .3 9.1 1.0 × 10 2 ρ 2 h 15.9 10.5 22.8 γ h 69.0 19.0 1.5 × 10 2 δ 1 h 38.8 25.4 54.0 δ 2 h NA 1.0 2.0 × 10 2 ω 1 cp·h − 1 1.2 × 10 7 1.0 × 10 6 3.0 × 10 8 ω 2 cp·h − 1 7.9 × 10 7 7.9 × 10 6 6.8 × 10 8 ω 3 cp·h − 1 1.1 × 10 6 1.6 × 10 5 1.0 × 10 7 ε %·h − 1 5.8 4.0 7.7 The Morris method was first applied to the number of infectious individuals at the theoretical epidemic peak to identify the parameters exerting the strongest influence on the model’s outputs. These key parameters were then selected for a second, time-resolved sensitivity analysis designed to assess how their influence evolved throughout the course of the epidemic. The number of infectious individuals at every two-hour time point was used as the model output, with 20 random trajectories and 100 simulations performed for each parameter set. The resulting data were visualized using the “geom_smooth” function from the ggplot2 package (Wickham, Chang, et al., 2025 ), applying the LOESS method (Cleveland, 1979 ) to highlight general temporal trends. All R scripts (R Core Team, 2023 ) -including models, ABC approach and sensivity analyses- developed and used in this study are available at: https://gitlab.ifremer.fr/asim/ideal_oshv-1_sweird_model . RESULTS Estimation of infection-to-infectiousness time, infectious periods, and shedding rates The experimental approaches revealed differences between oysters that survived infection and those that succumbed to it (Supplementary Fig. 2) . Although the latent period followed a log-normal distribution in both groups, it was longer in surviving oysters (mean ρ 1 = 34.9 hours), than in oysters that died from infection (mean ρ 2 = 14 hours) (Supplementary Fig. 2A) . In addition, the log-transformed number of viral particles released per hour followed a normal distribution for non-surviving oysters ( ω 2 ), with a mean corresponding to 6.91 × 10 7 DNA copies per hour (cp.h⁻¹), more than 30 times higher than that of surviving oysters ( ω 1 ), whose log-transformed shedding rate followed a log-normal distribution with a mean value corresponding to 1.89 × 10 6 cp.h⁻¹ (Supplementary Fig. 2B) . Moreover, beyond comparative analyses, these experimental approaches allowed estimating the distribution of other key parameters. The infectious period of oyster that survive infection followed a gamma distribution with a mean of 66.5 hours ( γ ), the infectious period of alive oyster that succumb to infection followed a log-normal distribution with a mean of 96.7 hours ( δ 1 ), and the log-transformed viral shedding rate of infectious dead oysters was also log-normally distributed, with a mean corresponding to 9.97 × 10 5 cp.h⁻¹ ( ω 3 ). Estimation of the 50% infectious concentration and virus inactivation rate in seawater The resulting infection rates as a function of the log-transformed injected viral dose from the third experimental approach (Supplementary Fig. 1C) was used to estimate the 50% infectious concentration ( K ) and its 95% confidence interval (Supplementary Fig. 3A) . By identifying the x-coordinate on the linear regression corresponding to a 50% infection rate, the 50% infectious dose was estimated to be 2.01 × 10 3 cp, equivalent to 20.1 cp.µL − 1 given that 100 µL were injected per oyster. The 95% confidence interval was estimated to be [6.16 × 10 − 1 : 6.56 × 10 2 ] cp.µL − 1 . Additionally, the experimental setup implemented to assess the inactivation rate of viral particles in seawater (Supplementary Fig. 1D) revealed that oyster mortality ( M ) decreased as the resting time of the contaminated seawater increased (Supplementary Fig. 3B). Direct exposure to freshly contaminated seawater results in a 50% mortality rate, whereas a resting period of 2 to 4 hours reduced it to 40%. Moreover, when the contaminated seawater rested for 8 to 16 hours, mortality dropped to around 10%, and no mortality was observed after 20 hours. Then, using the previously estimated K value and the observed mortality rates ( M ), the Hill equation was used to infer the concentration of infectious viral particles remaining at each time point (0, 2, 4, 8, 12, 16, and 20 h) (Supplementary Fig. 3C) . Linear regression of these estimates against time yielded the slope coefficient (Supplementary Fig. 3D) used to estimate the viral particle inactivation rate in seawater under constant and controlled conditions ( ε ) (Supplementrary Fig. 3 E ) . This was estimated to be 5.87%·h − 1 with a 95% interval confidence of [5.05 : 8.92] %·h − 1 . Optimization of model simulations using ABC-calibration Parameters estimated from experimental data were used to perform initial model simulations. However these simulations exhibited a temporal delay and underestimated mortality relative to observed data ( Fig. 2 A ) . To reduce these discrepancies, an ABC-based approach was therefore used to refine parameters estimates. A total of more than 9.8 × 10 4 simulations, distributed over five ABC iterations, were required for the algorithm to converge from the prior distributions to the posterior distributions of all the model parameters (Supplementary Fig. 4) . Substantial differences between prior and posterior distributions were observed for several key parameters, based on comparisons of their median values. The most marked difference concerns the viral shedding rate of surviving oysters ( ω₁ ), which increased by 13.7% on the log-transformed scale. Notable decreases are also observed for the concentration inducing 50% infection ( K ), the infectious period δ₁ and the latent period ρ 2 with median reductions of 65.4%, 57.0%, and 19.7%, respectively. In contrast, other parameters showed limited posterior updating, with median shifts remaining below 15%. Additionnally, simulations relying on ABC-calibrated parameters showed mortality dynamics that were markedly closer to the observed data than those obtained using experimentally derived parameters (Fig. 2 B ) . These results indicate that the model calibrated using the ABC approach reproduces the observed patterns more accurately than the model using experimentally derived parameters, thereby supporting its validity. Sensitivity model analysis The Morris sensitivity analysis performed on the number of infectious individuals at the theoretical peak of the epidemic (t = 19), using ABC-calibrated values ( Table 2 ) , revealed clear differences in parameter influence on the model dynamics ( Fig. 3 A ) . The shedding rate ω 1 exhibited the largest mean absolute effect ( µ k * ) and was associated with a high standard deviation ( σ k > σ) , indicating a strong overall and variable influence of this parameter on the number of infectious individuals at the peak. Other parameters, such as γ, K, Φ, ρ 1 , ρ 2 and ω 2 also exhibited substantial mean absolute effects, and were associated with lower standard deviations. Furthermore, examining how the influence of these parameter variations evolves over time during the simulation revealed distinct trends ( Fig. 3 B ) . The early stages of the simulation were primarily driven by parameters ω 1 , ω 2 and K . However, after 50 hours of simulation, the influence of these parameters had markedly decreased and had been surpassed by parameters such as Φ , γ and ρ₁ which exhibited a significantly stronger impact at this stage than at the beginning of the simulation. In contrast, the influence of ρ₂ appeared relatively constant throughout the simulation. DISCUSSION The experimental approaches developed in this study enabled the estimation of parameters of the proposed model, allowing simulations specifically tailored to the epidemiological dynamics of the OsHV-1 µVar originating from Marennes-Oléron Bay in small M. gigas populations. In addition, combining ABC-based calibration with sensitivity analysis helped to identify the key drivers of epidemic dynamics, while also highlighting parameters that were likely misestimated and reducing discrepancies between observed and simulated data. Comparison of parameter estimates across OsHV-1 microvariants The experimental approaches enabled parameter estimations consistent with the literature. For example, considering the case of viral particle inactivation in seawater ( ε ), precise estimates of this parameter remained until now scarce due to its strong dependence on multiple environmental factors (Vigneron et al., 2004 ). However, it as been shown on an OsHV-1 microvariant originated from Australia that, starting from viral loads exceeding 10⁶ cp.µL⁻¹, a drastic reduction in detectable viral DNA can occur within the first 24 hours, dropping to below 10 cp.µL⁻¹ (P. Hick et al., 2016 ). Although this variant might be genetically and phenotypically different from the OsHV-1 µVar isolated in 2014 in Marennes-Oléron Bay, this observation is consistent with our findings. Indeed, our results show that virus-contaminated seawater no longer causes mortality after 20 hours of resting time, which supports the estimated degradation rate of 5.87% and corresponds to an average viral infectivity period in seawater of approximately 17 hours. Similarly, the estimated concentration required to infect 50% of individuals in the present study (K ≈ 20 cp.µL⁻¹) is consistent with the literature, as it falls within the same order of magnitude as the value previously estimated for the same variant and used in another model (≈ 80 cp.µL⁻¹) (Ferreira et al., 2021 ). Additionnaly, our results on the infectious period prior to death (96.7 hours, approximately 4 days), are also consistent with values used for the same parameter in previous modelling studies based on OsHV-1 µVar from other origins (5.8 and 5 days) (Adekunle et al., 2025 ; Ferreira et al., 2021 ). However, certain parameter estimates susbtantially differ from other values reported in the literature. For instance, the shedding rate of oysters that succumb to the infection was estimated at 6.9 × 10 7 cp.h⁻¹ in our study, whereas previous estimates based on an American microvariant reported a value of ≈ 3 × 10 6 cp.h⁻¹ (Ferreira et al., 2021 ). Although these differences may be explained by several factors, including environmental conditions and the oyster stocks used in the experiments, they may also reflect genetic and phenotypic variations among viruses from distinct origins, known to induce distinct host responses and, consequently, distinct shedding rates (Agnew-Camiener et al., 2026 ). This example support the development of a model framework that can be calibrated to the specific viral variant under study, thereby improving predictive performance for viral dynamics. Discrepencies due to model assumptions addressed using ABC approach Although the experimental approaches implemented provided parameter estimates that were mostly consistent with the existing literature, the simulations outputs nevertheless differed from the observed mortality kinetics data. The simulations using parameters calibrated using experimental data resulted in a mortality curve characterized by slower kinetics than those observed in validation data. Indeed, simulated mortality stabilizing only after approximately 500 hours, whereas the observed mortality plateaued around 100 hours, which is in line with previous experimental infections on microvariant form the same origin (Schikorski, Renault, et al., 2011b ). This mismatch may, in part, be attributed to the simplifying assumptions made during model implementation. In particular, the assumption that viral DNA quantified by qPCR reflects the number of infectious viral particles may bias parameter estimation, potentially leading to an overestimation of key parameters such as shedding rates. This may artificially accelerate the simulated epidemiological dynamics, even though these ultimately appear slower than those observed in the empirical data. Moreover, since the estimated 50% infectious concentration ( K ) was derived from PMA-qPCR data and is therefore not as affected by this overestimation (Renault et al., 2024 ), it may introduce a shift that could explain the differences observed in the infection kinetics. Additionally, this parameter, like several others, was estimated from experimental infections performed by injection and therefore does not account for the natural route of viral entry, which may have led to a misestimation of the number of viral particles required to initiate infection. Indeed, results of the ABC approach indicate that several adjustments were needed for a majority of the estimated parameter values, and most importantly for the key drivers of the transmission dynamics highlighted by the sensitivity analysis. This is, for example, the case for parameter K , which was identified as an important parameter of the model and as potentially overestimated, with a posterior median adjusted to a value approximately 3 times lower than the prior median. This is also the case for the viral shedding rate of oysters that survive infection ( ω₁ ), whose posterior median was more than 7 times higher than the prior median. Then, by refining posterior distributions using validation data, the ABC approach therefore helps adjust parameter values and produce simulations that more closely