The use of a mass-action model to validate the output from a stochastic simulation model of bovine viral diarrhoea virus spread in a closed dairy herd

Deterministic and stochastic effects in spreading dynamics: A case study of bovine viral diarrhea

Bovine viral diarrhea (BVD) is a disease in cattle with complex transmission dynamics that causes substantial economic losses and affects animal welfare. The infection can be transient or persistent. The mostly asymptomatic persistently infected hosts are the main source for transmission of the virus. This characteristic makes it difficult to control the spreading of BVD. We develop a deterministic compartmental model for the spreading dynamics of BVD within a herd and derive the basic reproduction number. This epidemiological quantity indicates that identification and removal of persistently infected animals is a successful control strategy if the transmission rate of transiently infected animals is small. Removing persistently infected animals from the herd at birth results in recurrent outbreaks with decreasing peak prevalence. We propose a stochastic version of the compartmental model that includes stochasticity in the transmission parameters. This stochasticity leads to sustained oscillations in cases where the deterministic model predicts oscillations with decreasing amplitude. The results provide useful information for the design of control strategies.

Assessment of the cost effectiveness of compulsory testing of introduced animals and bulk tank milk testing for bovine viral diarrhea in Japan

Bovine viral diarrhea (BVD) is a chronic disease of cattle caused by infection with BVD virus (BVDV) and can result in economic losses within the livestock industry. In Japan, the test and culling policy is a basic control measure, and implementation of an adequate vaccination program is recommended as a national policy. In addition, optional control measures, including compulsory testing of introduced animals and bulk tank milk (BTM) testing as a mass screening method, are used in several provinces, but their efficacy has not been completely assessed. We evaluated these control measures using the scenario tree model of BVD in Japan, developed in the previous study. The model outputs indicated that compulsory testing of all introduced cattle, rather than only heifers and/or non-vaccinated cattle, was cost effective and reduced the risk of BVDV introduction due to animal movement and that BTM testing could effectively monitor most part of the cattle population. Vaccination coverage and BVDV prevalence among introduced cattle could also affect the cost effectiveness of compulsory testing of targeted cattle, particularly under low vaccination coverage or high BVDV prevalence. However, even with the implementation of a highly effective monitoring scheme for many years, BVD risk could not be eliminated; it instead converged at a very low level (0.02%). Disease models with a cost-effective output could be a powerful tool in developing a control scheme for chronic animal diseases, including BVD, with the consent of relevant stakeholders.

Farm productive contexts and the dynamics of bovine viral diarrhea (BVD) transmission

Bovine viral diarrhea (BVD) is a viral disease that affects cattle and that is endemic to many European countries. It has a markedly negative impact on the economy, through reduced milk production, abortions, and a shorter lifespan of the infected animals. Cows becoming infected during gestation may give birth to Persistently Infected (PI) calves, which remain highly infective throughout their life, due to the lack of immune response to the virus. As a result, they are the key driver of the persistence of the disease both at herd scale, and at the national level. In the latter case, the trade-driven movements of PIs, or gestating cows carrying PIs, are responsible for the spatial dispersion of BVD. Past modeling approaches to BVD transmission have either focused on within-herd or between-herd transmission. A comprehensive portrayal, however, targeting both the generation of PIs within a herd, and their displacement throughout the country due to trade transactions, is still missing. We overcome this by designing a multiscale metapopulation model of the spatial transmission of BVD, accounting for both within-herd infection dynamics, and its spatial dispersion. We focus on Italy, a country where BVD is endemic and seroprevalence is very high. By integrating simple within-herd dynamics of PI generation, and the highly-resolved cattle movement dataset available, our model requires minimal arbitrary assumptions on its parameterization. We use our model to study the role of the different productive contexts of the Italian market, and test possible intervention strategies aimed at prevalence reduction. We find that dairy farms are the main drivers of BVD persistence in Italy, and any control strategy targeting these farms would lead to significantly higher prevalence reduction, with respect to targeting other production compartments. Our multiscale metapopulation model is a simple yet effective tool for studying BVD dispersion and persistence at country level, and is a good instrument for testing targeted strategies aimed at the containment or elimination of this disease. Furthermore, it can readily be applied to any national market for which cattle movement data is available.

Economic risk analysis model for bovine viral diarrhea virus biosecurity in cow-calf herds

A stochastic model was designed to calculate the cost-effectiveness of biosecurity strategies for bovine viral diarrhea virus (BVDV) in cow-calf herds. Possible sources of BVDV introduction considered were imported animals, including the calves of pregnant imports, and fenceline contact with infected herds, including stocker cattle raised in adjacent pastures. Spread of BVDV through the herd was modeled with a stochastic SIR model. Financial consequences of BVDV, including lost income, treatment costs, and the cost of biosecurity strategies, were calculated for 10 years, based on the risks of a herd with a user-defined import profile. Results indicate that importing pregnant animals and stockers increased the financial risk of BVDV. Strategic testing in combination with vaccination most decreased the risk of high-cost outbreaks in most herds. The choice of a biosecurity strategy was specific to the risks of a particular herd.

Network modeling of BVD transmission

Endemic diseases of cattle, such as bovine viral diarrhea, have significant impact on production efficiency of food of animal origin with consequences for animal welfare and climate change reduction targets. Many modeling studies focus on the local scale, examining the on-farm dynamics of this infectious disease. However, insight into prevalence and control across a network of farms ultimately requires a network level approach. Here, we implement understanding of infection dynamics, gained through these detailed on-farm modeling studies, to produce a national scale model of bovine viral diarrhea virus transmission. The complex disease epidemiology and on-farm dynamics are approximated using SIS dynamics with each farm treated as a single unit. Using a top down approach, we estimate on-farm parameters associated with contraction and subsequent clearance from infection at herd level. We examine possible control strategies associated with animal movements between farms and find measures targeted at a small number of high-movement farms efficient for rapid and sustained prevalence reduction.

