Modelling the spread of bovine viral diarrhea virus (BVDV) in a beef cattle herd and its impact on herd productivity.

Bovine viral diarrhea virus (BVDV) is a common pathogen of cattle herds that causes economic losses due to reproductive disorders in breeding cattle and increased morbidity and mortality amongst infected calves. Our objective was to evaluate the impact of BVDV spread on the productivity of a beef cow-calf herd using a stochastic model in discrete time that accounted for (1) the difference in transmission rates when animals are housed indoors versus grazing on pasture, (2) the external risk of disease introductions through fenceline contact with neighboring herds and the purchase of infected cattle, and (3) the risk of individual pregnant cattle generating persistently infected (PI) calves based on their stage in gestation. The model predicted the highest losses from BVDV during the first 3 years after disease was introduced into a naive herd. During the endemic phase, the impact of BVDV on the yearly herd productivity was much lower due to herd immunity. However, cumulative losses over 10 years in an endemic situation greatly surpassed the losses that occurred during the acute phase. A sensitivity analysis of key model parameters revealed that herd size, the duration of breeding, grazing, and selling periods, renewal rate of breeding females, and the level of numerical productivity expected by the farmer had a significant influence on the predicted losses. This model provides a valuable framework for evaluating the impact of BVDV and the efficacy of different control strategies in beef cow-calf herds.

A spatio-temporal model to describe the spread of Salmonella within a laying flock.

Salmonella is one of the major sources of toxi-infection in humans, most often because of consumption of poultry products. The main reason for this association is the presence in hen flocks of silent carriers, i.e. animals harboring Salmonella without expressing any visible symptoms. Many prophylactic means have been developed to reduce the prevalence of Salmonella carrier-state. While none allows a total reduction of the risk, synergy could result in a drastic reduction of it. Evaluating the risk by modeling would be very useful to estimate such gain in food safety. Here, we propose an individual-based model which describes the spatio-temporal spread of Salmonella within a laying flock and takes into account the host response to bacterial infection. The model includes the individual bacterial load and the animals' ability to reduce it thanks to the immune response, i.e. maximum bacterial dose that the animals may resist without long term carriage and, when carriers, length of bacterial clearance. For model validation, we simulated the Salmonella spread under published experimental conditions. There was a good agreement between simulated and observed published data. This model will thus allow studying the effects, on the spatiotemporal distribution of the bacteria, of both mean and variability of different elements of host response.

A modelling framework based on MDP to coordinate farmers' disease control decisions at a regional scale.

The effectiveness of infectious disease control depends on the ability of health managers to act in a coordinated way. However, with regards to non-notifiable animal diseases, farmers individually decide whether or not to implement control measures, leading to positive and negative externalities for connected farms and possibly impairing disease control at a regional scale. Our objective was to facilitate the identification of optimal incentive schemes at a collective level, adaptive to the epidemiological situation, and minimizing the economic costs due to a disease and its control. We proposed a modelling framework based on Markov Decision Processes (MDP) to identify effective strategies to control PorcineReproductive andRespiratorySyndrome (PRRS), a worldwide endemicinfectiousdisease thatsignificantly impactspig farmproductivity. Using a stochastic discrete-time compartmental model representing PRRS virus spread and control within a group of pig herds, we defined the associated MDP. Using a decision-tree framework, we translated the optimal policy into a limited number of rules providing actions to be performed per 6-month time-step according to the observed system state. We evaluated the effect of varying costs and transition probabilities on optimal policy and epidemiological results. We finally identifiedan adaptive policy that gave the best net financial benefit. The proposed framework is a tool for decision support as it allows decision-makers to identify the optimal policy and to assess its robustness to variations in the values of parameters representing an impact of incentives on farmers' decisions.

Sensitivity analysis to identify key-parameters in modelling the spread of bovine viral diarrhoea virus in a dairy herd.