match the observed data, thereby improving predictions of OsHV-1 µVar infection dynamics in a local M. gigas population at an hourly time scale. Key drivers of OsHV-1 uVar dynamics The sensitivity analysis, conducted using parameters ranges resulting from the ABC approach, revealed that all model parameters influence the transmission dynamics, with their relative impact varying throughout the course of the epidemic. However, some parameters stand out because of their particularly strong influence. This is the case for the viral shedding rate of recovering oysters ( ω₁ ), which emerged as the main driver of the epidemiological dynamics. This is consistent with previous studies showing the central role of shedding in infection spread and epidemic progression (Faisal et al., 2019 ; Hershberger et al., 2010 ). Sensitivity analyses also highlighted the strong influence of the concentration causing 50% infection ( K ) in viral dynamics during the early stages of the simulation. This finding supports the high transmissibility of OsHV-1 consistent with an estimated 50% infection dose of 2 × 10³ cp, which appears lower than that reported for other herpesviruses, such as HSV-2, for which transmission is considered unlikely below 10⁴ cp (Schiffer et al., 2014 ). Additionally, experimental approaches revealed distinct parameters values between oysters that survived infection and oysters that succumbed to it. These results emphasize the crucial importance of integrating both phenotypes, and thus both epidemiological pathways, into the modeling approach to accurately capture the viral transmission dynamics (Segarra, Mauduit, et al., 2014 ). Moreover, these observations, together with the sensitivity analysis, also underscore the crucial role of oyster survival probability associated with potential genetic resistance (Dégremont, Garcia, et al., 2015) and highlight the need to explore how its variation influence viral dynamics and the potential outcomes of selective breeding programs. Further developments towards spatial and biologically realistic modeling The dynamics of OsHV-1 µVar transmission within a M. gigas population constitute a multifactorial biological process, requiring simplifying approximations to enable effective modelling. However, incorporating key biological, environmental and anthropogenic factors is essential to enhance the predictive accuracy of such a model and to extend its relevance beyond controlled experimental settings, allowing for its application under natural conditions. Developing a realistic model requires accounting for variations in oyster farming density, a major driver of viral replication and epidemic spread. Oyster densities fluctuate seasonally in relation to production cycles and are influenced by natural recruitment and the introduction of hatchery-produced spats or juveniles from other regions ( Fig. 4 A ) (Lupo et al., 2016 ), as well as natural mortality ( Fig. 4 B ) . Additionnaly, as studies have reported OsHV-1 DNA and protein in asymptomatic oyster (Arzul et al., 2002 ; Segarra et al., 2016 ) together with viral particle shedded from previously recovered oysters (Degremont & Benabdelmouna, 2014 ), it is therefore strongly suspected that OsHV-1 may exhibit a persistance phase ( Fig. 4 C ) . Then, under favorable environmental conditions, recovered oysters may become infectious again, impacting the number of infectious individuals and therefore the dynamics of the virus. Including such a multi-annual dimension would allow recovered oysters to transition either to a persistence compartment, representing individuals that still carry the virus, or to the susceptible state ( Fig. 4 D ) , representing young oysters that remain vulnerable to infection, with newly settled or hatchery-produced spat. Incorporating environmental factors is also a key step in developing a realistic model, as they influence both the virus and its host ( Fig. 4 E ) . Temperature for example is a critical driver of infection dynamics, with a specific range facilitating viral infection and spread (Delisle et al., 2018 ; Renault et al., 2014 ). It’s also the case for salinity, pH, and turbidity, which are known to influence the stability of herpesviruses in aquatic environments (Dayaram et al., 2017 ) and have been shown to affect OsHV-1 infection dynamics (Fuhrmann et al., 2019 ; Renault et al., 2014 ; Soletchnik et al., 2007 ). In addition, environmental conditions can affect filtration activity of oysters, thereby increasing the infection risk (Pousse et al., 2018 ), but also impact the oyster microbiome, a key determinant of sensitivity to OsHV-1 µVar infection (Pathirana et al., 2017 ). Moreover, phenotypic differences in infection outcome varies also with developmental stage and individual size (P. M. Hick et al., 2018 ), which represent key epidemiological parameters that should be also explicitly considered in future developments of a climate-sensitive model ( Fig. 4 F ) . Other factors also play a key role in the epidemiological dynamics of OsHV-1 by exerting a direct influence on the virus itself. By affecting viral spread and transmission, hydrodynamics should be carefully considered especially in the context spatial modelling ( Fig. 4 G ) (Lupo et al., 2019 ; Murray, 2013 ). Additionally, alternative transmission pathways, such as other host species, could be considered as different virus OsHV-1 genotypes are reported in other bivalve species worldwide and the virus appears as evolving quite rapidly for a herpesvirus (Delmotte et al., 2022 ; Morga et al., 2021 ). Nevertheless, existing evidence suggests that potential alternative hosts are limited (Camille Pelletier, 2024 ), and other filter-feeders appear to have no significant impact on viral concentrations (Pernet et al., 2021 ). CONCLUSION By combining experimental data, ABC-based approach, and sensitivity analysis, we provide an calibrated framework for investigating the epidemiological dynamics of OsHV-1 µVar within a local M. gigas population. Beyond reproducing observed infection dynamics, this modeling framework serves as a powerful tool to identify the key drivers shaping epidemic trajectories, notably highlighting the critical role of inter-individual variability in host ability to survive infection and viral shedding rates, particularly during the early stages of the epidemic. Building on this foundation, extending the model toward a spatially explicit framework represents a key next step. Incorporating hydrodynamics, farming practices, and environmentally driven variability in the virus-host relationship would enable a more realistic representation of OsHV-1 transmission, providing a valuable tool to support decision-making and mitigate the impact of the virus. Declarations Author Contribution BM, NF, BP, TR and MJ designed and carried out the experimental approaches described in this study. JT analysed the data and integrated them into a modelling approach developed by JT, CL and MJ. JT and MJ drafted the manuscript, figures and tables, with substantial contributions from IA. All authors reviewed the manuscript. Acknowledgement The authors acknowledge the French National Research Agency (ANR) for funding Jules Trillaud’s PhD. We also thank Mickael Mege, Fabrice Pernet and Jacqueline Le Grand for their contribution to the experimental work used for model parameter estimation. 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Virus Res 155(1):28–34. https://doi.org/10.1016/J.VIRUSRES.2010.07.031 Schikorski D, Renault T, Saulnier D, Faury N, Moreau P, Pépin JF (2011a) Experimental infection of Pacific oyster Crassostrea gigas spat by ostreid herpesvirus 1: demonstration of oyster spat susceptibility. Vet Res 42(1):27. https://doi.org/10.1186/1297-9716-42-27 Schikorski D, Renault T, Saulnier D, Faury N, Moreau P, Pépin JF (2011b) Experimental infection of Pacific oyster Crassostrea gigas spat by ostreid herpesvirus 1: demonstration of oyster spat susceptibility. Vet Res 42(1). https://doi.org/10.1186/1297-9716-42-27 Segarra A (2014) Etude des interactions hôte/virus chez l’huître creuse Crassostrea gigas et son virus Ostreid herpesvirus 1 . https://archimer.ifremer.fr/doc/00252/36297/ Segarra A, Baillon L, Faury N, Tourbiez D, Renault T (2016) Detection and distribution of ostreid herpesvirus 1 in experimentally infected Pacific oyster spat. J Invertebr Pathol 133:59–65. https://doi.org/10.1016/J.JIP.2015.11.013 Segarra A, Baillon L, Tourbiez D, Benabdelmouna A, Faury N, Bourgougnon N, Renault T (2014) Ostreid herpesvirus type 1 replication and host response in adult Pacific oysters, Crassostrea gigas. Vet Res 45(1):103. https://doi.org/10.1186/S13567-014-0103-X/FIGURES/6 Segarra A, Mauduit F, Faury N, Trancart S, Dégremont L, Tourbiez D, Haffner P, Barbosa-Solomieu V, Pépin JF, Travers MA, Renault T (2014) Dual transcriptomics of virus-host interactions: comparing two Pacific oyster families presenting contrasted susceptibility to ostreid herpesvirus 1. BMC Genomics 15(1). https://doi.org/10.1186/1471-2164-15-580 Segarra A, Pépin JF, Arzul I, Morga B, Faury N, Renault T (2010) Detection and description of a particular Ostreid herpesvirus 1 genotype associated with massive mortality outbreaks of Pacific oysters, Crassostrea gigas, in France in 2008. Virus Res 153(1):92–99. https://doi.org/10.1016/J.VIRUSRES.2010.07.011 Siettos CI, Russo L (2013) Mathematical modeling of infectious disease dynamics. Virulence 4(4):295–306. https://doi.org/10.4161/VIRU.24041 Soletchnik P, Ropert M, Mazurié J, Fleury G, P., Le Coz F (2007) coasts France Aquaculture 271(1–4):384–400. https://doi.org/10.1016/J.AQUACULTURE.2007.02.049 . Relationships between oyster mortality patterns and environmental data from monitoring databases along the Tang L, Zhou Y, Wang L, Purkayastha S, Zhang L, He J, Wang F, Song PXK (2020) A Review of Multi-Compartment Infectious Disease Models. Int Stat Rev 88(2):462–513. https://doi.org/10.1111/INSR.12402 Vigneron V, Solliec G, Montanie H, Renault T, Montanie H, Renault T (2004) Detection of ostreid herpesvirus 1 (OsHV-1) DNA in seawater by PCR: influence of water parameters in bioassays. Dis Aquat Organ 62(1–2):35–44. https://archimer.ifremer.fr/doc/00000/2909/ Webb SC, Fidler A, Renault T (2007) Primers for PCR-based detection of ostreid herpes virus-1 (OsHV-1): Application in a survey of New Zealand molluscs. Aquaculture 272(1–4):126–139. https://doi.org/10.1016/J.AQUACULTURE.2007.07.224 Wickham H (2025) Flexibly Reshape Data: A Reboot of the Reshape Package [R package reshape2 version 1.4.5]. CRAN: Contributed Packages. https://doi.org/10.32614/CRAN.PACKAGE.RESHAPE2 Wickham H, Chang W, Henry L, Pedersen TL, Takahashi K, Wilke C, Woo K, Yutani H, Dunnington D, van den Brand T (2025) Create Elegant Data Visualisations Using the Grammar of Graphics [R package ggplot2 version 4.0.0]. CRAN: Contributed Packages. https://doi.org/10.32614/CRAN.PACKAGE.GGPLOT2 Wickham H, François R, Henry L, Müller K, Vaughan D (2014) dplyr: A Grammar of Data Manipulation. CRAN: Contributed Packages. https://doi.org/10.32614/CRAN.PACKAGE.DPLYR Wickham H, Vaughan D, Girlich M (2025) Tidy Messy Data [R package tidyr version 1.3.2]. CRAN: Contributed Packages. https://doi.org/10.32614/CRAN.PACKAGE.TIDYR Wu J, Dhingra R, Gambhir M, Remais JV (2013) Sensitivity analysis of infectious disease models: methods, advances and their application. J Royal Soc Interface 10(86). https://doi.org/10.1098/RSIF.2012.1018 Additional Declarations No competing interests reported. Supplementary Files SUPPLEMENTARYFIGURES.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9246047","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":616670983,"identity":"9720d2df-aa8c-4d49-bee9-561a981523a3","order_by":0,"name":"Jules Trillaud","email":"","orcid":"","institution":"Ifremer","correspondingAuthor":false,"prefix":"","firstName":"Jules","middleName":"","lastName":"Trillaud","suffix":""},{"id":616670984,"identity":"d90e8f21-ceb6-4fc3-9f8f-08dd380cb56a","order_by":1,"name":"Coralie Lupo","email":"","orcid":"","institution":"Ministry of Agriculture","correspondingAuthor":false,"prefix":"","firstName":"Coralie","middleName":"","lastName":"Lupo","suffix":""},{"id":616670985,"identity":"e7190b43-5f1b-4a1f-a8d5-0e759863b223","order_by":2,"name":"Benjamin Morga","email":"","orcid":"","institution":"Ifremer","correspondingAuthor":false,"prefix":"","firstName":"Benjamin","middleName":"","lastName":"Morga","suffix":""},{"id":616670986,"identity":"9260c8f4-2d7e-4058-8efc-aee73efda10d","order_by":3,"name":"Nicole Faury","email":"","orcid":"","institution":"Ifremer","correspondingAuthor":false,"prefix":"","firstName":"Nicole","middleName":"","lastName":"Faury","suffix":""},{"id":616670987,"identity":"015b5bce-1603-45d3-b2c7-a1f05d4fb916","order_by":4,"name":"Bruno Petton","email":"","orcid":"","institution":"Ifremer, UBO, CNRS, IRD","correspondingAuthor":false,"prefix":"","firstName":"Bruno","middleName":"","lastName":"Petton","suffix":""},{"id":616670988,"identity":"0196dd9f-cd18-465b-b477-038ed813094f","order_by":5,"name":"Tristan Renault","email":"","orcid":"","institution":"Ifremer","correspondingAuthor":false,"prefix":"","firstName":"Tristan","middleName":"","lastName":"Renault","suffix":""},{"id":616670989,"identity":"792dec18-e8ad-46f4-9f68-c0906c35443e","order_by":6,"name":"Isabelle Arzul","email":"","orcid":"","institution":"Ifremer","correspondingAuthor":false,"prefix":"","firstName":"Isabelle","middleName":"","lastName":"Arzul","suffix":""},{"id":616670992,"identity":"0acd9afb-b275-42b7-a1d1-7e700a9b7d5b","order_by":7,"name":"Maude Jacquot","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/klEQVRIiWNgGAWjYJACCQYGNiizQoIfypIjUsuBMxKSDRCmMSEtUHCwjYGwFt32M4Y3PjDwyfO35xg+/jjPQsK8vTvxcQWDQT4uLWZncowtZzCwGc4488bY4OA2CQmZM2c3G55hMLBswKXlQI6ZNA8DG+MGiRwzCaCWOgmJ3G1A1/0xwGnL+Tdm0n8Y2OwhWuZISEjIv93+s4HBALeWG0BbgCGWCNHSANQiwbuNEb+WZ8WWPQZsyTPOPCs2OHMMqIMnd7NkgwEeLeeTN974UXHMtr89eeODihqgV9jPbvzYUIFbCwQYHAMSCSgi+DUAQQ26llEwCkbBKBgFCAAAgXFQ8k/Z7K4AAAAASUVORK5CYII=","orcid":"","institution":"Ifremer","correspondingAuthor":true,"prefix":"","firstName":"Maude","middleName":"","lastName":"Jacquot","suffix":""}],"badges":[],"createdAt":"2026-03-27 14:53:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9246047/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9246047/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106347511,"identity":"a8f48b98-edfc-4f73-bb8f-0d21ce3d28f2","added_by":"auto","created_at":"2026-04-07 16:40:16","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":82272,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDeveloped SWEIRD compartmental model\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003e.