A stochastic modelling approach to describing the dynamics of an experimental furunculosis epidemic in Chinook salmon, Oncorhynchus tshawytscha (Walbaum)

A susceptible-infected-removed (SIR) stochastic model was compared to a susceptible-latent-infectious-removed (SLIR) stochastic model in terms of describing and capturing the variation observed in replicated experimental furunculosis epidemics, caused by Aeromonas salmonicida. The epidemics had been created by releasing a single infectious fish into a group of susceptible fish (n = 43) and progress of the epidemic was observed for 10 days. This process was replicated in 70 independent groups. The two stochastic models were run 5000 times and after every run and every 100 runs, daily mean values of each compartment were compared to the observed data. Both models, the SIR model (R(2) = 0.91), and the SLIR model (R(2) = 0.90) were successful in predicting the number of fish in each category at each time point in the experimental data. Moreover, between-replicate variability in the stochastic model output was similar to between-replicate variability in the experimental data. Generally, there was little change in the goodness of fit (R(2)) after 200 runs in the SIR model whereas 500 runs were necessary to have stable predictions with the SLIR model. In the SIR model, on an individual replicate basis, approximately 80% of 5000 simulated replicates had R(2) = 0.7 and above, whereas this ratio was slightly higher (82%) with the SLIR model. In brief, both models were equally effective in predicting the observed data and its variance but the SLIR model was advantageous because it differentiated the latent, i.e. infected but not having the ability to discharge pathogen, from the infectious fish.

Review and critical discussion of assumptions and modelling options to study the spread of the bovine viral diarrhoea virus (BVDV) within a cattle herd

Relevance of epidemiological models depends on assumptions on the population structure and dynamics, on the biology of the host-parasite interaction, and on mathematical modelling. In this paper we reviewed published models of the bovine viral diarrhoea virus (BVDV) spread within a herd. Modelling options and assumptions on herd dynamics and BVDV transmission were discussed. A cattle herd is a population with a controlled size. Animals are separated into subgroups according to their age or their physiological status inducing heterogeneity of horizontal transmission. Complexity of models results from: (1) horizontal and vertical virus transmission, (2) birth of persistently infected animals, (3) excretion by transiently and persistently infected animals. Areas where there was a lack of knowledge were identified. Assumptions on the force of infection used to model the horizontal virus transmission were presented and discussed. We proposed possible ways of improving models (e.g. force of infection, validation) and essential model features for further BVDV models.

Identifying critical parameters in the dynamics and control of microparasite infection using a stochastic epidemiological model

A stochastic epidemic model is presented to study infection transmission dynamics, and hence epidemic severity and disease incidence, in a closed population. The aim was to understand the relative importance of various parameters that influence the dynamics of potential epidemics, particularly when the genetic mechanisms of resistance or tolerance to infection are considered. Simulations explored the effect of varying the transmission coefficient, latent period, recovery period, mortality rate, and the period of loss of immunity on overall epidemic outcomes. The critical parameters influencing the transmission of infection, and hence disease incidence, were the transmission coefficient, the latent period, and the recovery period; the period of loss of immunity had only trivial effects. Ideally, control strategies should decrease the transmission coefficient and/or increase the latent period and/or decrease the recovery period. By equating measured traits with disease transmission parameters, the model described in this paper can be used to identify which disease resistance genes or QTL will be truly effective in helping to develop disease-resistant livestock that suffer fewer epidemics and side-effects of infection. In particular, emphases should be placed on finding genes that decrease the transmission of infection, increase the latent period, or decrease the recovery period.

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.

Measuring health and disease: progress in analytical approaches

In this paper, Dr. Martin reviews the progress in analytical approaches used in veterinary medicine between the 1970s and today. The newer applications are used in such activities as monitoring/surveillance, analysis of observational study data, evaluation of tests in the absence of gold standards, the analysis of clustered data (including geographically clustered data) and modeling disease in populations. Future work will be more complex but will demand an increased emphasis on ways to enhance our biological understanding of the results of data analysis and modeling.

Pooled-sample testing as a herd-screening tool for detection of bovine viral diarrhea virus persistently infected cattle

The study was conducted to develop methodology for least-cost strategies for using polymerase chain reaction (PCR)/probe testing of pooled blood samples to identify animals in a herd persistently infected with bovine viral diarrhea virus (BVDV). Cost was estimated for 5 protocols using Monte Carlo simulations for herd prevalences of BVDV persistent infection (BVDV-PI) ranging from 0.5% to 3%, assuming a cost for a PCR/probe test of $20. The protocol associated with the least cost per cow involved an initial testing of pools followed by repooling and testing of positive pools. For a herd prevalence of 1%, the least cost per cow was $2.64 (95% prediction interval = $1.72, $3.68), where pool sizes for the initial and repooled testing were 20 and 5 blood samples per pool, respectively. Optimization of the least cost for pooled-sample testing depended on how well a presumed prevalence of BVDV-PI approximated the true prevalence of BVDV infection in the herd. As prevalence increased beyond 3%, the least cost increased, thereby diminishing the competitive benefit of pooled testing. The protocols presented for sample pooling have general application to screening or surveillance using a sensitive diagnostic test to detect very low prevalence diseases or pathogens in flocks or herds.