A coupling construction for spin systems with infinite range interactions

Given a countable set of sites and a collection of flip rates at each site, we give a sufficient condition on the long-range dependancies of the flip rates ensuring the well-definedness of the corresponding spin system. This hypothesis has already been widely used since the interacting particle systems were introduced, but our construction brings a new insight to understand why it is natural. The process is first constructed as a limit of finite spin systems. Then we identify its generator and give a simple criterion for a measure to be invariant with respect to it.Comment: 12 page

Some results about ergodicity in shape for a crystal growth model

International audienceWe study a crystal growth Markov model proposed by Gates and Westcott (\cite{Kinetics1}, \cite{Kinetics2}). This is an aggregation process where particles are packed in a square lattice accordingly to prescribed deposition rates. This model is parametrized by three values $(\beta_i,~i=0,1,2)$ corresponding to deposition rates on three different types of loci. The main problem is to determine, for the shape of the crystal, when recurrence and when ergodicity do occur. In \cite{AMS} and \cite{MarkovModels} sufficient conditions are given both for ergodicity and transience. We establish some improved conditions and give a precise description of the asymptotic behavior in a special case

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

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

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

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

Modelling transmission and control of Mycobacterium avium subspecies paratuberculosis within Irish dairy herds with compact spring calving

Paratuberculosis is a chronic bacterial infection of the intestine in cattle caused by Mycobacterium avium subspecies paratuberculosis (Map). To better understand Map transmission in Irish dairy herds, we adapted the French stochastic individual-based epidemiological simulation model to account for seasonal herd demographics. We investigated the probability of Map persistence over time, the within-herd prevalence over time, and the relative importance of transmission pathways, and assessed the relative effectiveness of test-and-cull control strategies. We investigated the impact on model outputs of calf separation from cows (calves grazed on pasture adjacent to cows vs. were completely separated from cows) and test-and-cull. Test-and-cull scenarios consisted of highly test-positive cows culled within 13 or 4 weeks after detection, and calf born to highly test-positive cows kept vs removed. We simulated a typical Irish dairy herd with on average 82 lactating cows, 112 animals in total. Each scenario was iterated 1000 times to adjust variation caused by stochasticity. Map was introduced in the fully naive herd through the purchase of a moderately infectious primiparous cow. Infection was considered to persist when at least one infected animal remained in the herd or when Map was present in the environment. The probability of Map persistence 15 years after introduction ranged between 32.2-42.7 % when calves and cows had contact on pasture, and between 18.9-29.4 % when calves and cows were separated on pasture. The most effective control strategy was to cull highly test-positive cows within four weeks of detection (absolute 10 % lower persistence compared to scenarios without control). Removing the offspring of highly test-positive dams did not affect either Map persistence or within-herd prevalence of Map. Mean prevalence 15 years after Map introduction was highest (63.5 %) when calves and cows had contact on pasture. Mean prevalence was 15 % lower (absolute decrease) when cows were culled within 13 weeks of a high test-positive result, and 28 % lower when culled within 4 weeks. Around calving, the infection rate was high, with calves being infected in utero or via the general indoor environment (most important transmission routes). For the remainder of the year, the incidence rate was relatively low with most calves being infected on pasture when in contact with cows. Testing and culling was an effective control strategy when it was used prior to the calving period to minimize the number of highly infectious cows present when calves were born