Impact of the Infection Period Distribution on the Epidemic Spread in a Metapopulation Model

Epidemic models usually rely on the assumption of exponentially distributed sojourn times in infectious states. This is sometimes an acceptable approximation, but it is generally not realistic and it may influence the epidemic dynamics as it has already been shown in one population. Here, we explore the consequences of choosing constant or gamma-distributed infectious periods in a metapopulation context. For two coupled populations, we show that the probability of generating no secondary infections is the largest for most parameter values if the infectious period follows an exponential distribution, and we identify special cases where, inversely, the infection is more prone to extinction in early phases for constant infection durations. The impact of the infection duration distribution on the epidemic dynamics of many connected populations is studied by simulation and sensitivity analysis, taking into account the potential interactions with other factors. The analysis based on the average nonextinct epidemic trajectories shows that their sensitivity to the assumption on the infectious period distribution mostly depends on , the mean infection duration and the network structure. This study shows that the effect of assuming exponential distribution for infection periods instead of more realistic distributions varies with respect to the output of interest and to other factors. Ultimately it highlights the risk of misleading recommendations based on modelling results when models including exponential infection durations are used for practical purposes

Inference using a composite-likelihood approximation for stochastic metapopulation model of disease spread

Spatio-temporal pathogen spread is often partially observed at the metapopulation scale. Available data correspond to proxies and are incomplete, censored and heterogeneous. Moreover, representing such biological systems often leads to complex stochastic models. Such complexity together with data characteristics make the analysis of these systems a challenge. Our objective was to develop a new inference procedure to estimate key parameters of stochastic metapopulation models of animal disease spread from longitudinal and spatial datasets, while accurately accounting for characteristics of census data. We applied our procedure to provide new knowledge on the regional spread of \emph{Mycobacterium avium} subsp. \emph{paratuberculosis} (\emph{Map}), which causes bovine paratuberculosis, a worldwide endemic disease. \emph{Map} spread between herds through trade movements was modeled with a stochastic mechanistic model. Comprehensive data from 2005 to 2013 on cattle movements in 12,857 dairy herds in Brittany (western France) and partial data on animal infection status in 2,278 herds sampled from 2007 to 2013 were used. Inference was performed using a new criterion based on a Monte-Carlo approximation of a composite likelihood, coupled to a numerical optimization algorithm (Nelder-Mead Simplex-like). Our criterion showed a clear superiority to alternative ones in identifying the right parameter values, as assessed by an empirical identifiability on simulated data. Point estimates and profile likelihoods allowed us to establish the initial state of the system, identify the risk of pathogen introduction from outside the metapopulation, and confirm the assumption of the low sensitivity of the diagnostic test. Our inference procedure could easily be applied to other spatio-temporal infection dynamics, especially when ABC-like methods face challenges in defining relevant summary statistics

Predicting fadeout versus persistence of paratuberculosis in a dairy cattle herd for management and control purposes: a modelling study

Epidemiological models enable to better understand the dynamics of infectious diseases and to assess ex-ante control strategies. For Mycobacterium avium subsp. paratuberculosis (Map), possible transmission routes have been described, but Map spread in a herd and the relative importance of the routes are currently insufficiently understood to prioritize control measures. We aim to predict early after Map introduction in a dairy cattle herd whether infection is likely to fade out or persist, when no control measures are implemented, using a modelling approach. Both vertical transmission and horizontal transmission via the ingestion of colostrum, milk, or faeces present in the contaminated environment were modelled. Calf-to-calf indirect transmission was possible. Six health states were represented: susceptible, transiently infectious, latently infected, subclinically infected, clinically affected, and resistant. The model was partially validated by comparing the simulated prevalence with field data. Housing facilities and contacts between animals were specifically considered for calves and heifers. After the introduction of one infected animal in a naive herd, fadeout occurred in 66% of the runs. When Map persisted, the prevalence of infected animals increased to 88% in 25 years. The two main transmission routes were via the farm's environment and in utero transmission. Calf-to-calf transmission was minor. Fadeout versus Map persistence could be differentiated with the number of clinically affected animals, which was rarely above one when fadeout occurred. Therefore, early detection of affected animals is crucial in preventing Map persistence in dairy herds

A stochastic model to study rift valley fever persistence with different seasonal patterns of vector abundance: New insights on the endemicity in the tropical island of Mayotte