\u003c/strong\u003e\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003ePossible oyster states include susceptible (S); exposed and infectious oysters that will survive (\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e) or succumb to infection (\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e \u003c/em\u003eand \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e); recovered (R); dead shedding (\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e) and dead non-shedding oysters (D). \u003cem\u003eW\u003c/em\u003e denotes the viral concentration in seawater. Solid arrows represent oyster transitions, whereas dashed arrows represent virus dynamics. Model parameters are \u003cem\u003eΦ\u003c/em\u003e (survival probability); \u003cem\u003eβ\u003c/em\u003e (probability of infection); \u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e (latent periods); \u003cem\u003eγ\u003c/em\u003e, \u003cem\u003eδ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eδ\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e (infectious periods); \u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e (shedding rates); \u003cem\u003eε\u003c/em\u003e (viral inactivation rate); and \u003cem\u003eV\u003c/em\u003e (seawater volume).\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9246047/v1/e0a3dc44b407d46c604aa0b4.jpg"},{"id":106347512,"identity":"095bb9b6-b1a2-4749-9ccf-572d795831a0","added_by":"auto","created_at":"2026-04-07 16:40:16","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":97447,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eImpact of ABC calibration on model performance.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e(A) Mean agregation of 1,000 simulations outputs using estimation of parameters from experimental approaches. (B) Mean agregation of 1,000 simulations outputs using parameters calibrated from the ABC approach.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9246047/v1/4631b4492083ba02032f55fa.jpg"},{"id":106347561,"identity":"d73a81c5-16be-4b5b-bec6-ed5eee735072","added_by":"auto","created_at":"2026-04-07 16:40:26","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":159818,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSWEIRD model sensitivity analysis.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e(A) Morris sensitivity analysis applied to assess the individual effect of each parameter on the number of infected individuals at t = 19 hours. Elementary effects were combined across the random trajectories using the absolute mean effect on the model output for each parameter (μ\u003csub\u003ek\u003c/sub\u003e*). (B) Morris sensitivity analysis was performed at 2-hour intervals throughout the simulation to assess the individual effect of each parameter on the number of infected individuals.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9246047/v1/2524bf87a1ba2fd4c67b5c08.jpg"},{"id":106347510,"identity":"ea02d49d-5d57-4018-8ddb-559eccfc69d1","added_by":"auto","created_at":"2026-04-07 16:40:16","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":99396,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePerspectives for further biologically realistic developments of the SWEIRD model\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e(A) \u003cstrong\u003eAddition of oysters originating from natural settlement or hatchery production\u003c/strong\u003e. (B) \u003cstrong\u003eNatural mortality. \u003c/strong\u003e(C) \u003cstrong\u003eViral persistence in\u003c/strong\u003epreviously infected and recovered oysters. (D) Multi-year dynamics, allowing recovered oysters to become suceptible again. (E) \u003cstrong\u003eEffects of environmental factors\u003c/strong\u003e. (F) \u003cstrong\u003eInfluence of individual development stage\u003c/strong\u003e. (G) Hydrodynamic processes influencing local viral concentration.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9246047/v1/73a0a018fb84f8324f2e5697.jpg"},{"id":106404394,"identity":"36f24703-2b88-4e0b-bd3a-e7339d6cbb6d","added_by":"auto","created_at":"2026-04-08 09:15:56","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2215124,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9246047/v1/d9e1d115-910a-4bca-a62c-19943698a723.pdf"},{"id":106347642,"identity":"ff21ecfc-c4c4-4d4c-8a37-17e8d4f3ffa3","added_by":"auto","created_at":"2026-04-07 16:40:47","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1024606,"visible":true,"origin":"","legend":"","description":"","filename":"SUPPLEMENTARYFIGURES.docx","url":"https://assets-eu.researchsquare.com/files/rs-9246047/v1/4361dffaac1939bcb63a5f3a.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eUnravelling key drivers of Ostreid herpesvirus type 1 (OsHV- 1) transmission dynamics in Pacific oysters through a data-driven epidemiological modeling approach\u003c/p\u003e","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eIn 2022, the global production of farmed aquatic animals reached 94\u0026nbsp;million tonnes (FAO, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Mollusk accounted for 20% of this production, led by the Pacific oyster, \u003cem\u003eMagallana gigas\u003c/em\u003e (formerly \u003cem\u003eCrassostrea gigas\u003c/em\u003e), generating revenues exceeding 1.5\u0026nbsp;billion US dollars in the same year (FAO, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). However, despite overall growth, this production has decreased in certain countries. In France, for example, it has steadily declined at an average rate of 0.05% per year since 1950 (Botta et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Although influenced by multiple factors, this decline mainly reflects historical and ongoing health challenges faced by the oyster industry, inducing substantial economic losses and concerns for producers and coastal activities (Girard \u0026amp; P\u0026eacute;rez Ag\u0026uacute;ndez, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Among these, the Ostreid HerpesVirus type 1 (OsHV-1) (Davison et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Renault, \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) stands out as a central issue, causing reccurrent annual mortality in Pacific oyster spat, leading to losses ranging from 40% to 100% in affected regions (Garcia et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Renault, Cochennec, et al., \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e1994\u003c/span\u003e; Renault, Le Deuff, et al., \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e1994\u003c/span\u003e; Segarra, \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOsHV-1 was first identified in France in the early 1990s following unexpected mortality events among Pacific oyster spat (Renault et al., \u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e1995\u003c/span\u003e; Renault, Le Deuff, et al., \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e1994\u003c/span\u003e). These outbreaks rapidly extended beyond France, and the virus, along with several of its variants, was subsequently detected in Pacific oyster farming areas worldwide (Hwang et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Jenkins et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; S. E. Keeling et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Renault et al., \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). In 2008, a marked shift in viral infection distribution was observed in France, with nearly all production sites reporting spat mortality rates ranging from 80 to 100% within a few days (EFSA, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). This unprecedented increase in mortality was associated with the emergence of an OsHV-1 variant designated as OsHV-1 \u0026micro;Var (Segarra et al., \u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Since then, this variant has remained highly virulent, causing recurrent outbreaks when seawater temperatures exceed approximately 16\u0026deg;C (Alfaro et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Renault et al., \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). OsHV-1 is transmitted throught waterborne pathways following the release of viral particles by infectious oysters in seawater (Schikorski, Faury, et al., \u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Schikorski, Renault, et al., \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2011a\u003c/span\u003e). The virus primarily affects larvae, spat (\u0026lt;\u0026thinsp;6 months old), and juvenile oysters (6\u0026ndash;12 months old), which experience substantially higher mortality rates than adults (Green et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; P. M. Hick et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Segarra, Baillon, et al., \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eStudies investigating interactions between OsHV-1 and its host have highlighted inter-individual variability in resistance to infection, with some oysters able to limit viral replication and survive infection (D\u0026eacute;gremont, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; D\u0026eacute;gremont et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Among the factors involved, host genetics has emerged as a major determinant of this resistance (Az\u0026eacute;ma et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; D\u0026eacute;gremont, Lamy, et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; D\u0026eacute;gremont, Nourry, et al., 2015). However, the high costs associated with research and genetic selection constrain both the large-scale implementation and evaluation of breeding programs (Delomas et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In addition, the oyster production cycle, which lasts approximately three years and relies on both wild-caught and hatchery-produced spat, is characterized by a diversity of zootechnical practices and numerous transfers between sites at different growing stages. This structural complexity, together with the range of stakeholders involved, makes the development of effective and sustainable OsHV-1 mitigation strategies particularly challenging. Given these issues, epidemiological modelling stands out as a particularly suitable and adapted approach, enabling a deeper understanding of infection dynamics, evaluating risks, and assessing the effectiveness of potential management strategies to guide decision-making (M. J. Keeling \u0026amp; Rohani, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Pernet et al., \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Renault, \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eModeling approaches are widely used to study pathogen dynamics, not only in human health (Marques et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Tang et al., \u003cspan citationid=\"CR82\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), but also in livestock species (Doeschl-Wilson, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Siettos \u0026amp; Russo, \u003cspan citationid=\"CR80\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). In aquatic production systems, adaptations of the Susceptible, Exposed, Infectious, Recovered (SEIR) framework (Kermack \u0026amp; Mckendrick, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e1927\u003c/span\u003e) have been applied to both wild fish populations (Gim\u0026eacute;nez-Romero et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Murray et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2001\u003c/span\u003e) and aquacultured fish species (Murray, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Salama \u0026amp; Murray, \u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). In the context of marine mollusk diseases, the availability of epidemiological models remains relatively scarce. Nevertheless, specific models have been developed to examine the dynamics of pathogens such as the parasite \u003cem\u003ePerkinsus marinus\u003c/em\u003e in \u003cem\u003eCrassostrea virginica\u003c/em\u003e (Bidegain et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) and the bacterium \u003cem\u003eVibrio aestuarianus\u003c/em\u003e in \u003cem\u003eM. gigas\u003c/em\u003e (Lupo et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Similary, only a few studies have explored modeling approaches for OsHV-1, both within populations of \u003cem\u003eM. gigas\u003c/em\u003e (Ferreira et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) and in co-culture systems involving \u003cem\u003eM. gigas\u003c/em\u003e and \u003cem\u003eCrassostrea virginica\u003c/em\u003e (Adekunle et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). These studies provide a basis for exploring the epidemiological dynamics of OsHV-1 by calibrating, respectively, a Susceptible, Exposed, Infectious, Dead (SEID) and a Susceptible, Infectious, Dead (SID) model. However, none of the existing models account for host survival following infection, a key factor influencing OsHV-1 dynamics that exhibits considerable variation across oyster populations (D\u0026eacute;gremont et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Accounting for this biological trait is essential for realistic epidemiological modeling and supports the inclusion of a R compartment, as in SEIR models, to represent indiviuals surviving infection and their effect on transmission dynamics. Furthermore, parameters estimates used in the existing models derived from diverse literature sources and therefore may reflect OsHV-1 \u0026micro;Var of different origins, likely corresponding to different microvariants. This is particulary important because such variants have been shown to induce distinct responses within the same oyster population (Agnew-Camiener et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2026\u003c/span\u003e; Friedman et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Consequently, model calibration should be performed specifically for the microvariant under study in order to improve predictive accuracy and capture specific epidemiological patterns of a geographic region.\u003c/p\u003e \u003cp\u003eIn this context, we developed a compartmental model to simulate the dynamics of OsHV-1 \u0026micro;Var in \u003cem\u003eM. gigas\u003c/em\u003e populations and calibrated its parameters using OsHV-1 \u0026micro;Var viruses isolated from the Marennes-Ol\u0026eacute;ron Bay in 2014. Our objectives were to i) adapt the SEIR model structure by introducing two distinct pathways to differentiate between oysters that survive or succumb to infection, ii) estimate model parameter values using dedicated experimental data in combination with Approximate Bayesian Computation (ABC) inference techniques and iii) conduct a sensitivity analysis to identify the parameters that most influence disease dynamics and model outcomes.\u003c/p\u003e"},{"header":"MATERIAL AND METHODS","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eAdaptation of the SEIR compartmental model\u003c/h2\u003e \u003cp\u003eWe developed a Susceptible, Water, Exposed, Infectious, Recovered and Dead (SWEIRD) model extending the classical SEIR framework, by explicitly incorporating OsHV-1 concentration (\u003cem\u003eW\u003c/em\u003e) and by distinguishing oysters that survive or succumb to the infection, through separate pathways leading to the Recovered (\u003cem\u003eR\u003c/em\u003e) or Dead (\u003cem\u003eD\u003c/em\u003e) compartment, respectively \u003cb\u003e(\u003c/b\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e)\u003c/b\u003e. As virus transmission occurs through direct waterborne exposure, the infection rate of susceptible oysters (\u003cem\u003eS\u003c/em\u003e) is defined as the infection probability \u003cem\u003eβ\u003c/em\u003e (1).\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\left(1\\right)\\:\\:\\:\\:\\:\\beta\\:=\\frac{W}{W+K}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThis probability is modeled with a logistic dose-response function, capturing the non-linear relationship between the viral concentration in seawater (\u003cem\u003eW\u003c/em\u003e) and the infection probability to better represent transmission dynamics. This function is derived from the well-established Hill equation (Hill et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e1910\u003c/span\u003e) where \u003cem\u003eK\u003c/em\u003e refers to the 50% infectious concentration, defined as the concentration resulting in a 50% probability of infection. The infected oysters are distributed between the two distinct pathways based on \u003cem\u003eΦ\u003c/em\u003e, the probability of an oyster to survive the infection. Oysters that will survive progress from the exposed (infected not yet infectious) stage (\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e) to the infectious stage (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e) before ultimately transitioning to the recovered compartment (\u003cem\u003eR\u003c/em\u003e). In contrast, oysters that will succumb to infection progress from the exposed compartment (\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e) to the infectious compartment (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e) and then enter a transient compartment of recently deceased oysters (\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e) that continue to shed viral particles, before reaching the final dead compartment (\u003cem\u003eD\u003c/em\u003e) which no longer contributes to the evolution of viral concentration in seawater. All inter-compartmental transition rates in the model are governed by parameters estimated from experimental approaches.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eExperimental data acquisition for model parameter calibration and validation\u003c/h3\u003e\n\u003cp\u003eSeveral experimental infection approaches were implemented to estimate the model parameters, either as value distributions or as single-point values (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Moreover, these parameters were estimated using a viral suspension prepared from dead oysters collected in Marennes-Ol\u0026eacute;ron Bay in 2014, according to a previously published protocol (Schikorski, Renault, et al., \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2011a\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eEstimation and implementation of SWEIRD model parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSymbol\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMeaning\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEstimation approach\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEstimation used\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSample size\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eStochasticity\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eΦ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eProbability of an oyster to survive infection\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMean survival rate of the validation experimental data\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSingle estimation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMultinomial draw\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eProbability of a susceptible oyster to become infected\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLogistic dose-response function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEstimation at each step\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eBinomial draw\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eK\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eConcentration of virus that yields a 50% chance of becoming infected\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRegression between infection rate and log-transformed injected dose\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSingle estimation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eρ\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLatent period of oysters that survive infection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTime between virus injection and detection in the tank for oyster that survive infection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDensity function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDensity\u0026thinsp;+\u0026thinsp;Binomial draw\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eρ\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLatent period of alive oysters that succumb to infection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTime between virus injection and detection in the tank for oysters that succumb to infection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDensity function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDensity\u0026thinsp;+\u0026thinsp;Binomial draw\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eγ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInfectious period of oysters that survive infection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVirus detection period for oysters that survive infection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDensity function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDensity\u0026thinsp;+\u0026thinsp;Binomial draw\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eδ\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInfectious period of alive oysters that succumb to infection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVirus detection period till death for oysters that succumb to infection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDensity function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDensity\u0026thinsp;+\u0026thinsp;Binomial draw\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eδ\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInfectious period of dead oysters\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDelay before removing dead oysters in the validation experimental setup\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSingle estimation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eBinomial draw\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eω\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVirus shedding rate of infectious oysters that survive infection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExperimental volume \u0026times; concentration of virus for infectious oysters that survive infection / time spent in tank\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDensity function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDensity\u0026thinsp;+\u0026thinsp;Poisson draw\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eω\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVirus shedding rate of alive oysters that succumb to infection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExperimental volume \u0026times; concentration of virus for infectious alive oyster that succumb to infection / time spent in tank\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDensity function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDensity\u0026thinsp;+\u0026thinsp;Poisson draw\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eω\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVirus shedding rate of infectious dead oysters\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExperimental volume \u0026times; concentration of virus for infectious dead oysters / time spent in tank\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDensity function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDensity\u0026thinsp;+\u0026thinsp;Poisson draw\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eε\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRate of viral particles inactivation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eProportion of viral particles that become non-infectious within one hour\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSingle estimation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePoisson draw\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVolume of the simulation environment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVolume of the validation experimental setup\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSingle estimation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe first experimental approach was designed to estimate, latent periods, \u003cem\u003ei.e.\u003c/em\u003e the time required for infected oysters to become infectious (\u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e), infectious periods (\u003cem\u003eγ\u003c/em\u003e and \u003cem\u003eδ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e), and viral shedding rates (\u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e) \u003cb\u003e(Supplementary Fig.