Models have been developed to represent the spread of bovine viral diarrhoea virus (BVDV) in cattle herds. Whereas the herd dynamics is well known, biological data are missing to estimate the parameters of the infection process. Our objective was to identify the parameters of the infection process that highly influence the spread of BVDV in a dairy herd. A stochastic compartmental model in discrete time represented BVDV infection in a typical Holstein dairy herd structured into five groups (calves, young versus older heifers, lactating versus dry cows). Model sensitivity was analysed for variations in the probability of birth of persistently infected (P) calves (b(P)), mortality of P animals (m(P)), within- and between-group transmission rates for P and transiently infected (T) animals (respectively, beta(w)(P),beta(b)(P),beta(w)(T),beta(b)(T)). Three to five values were tested per parameter. All possible combinations of parameter values were explored, representing 3840 scenarios with 200 runs for each. Outputs were: virus persistence 1 year after introduction, time needed to reach a probability of 80% for the herd to be virus-free, epidemic size, mean numbers of immune dams carrying a P foetus, of P and of T animals in infected herds. When considered together, m(P) and beta(b)(P) accounted for 40-80% of variance of all outputs; b(P) and beta(w)(T) accounted each for less than 20% of variance; beta(b)(T) and beta(w)(P) accounted for almost no percent of variance of the outputs. Parameters beta(w)(T) and b(P) needed to be more precisely estimated. The influence of m(P) indicated the effectiveness of culling P calves, the influence of beta(b)(P) indicated the role of the herd structure in BVDV spread, whereas the influence of b(P) indicated the possible role of vaccination programs in controlling within-herd BVDV spread.

Assessment of strategies to control BVDV spread in a dairy herd using computer simulation.

The efficiency of a test-and-cull programme to control BVDV spread within a dairy herd was assessed using a stochastic model. A single virus introduction by a non-PI dam carrying a PI foetus was simulated in a typical western-France dairy herd. Herd monitoring in test-and-cull programme enabled us to detect virus spread within 1 year after introduction in 87% of the replications. The test-and-cull programme reduced the length of the virus persistence. The extent of infection was moderately reduced.

A model of the spread of the bovine viral-diarrhoea virus within a dairy herd.

Wet BVDSim (a stochastic simulation model) was developed to study the dynamics of the spread of the bovine viral-diarrhoea virus (BVDV) within a dairy herd. This model took into account herd-management factors (common in several countries), which influence BVDV spread. BVDSim was designed as a discrete-entity and discrete-event simulation model. It relied on two processes defined at the individual-animal level, with interactions. The first process was a semi-Markov process and modelled the herd structure and dynamics (demography, herd management). The second process was a Markov process and modelled horizontal and vertical virus transmission. Because the horizontal transmission occurs by contacts (nose-to-nose) and indirectly, transmission varied with the separation of animals into subgroups. Vertical transmission resulted in birth of persistently infected (PI) calves. Other possible consequences of a BVDV infection during the pregnancy period were considered (pregnancy loss, immunity of calves). The outcomes of infection were modelled according to the stage of pregnancy at time of infection. BVDV pregnancy loss was followed either by culling or by a new artificial insemination depending on the modelled farmer's decision. Consistency of the herd dynamics in the absence of any BVDV infection was verified. To explore the model behaviour, the virus spread was simulated over 10 years after the introduction of a near-calving PI heifer into a susceptible 38 cow herd. Different dynamics of the virus spread were simulated, from early clearance to persistence of the virus 10 years after its introduction. Sensitivity of the model to the uncertainty on transmission coefficient was analysed. Qualitative validation consisted in comparing the bulk-milk ELISA results over time in a sample of herds detected with a new infection with the ones derived from simulations.

Approach for qualitative validation using aggregated data for a stochastic simulation model of the spread of the bovine viral-diarrhoea virus in a dairy cattle herd.

Qualitative validation consists in showing that a model is able to mimic available observed data. In population level biological models, the available data frequently represent a group status, such as pool testing, rather than the individual statuses. They are aggregated. Our objective was to explore an approach for qualitative validation of a model with aggregated data and to apply it to validate a stochastic model simulating the bovine viral-diarrhoea virus (BVDV) spread within a dairy cattle herd. Repeated measures of the level of BVDV-specific antibodies in the bulk-tank milk (total milk production of a herd) were used to summarise the BVDV herd status. First, a domain of validation was defined to ensure a comparison restricted to dynamics of pathogen spread well identified among observed aggregated data (new herd infection with a wide BVDV spread). For simulations, scenarios were defined and simulation outputs at the individual animal level were aggregated at the herd level using an aggregation function. Comparison was done only for observed data and simulated aggregated outputs that were in the domain of validation. The validity of our BVDV model was not rejected. Drawbacks and ways of improvement of the approach are discussed.