Rift Valley fever (RVF) is a zoonotic vector-borne disease causing abortion storms in cattle and human epidemics in Africa. Our aim was to evaluate RVF persistence in a seasonal and isolated population and to apply it to Mayotte Island (Indian Ocean), where the virus was still silently circulating four years after its last known introduction in 2007. We proposed a stochastic model to estimate RVF persistence over several years and under four seasonal patterns of vector abundance. Firstly, the model predicted a wide range of virus spread pat- terns, from obligate persistence in a constant or tropical environment (without needing verti- cal transmission or reintroduction) to frequent extinctions in a drier climate. We then identified for each scenario of seasonality the parameters that most influenced prediction variations. Persistence was sensitive to vector lifespan and biting rate in a tropical climate, and to host viraemia duration and vector lifespan in a drier climate. The first epizootic peak was primarily sensitive to viraemia duration and thus likely to be controlled by vaccination, whereas subsequent peaks were sensitive to vector lifespan and biting rate in a tropical cli- mate, and to host birth rate and viraemia duration in arid climates. Finally, we parameterized the model according to Mayotte known environment. Mosquito captures estimated the abundance of eight potential RVF vectors. Review of RVF competence studies on these species allowed adjusting transmission probabilities per bite. Ruminant serological data since 2004 and three new cross-sectional seroprevalence studies are presented. Transmis- sion rates had to be divided by more than five to best fit observed data. Five years after introduction, RVF persisted in more than 10% of the simulations, even under this scenario of low transmission. Hence, active surveillance must be maintained to better understand the risk related to RVF persistence and to prevent new introductions. (Résumé d'auteur

Seasonal and spatial heterogeneities in host and vector abundances impact the spatiotemporal spread of bluetongue

Bluetongue (BT) can cause severe livestock losses and large direct and indirect costs for farmers. To propose targeted control strategies as alternative to massive vaccination, there is a need to better understand how BT virus spread in space and time according to local characteristics of host and vector populations. Our objective was to assess, using a modelling approach, how spatiotemporal heterogeneities in abundance and distribution of hosts and vectors impact the occurrence and amplitude of local and regional BT epidemics. We built a reaction–diffusion model accounting for the seasonality in vector abundance and the active dispersal of vectors. Because of the scale chosen, and movement restrictions imposed during epidemics, host movements and wind-induced passive vector movements were neglected. Four levels of complexity were addressed using a theoretical approach, from a homogeneous to a heterogeneous environment in abundance and distribution of hosts and vectors. These scenarios were illustrated using data on abundance and distribution of hosts and vectors in a real geographical area. We have shown that local epidemics can occur earlier and be larger in scale far from the primary case rather than close to it. Moreover, spatial heterogeneities in hosts and vectors delay the epidemic peak and decrease the infection prevalence. The results obtained on a real area confirmed those obtained on a theoretical domain. Although developed to represent BTV spatiotemporal spread, our model can be used to study other vector-borne diseases of animals with a local to regional spread by vector diffusion

The effect of risk-based trading and within-herd measures on Mycobacterium avium subspecies paratuberculosis spread within and between Irish dairy herds

Johne’s disease (bovine paratuberculosis) is an endemic disease caused by Mycobacterium avium subspecies paratuberculosis (Map). Map is transmitted between herds primarily through movement of infected but undetected animals. Within infected herds, possible control strategies include improving herd hygiene by reducing calf exposure to faeces from cows, reducing stress in cows resulting in a longer latently infected period where shedding is minimal, or culling highly test-positive cows soon after detection. Risk-based trading can be a strategy to reduce the risk that Map spreads between herds. Our objective was to assess whether within-herd measures combined with risk-based trading could effectively control Map spread within and between dairy cattle herds in Ireland. We used a stochastic individual-based and between-herd mechanistic epidemiological model to simulate Map transmission. Movement and herd demographic data were available from 1st January 2009–31st December 2018. In total, 13,353 herds, with 4,494,768 dairy female animals, and 72,991 bulls were included in our dataset. The movement dataset consisted of 2,304,149 animal movements. For each herd, a weekly indicator was calculated that reflected the probability that the herd was free from infection. The indicator value increased when a herd tested negative, decreased when animals were introduced into a herd, and became 0 when a herd tested positive. Based on this indicator value, four Johne’s assurance statuses were distinguished: A) ≥ 0.7 – 1.0, B) ≥ 0.3 – 0.0 – < 0.3, and D) 0.0. A is the highest and D the lowest Johne’s assurance status. With risk-based trading some of the observed movements between herds were redirected based on Johne’s assurance status with the aim of reducing the risk that a non-infected herd acquired an infected animal. Risk-based trading effectively reduced the increase in herd prevalence over a 10-year-period in Ireland: from 50% without risk-based trading to 42% with risk-based trading in the metapopulation only, and 26% when external purchases were risk-based as well. However, for risk-based trading to be effective, a high percentage of dairy herds had to participate. The most important within-herd measures were improved herd hygiene and early culling of highly infectious cows. These measures reduced both herd and within-herd prevalence compared to the reference scenario. Combining risk-based trading with within-herd measures reduced within-herd prevalence even more effectively.Department of Agriculture, Food and the Marin