\u0026nbsp;1A)\u003c/b\u003e. To this end, a group of 63 specific pathogen-free Pacific oyster spats produced in Ifremer hatcheries (mean weight of 3.39 g) were injected with 100 \u0026micro;L of a viral suspension, at a concentration of 2.2 x 10\u003csup\u003e5\u003c/sup\u003e copies of DNA per \u0026micro;L⁻\u0026sup1; (cp.\u0026micro;L⁻\u0026sup1;) in the adductor muscle and placed individually in 1 L tanks containing UV-filtered seawater at 22\u0026deg;C. The water was renewed at an average interval of 24 hours, with a 1.5 mL water sample being collected and undergoing quantitative polymerase chain reaction (qPCR) analysis at each renewal in order to assess viral DNA concentration (see above for more details). Monitoring was conducted for a maximum of 13 days post-injection (dpi), stopping upon the death of the oyster.\u003c/p\u003e \u003cp\u003eA second, similar experimental approach was implemented to obtain data for estimating the shedding rates of dead oysters (\u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e) \u003cb\u003e(Supplementary Fig.\u0026nbsp;1B)\u003c/b\u003e. A total of 10 specific pathogen-free Pacific oyster spats produced in Ifremer hatcheries (mean size of 4 cm) were injected with 100 \u0026micro;L of a 2.5 \u0026times; 10\u003csup\u003e7\u003c/sup\u003e cp.\u0026micro;L⁻\u0026sup1; viral suspension in the adductor muscle and subsequently maintained individually in 1 L tanks containing UV-filtered seawater at 22\u0026deg;C. Upon their death, oysters were maintained in the tank, and daily 1 mL water samples were collected for up to 7 dpi. The samples were then analyzed using qPCR to quantify the viral DNA concentration in the tank on each sampling day.\u003c/p\u003e \u003cp\u003eA third experimental approach was implemented to estimate the concentration required to infect 50% of oysters (\u003cem\u003eK\u003c/em\u003e) \u003cb\u003e(Supplementary Fig.\u0026nbsp;1C)\u003c/b\u003e. In this experiment, 80 specific pathogen-free Pacific oyster spats produced in Ifremer hatcheries (mean size of 4 cm) were injected with 100 \u0026micro;L of a viral suspension at 8 different concentrations, \u003cem\u003ei.e.\u003c/em\u003e 8 different doses of virus, with 10 oysters per concentration level. These suspensions were obtained through serial dilutions of viral solutions, and the concentrations were quantified using propidium monoazide (PMA) qPCR (see above). Oysters were then injected with suspensions ranging from 6.14 \u0026times; 10\u003csup\u003e2\u003c/sup\u003e to 1.00 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e cp.\u0026micro;L⁻\u0026sup1; and placed in clean tanks containing 0.5 L of UV-treated, filtered seawater maintained at 22\u0026deg;C. Seawater samples of 1 mL were collected daily from each tank for 7 dpi to monitor infection rate using PMA qPCR.\u003c/p\u003e \u003cp\u003eA fourth experimental approach was implemented to estimate the inactivation rate of viral particles in seawater (\u003cem\u003eε\u003c/em\u003e) \u003cb\u003e(Supplementary Fig.\u0026nbsp;1D)\u003c/b\u003e. To this end, seawater enriched with viral particles was prepared by injecting Pacific oysters with 100 \u0026micro;L of a 3.23 \u0026times; 10\u003csup\u003e5\u003c/sup\u003e cp.\u0026micro;L⁻\u0026sup1; viral suspension. After being left to rest for different durations (0, 2, 4, 8, 12, 16, and 20 hours), this contaminated water was then used to expose groups of 10 specific pathogen-free Pacific oyster spats produced in Ifremer hatcheries (mean size of 2.5 cm) at 20\u0026deg;C for 10 days. Mortality was monitored daily for each group and the oyster survival rate at the end was used to provide an estimation of the viral concentration at the begining of the exposure using the Hill equation and the estimated \u003cem\u003eK\u003c/em\u003e value. These estimated concentrations were then regressed against resting time using a linear model to determine the slope coefficient, which was subsequently used to estimate the viral particle inactivation rate in seawater under constant and controlled conditions.\u003c/p\u003e \u003cp\u003eFinally, a complementary experimental setup was employed to generate data for model validation. Five 3 L tanks of seawater were prepared, each maintained at 22\u0026deg;C and containing 10 oysters (including one injected with with 100 \u0026micro;L of OsHV-1 suspension) originating from Ifremer hatcheries (mean size of 3 cm). Over a 7-day period, oyster survival was monitored daily, and any dead oysters were removed from the tanks on a daily basis.\u003c/p\u003e\n\u003ch3\u003eDNA extraction, OsHV-1 quantification and data processing\u003c/h3\u003e\n\u003cp\u003eTotal DNA was extracted from seawater samples according to a previously described protocol (Pepin et al., \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) using virus-specific primers pairs targeting a region of the OsHV-1 \u0026micro;Var genome predicted to encode a DNA polymerase catalytic subunit (Webb et al., \u003cspan citationid=\"CR84\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Amplification specificity was verified by melting curve analysis, and absolute viral quantification was determined by comparing Ct values with a standard curve generated from an amplicon cloned into the pCR4-TOPO vector for OsHV-1 \u0026micro;Var. Additionally, except for the estimation of \u003cem\u003eK\u003c/em\u003e, PMA treatment, which allows the selective quantification of DNA copies associated with intact viral capsids only, was not applied prior to amplification. Consequently, the parameters were estimated from qPCR measurements reflecting viral DNA concentrations rather than concentrations of infectious viral particles (Renault et al., \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Despite the biases introduced by these approximations, viral DNA quantification results were considered throughout this study as proxies for the number of infectious particles in order to simplify model formulation and facilitate interpretation. Moreover, to reduce bias associated with qPCR measurement uncertainty, a detection threshold of 4 cp.\u0026micro;L⁻\u0026sup1; was applied to all water samples, and values below this threshold were set to zero (Pepin et al., \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). Then, only data from oysters that exhibited detectable viral shedding and subsequently either recovered (remained alive with no further detectable shedding) or died during the experiment were retained for the analysis, allowing individuals to be classified as surviving or succumbing following infection. Finally, for the experimental approach without daily water renewal, viral shedding rates were estimated from daily variations in viral DNA concentrations. Differences in viral copy numbers between consecutive water samples collected at times \u003cem\u003et\u003c/em\u003e and \u003cem\u003et\u0026ndash;1\u003c/em\u003e were calculated, and positive differences were interpreted as net viral release into the water. These values were converted into total viral DNA copies using the experimental volume and subsequently expressed as hourly excretion rates based on the sampling interval.\u003c/p\u003e\n\u003ch3\u003eAccounting for experimental variability into a stochastic framework\u003c/h3\u003e\n\u003cp\u003eIntroducing stochasticity into the modeling framework is essential to account for intrinsic random fluctuations and biological variability among individuals. Moreover, this is particularly important in small populations, where individual-level fluctuations do not average out and can substantially affect the overall system dynamics. Because our study focuses on small sample-sizes, stochasticity was incorporated into model transitions to better reflect the inherent variability of the system.\u003c/p\u003e \u003cp\u003eThe distributions of the latent periods (\u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e), the infectious periods (\u003cem\u003eγ\u003c/em\u003e and \u003cem\u003eδ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e) and viral shedding rates (\u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e) were compared to normal, log-normal and gamma distributions using the Akaike Information Criterion (Akaike, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1974\u003c/span\u003e) to identify the best fitting density function. The resulting probability density functions were then incorporated into the model to randomly assign parameter values at the beginning of each simulation, thus introducing a stochastic component that captures inter-individual variability \u003cb\u003e(\u003c/b\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e)\u003c/b\u003e. Moreover, to introduce a second stochastic layer accounting for intra-individual variability, a counterpart of the model\u0026rsquo;s ordinary differential equation system was implemented in discrete-time with a 1-hour time step. The transition rates (\u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e) between oyster compartments \u003cem\u003ei\u003c/em\u003e and \u003cem\u003ej\u003c/em\u003e were converted into transition probabilities (\u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e) using the expression \u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e= 1\u0026thinsp;\u0026minus;\u0026thinsp;exp(\u0026minus;\u0026thinsp;r\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)\u003c/em\u003e. The number of individuals transitioning from compartment \u003cem\u003ei\u003c/em\u003e to compartment \u003cem\u003ej\u003c/em\u003e (\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e) was then drawn from a Binomial distribution: \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e\u0026sim; Binomial (C\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)\u003c/em\u003e, where \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e represents the number of individuals in compartment \u003cem\u003ei\u003c/em\u003e. For rates associated with virus shedding (\u003cem\u003ers\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e), the number of OsHV-1 particles shed from compartment \u003cem\u003ei\u003c/em\u003e at each time step (\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e) was drawn from a Poisson distribution: \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e\u0026sim; Poisson (C\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e\u0026times; rs\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)\u003c/em\u003e, where \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e is still the number of individuals in compartment \u003cem\u003ei\u003c/em\u003e. The number of viral particles from oysters of each compartement is then divided by the simulation volume (\u003cem\u003eV\u003c/em\u003e) to determine its specific contribution to the overall viral concentration. Moreover, since all compartment contributions are expressed relative to the same volume (\u003cem\u003eV\u003c/em\u003e), they can be directly summed to the global viral concentration from the previous time step. The result is then corrected for the proportion of inactivated particles to obtain the updated viral concentration in \u003cem\u003eW\u003c/em\u003e.\u003c/p\u003e \u003cp\u003eParameters not associated with a distribution (\u003cem\u003eΦ, K\u003c/em\u003e, \u003cem\u003eδ₂\u003c/em\u003e, and \u003cem\u003eε\u003c/em\u003e) were fixed to single values derived from experimental estimation. However, stochasticity was still introduced for the decay rate of viral particles (\u003cem\u003eε\u003c/em\u003e) and the infectious period of dead oysters (\u003cem\u003eδ₂\u003c/em\u003e), using a Poisson and a Binomial draw, respectively. Stochasticity was also incorporated into the infection process by applying a Binomial draw using \u003cem\u003eβ\u003c/em\u003e to determine the number of individuals moving from the susceptible compartment (\u003cem\u003eS\u003c/em\u003e) at each time step \u003cb\u003e(\u003c/b\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e)\u003c/b\u003e.\u003c/p\u003e\n\u003ch3\u003eInitial settings for model simulation and comparison with validation data\u003c/h3\u003e\n\u003cp\u003eIn this study, all simulations were initialized identically to replicate the conditions under which the model validation data were obtained, allowing direct comparison between model outputs and observed oyster mortality kinetics. Each simulation began with nine susceptible oysters and one infected individual. Several key parameters were fixed: the probability of an oyster surviving infection (\u003cem\u003eΦ\u003c/em\u003e) was set to 0.375 (reflecting the 37.5% survival rate observed in validation data), the infectious period of dead oysters (\u003cem\u003eδ₂\u003c/em\u003e) was set to 24 hours (corresponding to the daily removal of dead individuals in the experimental setup) and the simulation volume (\u003cem\u003eV\u003c/em\u003e) was fixed at 3 L to reproduce the conditions of the validation experiment \u003cb\u003e(\u003c/b\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e).\u003c/b\u003e\u003c/p\u003e \u003cp\u003eUsing this standardized initialization, we first conducted 1,000 simulations and aggregated the outputs to perform an initial comparison with the validation data. This allowed us to assess the model\u0026rsquo;s ability to reproduce observed patterns before refining parameter estimates through an Approximate Bayesian Computation (ABC) approach. The model was implemented in R (R Core Team, \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), using the \u003cem\u003edplyr\u003c/em\u003e (Wickham et al., \u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) and \u003cem\u003etidyr\u003c/em\u003e (Wickham, Vaughan, et al., 2025) packages for data manipulation and \u003cem\u003eggplot2\u003c/em\u003e (Wickham, Chang, et al., \u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) and \u003cem\u003ereshape2\u003c/em\u003e (Wickham, \u003cspan citationid=\"CR85\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) packages for visualization.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eModel validation following ABC parameter adjustment\u003c/h2\u003e \u003cp\u003eAn ABC framework was then employed to refine model parameter distributions by comparing simulated outputs with observed data (Beaumont et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Csill\u0026eacute;ry et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). To reduce the computational cost and time typically associated with this type of approach, we adopted the adaptive ABC iterative algorithm (Lenormand et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), which estimates the posterior distribution of each parameter by progressively sampling from a series of intermediate distributions, thereby refining parameter estimates according to the observed data. At each iteration, parameter sets are sampled from the previous iteration\u0026rsquo;s distributions, and simulation errors are computed by comparing the aggregated mortality kinetics from 10 simulations per parameter set with the observed data. Only sets below a dynamically updated threshold (the 20th percentile of previously accepted errors) are retained. This process continues until 1,000 accepted sets are collected, forming updated parameter distributions progressively focusing on sets producing simulations that better fit the observed data. The algorithm terminates when the proportion of accepted simulations falls below 1%, indicating that further iterations are unlikely to significantly improve the model\u0026rsquo;s accuracy.\u003c/p\u003e \u003cp\u003eFor the initialization of this approach, we used densities derived from the experimental data as prior distributions. However, for parameters estimated as point values, we calculated confidence intervals using a bootstrap procedure with 1,000 iterations (Efron \u0026amp; Tibshirani, 1994) for \u003cem\u003eK\u003c/em\u003e and using the delta method (Oehlert, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e1992\u003c/span\u003e) implemented in the \u003cem\u003ecar\u003c/em\u003e package in \u003cem\u003eR\u003c/em\u003e (Fox et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) for \u003cem\u003eε\u003c/em\u003e. These confidence intervals (\u003cem\u003eCI = [CI₁, CI₂]\u003c/em\u003e) were then used to define normal prior distributions for each parameter, setting the mean equal to the point estimate and the standard deviation as σ = (CI₂ \u0026minus; CI₁) / (2 \u0026times; 1.96). The factor 1.96 corresponds to the 97.5th percentile of the standard normal distribution, ensuring that the resulting normal distribution matches the 95% confidence interval.\u003c/p\u003e \u003cp\u003eThe final parameter distributions obtained from the ABC approach were used to perform 1,000 new simulations, which were then aggregated to validate the model and the parameter calibration by comparing the simulated mortality with the observed data. This approach and the resulting final model was also implemented in R (R Core Team, \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), using the same packages for data manipulation and visualization as previously presented.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eExploring parameter influence through sensitivity analysis\u003c/h3\u003e\n\u003cp\u003eA sensitivity analysis using the Morris method (Morris, \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e1991\u003c/span\u003e) and the \u003cem\u003esensitivity\u003c/em\u003e package (Iooss et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) was performed to assess the effect of individual parameter variations on model dynamics while keeping the computational cost low (Wu et al., \u003cspan citationid=\"CR89\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). The method was applied generating 100 random trajectories across the parameter space (10 discrete levels, grid jump\u0026thinsp;=\u0026thinsp;2), varying one parameter at a time, and performing 100 simulations per parameter set to estimate the effect of individual parameter variations on model outputs. We used the 95% confidence intervals of the posterior distributions obtained from the ABC approach to define the lower and upper bounds for each parameter and parameters not experimentally estimated (\u003cem\u003eδ₂\u003c/em\u003e and \u003cem\u003eΦ\u003c/em\u003e), were included using bounds relative to values derived from validation data \u003cb\u003e(\u003c/b\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u003cb\u003e).\u003c/b\u003e\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSWEIRD model calibrated parameters and their sampling ranges for sensitivity analysis\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSymbol\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUnit\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLower bounds\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUpper bounds\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eΦ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eK\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecp\u0026middot;\u0026micro;L\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e67.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.7 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.4 \u0026times; 10\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eρ\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eh\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e38 .3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e9.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.0 \u0026times; 10\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eρ\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eh\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e15.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e22.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eγ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eh\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e69.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e19.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.5 \u0026times; 10\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eδ\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eh\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e38.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e25.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e54.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eδ\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eh\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.0 \u0026times; 10\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eω\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecp\u0026middot;h\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.2 \u0026times; 10\u003csup\u003e7\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.0 \u0026times; 10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.0 \u0026times; 10\u003csup\u003e8\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eω\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecp\u0026middot;h\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.9 \u0026times; 10\u003csup\u003e7\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.9 \u0026times; 10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.8 \u0026times; 10\u003csup\u003e8\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eω\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecp\u0026middot;h\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.1 \u0026times; 10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.6 \u0026times; 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.0 \u0026times; 10\u003csup\u003e7\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eε\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e%\u0026middot;h\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe Morris method was first applied to the number of infectious individuals at the theoretical epidemic peak to identify the parameters exerting the strongest influence on the model\u0026rsquo;s outputs. These key parameters were then selected for a second, time-resolved sensitivity analysis designed to assess how their influence evolved throughout the course of the epidemic. The number of infectious individuals at every two-hour time point was used as the model output, with 20 random trajectories and 100 simulations performed for each parameter set. The resulting data were visualized using the \u0026ldquo;geom_smooth\u0026rdquo; function from the \u003cem\u003eggplot2\u003c/em\u003e package (Wickham, Chang, et al., \u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), applying the LOESS method (Cleveland, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e1979\u003c/span\u003e) to highlight general temporal trends.\u003c/p\u003e \u003cp\u003eAll R scripts (R Core Team, \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) -including models, ABC approach and sensivity analyses- developed and used in this study are available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://gitlab.ifremer.fr/asim/ideal_oshv-1_sweird_model\u003c/span\u003e\u003cspan address=\"https://gitlab.ifremer.fr/asim/ideal_oshv-1_sweird_model\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eEstimation of infection-to-infectiousness time, infectious periods, and shedding rates\u003c/h2\u003e \u003cp\u003eThe experimental approaches revealed differences between oysters that survived infection and those that succumbed to it \u003cb\u003e(Supplementary Fig.\u0026nbsp;2)\u003c/b\u003e. Although the latent period followed a log-normal distribution in both groups, it was longer in surviving oysters (mean \u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;\u003cem\u003e=\u003c/em\u003e\u0026thinsp;34.9 hours), than in oysters that died from infection (mean \u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;\u003cem\u003e=\u003c/em\u003e\u0026thinsp;14 hours) \u003cb\u003e(Supplementary Fig.\u0026nbsp;2A)\u003c/b\u003e. In addition, the log-transformed number of viral particles released per hour followed a normal distribution for non-surviving oysters (\u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e), with a mean corresponding to 6.91 \u0026times; 10\u003csup\u003e7\u003c/sup\u003e DNA copies per hour (cp.h⁻\u0026sup1;), more than 30 times higher than that of surviving oysters (\u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e), whose log-transformed shedding rate followed a log-normal distribution with a mean value corresponding to 1.89 \u0026times; 10\u003csup\u003e6\u003c/sup\u003e cp.h⁻\u0026sup1; \u003cb\u003e(Supplementary Fig.\u0026nbsp;2B)\u003c/b\u003e.\u003c/p\u003e \u003cp\u003eMoreover, beyond comparative analyses, these experimental approaches allowed estimating the distribution of other key parameters. The infectious period of oyster that survive infection followed a gamma distribution with a mean of 66.5 hours (\u003cem\u003eγ\u003c/em\u003e), the infectious period of alive oyster that succumb to infection followed a log-normal distribution with a mean of 96.7 hours (\u003cem\u003eδ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e), and the log-transformed viral shedding rate of infectious dead oysters was also log-normally distributed, with a mean corresponding to 9.97 \u0026times; 10\u003csup\u003e5\u003c/sup\u003e cp.h⁻\u0026sup1; (\u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eEstimation of the 50% infectious concentration and virus inactivation rate in seawater\u003c/h2\u003e \u003cp\u003eThe resulting infection rates as a function of the log-transformed injected viral dose from the third experimental approach \u003cb\u003e(Supplementary Fig.\u0026nbsp;1C)\u003c/b\u003e was used to estimate the 50% infectious concentration (\u003cem\u003eK\u003c/em\u003e) and its 95% confidence interval \u003cb\u003e(Supplementary Fig.\u0026nbsp;3A)\u003c/b\u003e. By identifying the x-coordinate on the linear regression corresponding to a 50% infection rate, the 50% infectious dose was estimated to be 2.01 \u0026times; 10\u003csup\u003e3\u003c/sup\u003e cp, equivalent to 20.1 cp.\u0026micro;L\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e given that 100 \u0026micro;L were injected per oyster. The 95% confidence interval was estimated to be [6.16 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e : 6.56 \u0026times; 10\u003csup\u003e2\u003c/sup\u003e] cp.\u0026micro;L\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAdditionally, the experimental setup implemented to assess the inactivation rate of viral particles in seawater \u003cb\u003e(Supplementary Fig.\u0026nbsp;1D)\u003c/b\u003e revealed that oyster mortality (\u003cem\u003eM\u003c/em\u003e) decreased as the resting time of the contaminated seawater increased \u003cb\u003e(Supplementary Fig.\u0026nbsp;3B).\u003c/b\u003e Direct exposure to freshly contaminated seawater results in a 50% mortality rate, whereas a resting period of 2 to 4 hours reduced it to 40%. Moreover, when the contaminated seawater rested for 8 to 16 hours, mortality dropped to around 10%, and no mortality was observed after 20 hours. Then, using the previously estimated \u003cem\u003eK\u003c/em\u003e value and the observed mortality rates (\u003cem\u003eM\u003c/em\u003e), the Hill equation was used to infer the concentration of infectious viral particles remaining at each time point (0, 2, 4, 8, 12, 16, and 20 h) \u003cb\u003e(Supplementary Fig.\u0026nbsp;3C)\u003c/b\u003e. Linear regression of these estimates against time yielded the slope coefficient \u003cb\u003e(Supplementary Fig.\u0026nbsp;3D)\u003c/b\u003e used to estimate the viral particle inactivation rate in seawater under constant and controlled conditions (\u003cem\u003eε\u003c/em\u003e) \u003cb\u003e(Supplementrary\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eE\u003cb\u003e)\u003c/b\u003e. This was estimated to be 5.87%\u0026middot;h\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e with a 95% interval confidence of [5.05 : 8.92] %\u0026middot;h\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eOptimization of model simulations using ABC-calibration\u003c/h2\u003e \u003cp\u003eParameters estimated from experimental data were used to perform initial model simulations. However these simulations exhibited a temporal delay and underestimated mortality relative to observed data \u003cb\u003e(\u003c/b\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA\u003cb\u003e)\u003c/b\u003e. To reduce these discrepancies, an ABC-based approach was therefore used to refine parameters estimates.\u003c/p\u003e \u003cp\u003eA total of more than 9.8 \u0026times; 10\u003csup\u003e4\u003c/sup\u003e simulations, distributed over five ABC iterations, were required for the algorithm to converge from the prior distributions to the posterior distributions of all the model parameters \u003cb\u003e(Supplementary Fig.\u0026nbsp;4)\u003c/b\u003e. Substantial differences between prior and posterior distributions were observed for several key parameters, based on comparisons of their median values. The most marked difference concerns the viral shedding rate of surviving oysters (\u003cem\u003eω₁\u003c/em\u003e), which increased by 13.7% on the log-transformed scale. Notable decreases are also observed for the concentration inducing 50% infection (\u003cem\u003eK\u003c/em\u003e), the infectious period \u003cem\u003eδ₁\u003c/em\u003e and the latent period \u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e with median reductions of 65.4%, 57.0%, and 19.7%, respectively. In contrast, other parameters showed limited posterior updating, with median shifts remaining below 15%.\u003c/p\u003e \u003cp\u003eAdditionnally, simulations relying on ABC-calibrated parameters showed mortality dynamics that were markedly closer to the observed data than those obtained using experimentally derived parameters (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eB\u003cb\u003e)\u003c/b\u003e. These results indicate that the model calibrated using the ABC approach reproduces the observed patterns more accurately than the model using experimentally derived parameters, thereby supporting its validity.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eSensitivity model analysis\u003c/h2\u003e \u003cp\u003eThe Morris sensitivity analysis performed on the number of infectious individuals at the theoretical peak of the epidemic (t\u0026thinsp;=\u0026thinsp;19), using ABC-calibrated values \u003cb\u003e(\u003c/b\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u003cb\u003e)\u003c/b\u003e, revealed clear differences in parameter influence on the model dynamics \u003cb\u003e(\u003c/b\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA\u003cb\u003e)\u003c/b\u003e. The shedding rate \u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e exhibited the largest mean absolute effect (\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ek\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e*\u003c/em\u003e) and was associated with a high standard deviation (\u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003ek\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;\u003cem\u003eσ)\u003c/em\u003e, indicating a strong overall and variable influence of this parameter on the number of infectious individuals at the peak. Other parameters, such as \u003cem\u003eγ, K, Φ, ρ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e also exhibited substantial mean absolute effects, and were associated with lower standard deviations.\u003c/p\u003e \u003cp\u003eFurthermore, examining how the influence of these parameter variations evolves over time during the simulation revealed distinct trends \u003cb\u003e(\u003c/b\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB\u003cb\u003e)\u003c/b\u003e. The early stages of the simulation were primarily driven by parameters \u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eK\u003c/em\u003e. However, after 50 hours of simulation, the influence of these parameters had markedly decreased and had been surpassed by parameters such as \u003cem\u003eΦ\u003c/em\u003e, \u003cem\u003eγ\u003c/em\u003e and \u003cem\u003eρ₁\u003c/em\u003e which exhibited a significantly stronger impact at this stage than at the beginning of the simulation. In contrast, the influence of \u003cem\u003eρ₂\u003c/em\u003e appeared relatively constant throughout the simulation.\u003c/p\u003e \u003c/div\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003eThe experimental approaches developed in this study enabled the estimation of parameters of the proposed model, allowing simulations specifically tailored to the epidemiological dynamics of the OsHV-1 \u0026micro;Var originating from Marennes-Ol\u0026eacute;ron Bay in small \u003cem\u003eM. gigas\u003c/em\u003e populations. In addition, combining ABC-based calibration with sensitivity analysis helped to identify the key drivers of epidemic dynamics, while also highlighting parameters that were likely misestimated and reducing discrepancies between observed and simulated data.\u003c/p\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eComparison of parameter estimates across OsHV-1 microvariants\u003c/h2\u003e \u003cp\u003eThe experimental approaches enabled parameter estimations consistent with the literature. For example, considering the case of viral particle inactivation in seawater (\u003cem\u003eε\u003c/em\u003e), precise estimates of this parameter remained until now scarce due to its strong dependence on multiple environmental factors (Vigneron et al., \u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). However, it as been shown on an OsHV-1 microvariant originated from Australia that, starting from viral loads exceeding 10⁶ cp.\u0026micro;L⁻\u0026sup1;, a drastic reduction in detectable viral DNA can occur within the first 24 hours, dropping to below 10 cp.\u0026micro;L⁻\u0026sup1; (P. Hick et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Although this variant might be genetically and phenotypically different from the OsHV-1 \u0026micro;Var isolated in 2014 in Marennes-Ol\u0026eacute;ron Bay, this observation is consistent with our findings. Indeed, our results show that virus-contaminated seawater no longer causes mortality after 20 hours of resting time, which supports the estimated degradation rate of 5.87% and corresponds to an average viral infectivity period in seawater of approximately 17 hours. Similarly, the estimated concentration required to infect 50% of individuals in the present study (K\u0026thinsp;\u0026asymp;\u0026thinsp;20 cp.\u0026micro;L⁻\u0026sup1;) is consistent with the literature, as it falls within the same order of magnitude as the value previously estimated for the same variant and used in another model (\u0026asymp;\u0026thinsp;80 cp.\u0026micro;L⁻\u0026sup1;) (Ferreira et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Additionnaly, our results on the infectious period prior to death (96.7 hours, approximately 4 days), are also consistent with values used for the same parameter in previous modelling studies based on OsHV-1 \u0026micro;Var from other origins (5.8 and 5 days) (Adekunle et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Ferreira et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eHowever, certain parameter estimates susbtantially differ from other values reported in the literature. For instance, the shedding rate of oysters that succumb to the infection was estimated at 6.9 \u0026times; 10\u003csup\u003e7\u003c/sup\u003e cp.h⁻\u0026sup1; in our study, whereas previous estimates based on an American microvariant reported a value of \u0026asymp;\u0026thinsp;3 \u0026times; 10\u003csup\u003e6\u003c/sup\u003e cp.h⁻\u0026sup1; (Ferreira et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Although these differences may be explained by several factors, including environmental conditions and the oyster stocks used in the experiments, they may also reflect genetic and phenotypic variations among viruses from distinct origins, known to induce distinct host responses and, consequently, distinct shedding rates (Agnew-Camiener et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2026\u003c/span\u003e). This example support the development of a model framework that can be calibrated to the specific viral variant under study, thereby improving predictive performance for viral dynamics.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003eDiscrepencies due to model assumptions addressed using ABC approach\u003c/h2\u003e \u003cp\u003eAlthough the experimental approaches implemented provided parameter estimates that were mostly consistent with the existing literature, the simulations outputs nevertheless differed from the observed mortality kinetics data. The simulations using parameters calibrated using experimental data resulted in a mortality curve characterized by slower kinetics than those observed in validation data. Indeed, simulated mortality stabilizing only after approximately 500 hours, whereas the observed mortality plateaued around 100 hours, which is in line with previous experimental infections on microvariant form the same origin (Schikorski, Renault, et al., \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2011b\u003c/span\u003e). This mismatch may, in part, be attributed to the simplifying assumptions made during model implementation. In particular, the assumption that viral DNA quantified by qPCR reflects the number of infectious viral particles may bias parameter estimation, potentially leading to an overestimation of key parameters such as shedding rates. This may artificially accelerate the simulated epidemiological dynamics, even though these ultimately appear slower than those observed in the empirical data. Moreover, since the estimated 50% infectious concentration (\u003cem\u003eK\u003c/em\u003e) was derived from PMA-qPCR data and is therefore not as affected by this overestimation (Renault et al., \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), it may introduce a shift that could explain the differences observed in the infection kinetics. Additionally, this parameter, like several others, was estimated from experimental infections performed by injection and therefore does not account for the natural route of viral entry, which may have led to a misestimation of the number of viral particles required to initiate infection.\u003c/p\u003e \u003cp\u003eIndeed, results of the ABC approach indicate that several adjustments were needed for a majority of the estimated parameter values, and most importantly for the key drivers of the transmission dynamics highlighted by the sensitivity analysis. This is, for example, the case for parameter \u003cem\u003eK\u003c/em\u003e, which was identified as an important parameter of the model and as potentially overestimated, with a posterior median adjusted to a value approximately 3 times lower than the prior median. This is also the case for the viral shedding rate of oysters that survive infection (\u003cem\u003eω₁\u003c/em\u003e), whose posterior median was more than 7 times higher than the prior median. Then, by refining posterior distributions using validation data, the ABC approach therefore helps adjust parameter values and produce simulations that more closely match the observed data, thereby improving predictions of OsHV-1 \u0026micro;Var infection dynamics in a local \u003cem\u003eM. gigas\u003c/em\u003e population at an hourly time scale.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003eKey drivers of OsHV-1 uVar dynamics\u003c/h2\u003e \u003cp\u003eThe sensitivity analysis, conducted using parameters ranges resulting from the ABC approach, revealed that all model parameters influence the transmission dynamics, with their relative impact varying throughout the course of the epidemic. However, some parameters stand out because of their particularly strong influence. This is the case for the viral shedding rate of recovering oysters (\u003cem\u003eω₁\u003c/em\u003e), which emerged as the main driver of the epidemiological dynamics. This is consistent with previous studies showing the central role of shedding in infection spread and epidemic progression (Faisal et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Hershberger et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Sensitivity analyses also highlighted the strong influence of the concentration causing 50% infection (\u003cem\u003eK\u003c/em\u003e) in viral dynamics during the early stages of the simulation. This finding supports the high transmissibility of OsHV-1 consistent with an estimated 50% infection dose of 2 \u0026times; 10\u0026sup3; cp, which appears lower than that reported for other herpesviruses, such as HSV-2, for which transmission is considered unlikely below 10⁴ cp (Schiffer et al., \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAdditionally, experimental approaches revealed distinct parameters values between oysters that survived infection and oysters that succumbed to it. These results emphasize the crucial importance of integrating both phenotypes, and thus both epidemiological pathways, into the modeling approach to accurately capture the viral transmission dynamics (Segarra, Mauduit, et al., \u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Moreover, these observations, together with the sensitivity analysis, also underscore the crucial role of oyster survival probability associated with potential genetic resistance (D\u0026eacute;gremont, Garcia, et al., 2015) and highlight the need to explore how its variation influence viral dynamics and the potential outcomes of selective breeding programs.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003eFurther developments towards spatial and biologically realistic modeling\u003c/h2\u003e \u003cp\u003eThe dynamics of OsHV-1 \u0026micro;Var transmission within a \u003cem\u003eM. gigas\u003c/em\u003e population constitute a multifactorial biological process, requiring simplifying approximations to enable effective modelling. However, incorporating key biological, environmental and anthropogenic factors is essential to enhance the predictive accuracy of such a model and to extend its relevance beyond controlled experimental settings, allowing for its application under natural conditions.\u003c/p\u003e \u003cp\u003eDeveloping a realistic model requires accounting for variations in oyster farming density, a major driver of viral replication and epidemic spread. Oyster densities fluctuate seasonally in relation to production cycles and are influenced by natural recruitment and the introduction of hatchery-produced spats or juveniles from other regions \u003cb\u003e(\u003c/b\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA\u003cb\u003e)\u003c/b\u003e (Lupo et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), as well as natural mortality \u003cb\u003e(\u003c/b\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eB\u003cb\u003e)\u003c/b\u003e. Additionnaly, as studies have reported OsHV-1 DNA and protein in asymptomatic oyster (Arzul et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Segarra et al., \u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) together with viral particle shedded from previously recovered oysters (Degremont \u0026amp; Benabdelmouna, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), it is therefore strongly suspected that OsHV-1 may exhibit a persistance phase \u003cb\u003e(\u003c/b\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eC\u003cb\u003e)\u003c/b\u003e. Then, under favorable environmental conditions, recovered oysters may become infectious again, impacting the number of infectious individuals and therefore the dynamics of the virus. Including such a multi-annual dimension would allow recovered oysters to transition either to a persistence compartment, representing individuals that still carry the virus, or to the susceptible state \u003cb\u003e(\u003c/b\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eD\u003cb\u003e)\u003c/b\u003e, representing young oysters that remain vulnerable to infection, with newly settled or hatchery-produced spat.\u003c/p\u003e \u003cp\u003eIncorporating environmental factors is also a key step in developing a realistic model, as they influence both the virus and its host \u003cb\u003e(\u003c/b\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eE\u003cb\u003e)\u003c/b\u003e. Temperature for example is a critical driver of infection dynamics, with a specific range facilitating viral infection and spread (Delisle et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Renault et al., \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). It\u0026rsquo;s also the case for salinity, pH, and turbidity, which are known to influence the stability of herpesviruses in aquatic environments (Dayaram et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) and have been shown to affect OsHV-1 infection dynamics (Fuhrmann et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Renault et al., \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Soletchnik et al., \u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). In addition, environmental conditions can affect filtration activity of oysters, thereby increasing the infection risk (Pousse et al., \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), but also impact the oyster microbiome, a key determinant of sensitivity to OsHV-1 \u0026micro;Var infection (Pathirana et al., \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Moreover, phenotypic differences in infection outcome varies also with developmental stage and individual size (P. M. Hick et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), which represent key epidemiological parameters that should be also explicitly considered in future developments of a climate-sensitive model \u003cb\u003e(\u003c/b\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eF\u003cb\u003e)\u003c/b\u003e.\u003c/p\u003e \u003cp\u003eOther factors also play a key role in the epidemiological dynamics of OsHV-1 by exerting a direct influence on the virus itself. By affecting viral spread and transmission, hydrodynamics should be carefully considered especially in the context spatial modelling \u003cb\u003e(\u003c/b\u003eFig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eG\u003cb\u003e)\u003c/b\u003e (Lupo et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Murray, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Additionally, alternative transmission pathways, such as other host species, could be considered as different virus OsHV-1 genotypes are reported in other bivalve species worldwide and the virus appears as evolving quite rapidly for a herpesvirus (Delmotte et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Morga et al., \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Nevertheless, existing evidence suggests that potential alternative hosts are limited (Camille Pelletier, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), and other filter-feeders appear to have no significant impact on viral concentrations (Pernet et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e"},{"header":"CONCLUSION","content":"\u003cp\u003eBy combining experimental data, ABC-based approach, and sensitivity analysis, we provide an calibrated framework for investigating the epidemiological dynamics of OsHV-1 \u0026micro;Var within a local \u003cem\u003eM. gigas\u003c/em\u003e population. Beyond reproducing observed infection dynamics, this modeling framework serves as a powerful tool to identify the key drivers shaping epidemic trajectories, notably highlighting the critical role of inter-individual variability in host ability to survive infection and viral shedding rates, particularly during the early stages of the epidemic. Building on this foundation, extending the model toward a spatially explicit framework represents a key next step. Incorporating hydrodynamics, farming practices, and environmentally driven variability in the virus-host relationship would enable a more realistic representation of OsHV-1 transmission, providing a valuable tool to support decision-making and mitigate the impact of the virus.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eBM, NF, BP, TR and MJ designed and carried out the experimental approaches described in this study. JT analysed the data and integrated them into a modelling approach developed by JT, CL and MJ. JT and MJ drafted the manuscript, figures and tables, with substantial contributions from IA. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe authors acknowledge the French National Research Agency (ANR) for funding Jules Trillaud\u0026rsquo;s PhD. We also thank Mickael Mege, Fabrice Pernet and Jacqueline Le Grand for their contribution to the experimental work used for model parameter estimation.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe dataset and codes supporting the conclusions of this article are available at: https://gitlab.ifremer.fr/asim/ideal_oshv-1_sweird_model\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAdekunle FO, Bidegain G, Ben-Horin T (2025) Coculture with Eastern oysters is unlikely to reduce OsHV-1 impacts to farmed Pacific oysters: A modelling approach. 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J Royal Soc Interface 10(86). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1098/RSIF.2012.1018\u003c/span\u003e\u003cspan address=\"10.1098/RSIF.2012.1018\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"OsHV-1, Herpesvirus, Magallana gigas, Epidemiological modelling, Aquaculture, Mollusk diseases, Oyster mortality, Approximate Bayesian Computation, Sensitivity analysis","lastPublishedDoi":"10.21203/rs.3.rs-9246047/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9246047/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eOver the past few years, methodological advances have driven major progress in epidemiological modelling tools, improving our ability to understand pathogen dynamics and inform management strategies. However, these powerful approaches remain underused in marine mollusc health, despite their well-recognized potential to assess the impact of pathogens that threaten the long-term viability of the industry. This is notably the case for Ostreid herpesvirus type 1 (OsHV-1), a virus associated with recurrent mass mortalities of Pacific oyster spat worldwide. These recurring outbreaks underscore important gaps in our understanding of its transmission dynamics and the strategies required to mitigate epizootic events. To bridge this gap, we developed a stochastic compartmental epidemiological model that extends the classical SEIR framework by incorporating an environmental viral compartment and distinguishing between oysters that survive infection and those that succumb to it. Model parameters were estimated using targeted experimental data and integrated into stochastic simulations, enabling the model to reproduce the overall dynamics of the observed mortality kinetics and thereby supporting its validity. Remaining discrepancies were then addressed using an Approximate Bayesian Computation approach to refine parameter estimates and improve model accuracy. Additionally, sensitivity analysis identified viral shedding rates as the main drivers of epidemic dynamics. Through this integrative framework, we provide new insights into OsHV-1 transmission patterns and establish a foundation for future spatial modelling aimed at supporting disease management in oyster farming.\u003c/p\u003e","manuscriptTitle":"Unravelling key drivers of Ostreid herpesvirus type 1 (OsHV- 1) transmission dynamics in Pacific oysters through a data-driven epidemiological modeling approach","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-07 16:39:06","doi":"10.21203/rs.3.rs-9246047/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"74d7203a-16cc-4ee9-8803-b39c58ede4f0","owner":[],"postedDate":"April 7th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-07T16:39:11+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-07 16:39:06","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9246047","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9246047","identity":"rs-9246047","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}