Learning and strategic imitation in modelling farmers' dynamic decisions on bovine viral diarrhoea vaccination.

Considering human decision-making is essential for understanding the mechanisms underlying the propagation of real-life diseases. We present an extension of a model for pathogen spread that considers farmers' dynamic decision-making regarding the adoption of a control measure in their own herd. Farmers can take into account the decisions and observed costs of their trade partners or of their geographic neighbours. The model and construction of such costs are adapted to the case of bovine viral diarrhoea, for which an individual-based stochastic model is considered. Simulation results suggest that obtaining information from geographic neighbours might lead to a better control of bovine viral diarrhoea than considering information from trade partners. In particular, using information from all geographic neighbours at each decision time seems to be more beneficial than considering only the information from one geographic neighbour or trade partner at each time. This study highlights the central role that social dynamics among farmers can take in the spread and control of bovine viral diarrhoea, providing insights into how public policy efforts could be targeted in order to increase voluntary vaccination uptake against this disease in endemic areas.

Retrospective analysis of SARS-CoV-2 omicron invasion over delta in French regions in 2021-22: a status-based multi-variant model.

BACKGROUND: SARS-CoV-2 is a rapidly spreading disease affecting human life and the economy on a global scale. The disease has caused so far more then 5.5 million deaths. The omicron outbreak that emerged in Botswana in the south of Africa spread around the globe at further increased rates, and caused unprecedented SARS-CoV-2 infection incidences in several countries. At the start of December 2021 the first omicron cases were reported in France. METHODS: In this paper we investigate the spreading potential of this novel variant relatively to the delta variant that was also in circulation in France at that time. Using a dynamic multi-variant model accounting for cross-immunity through a status-based approach, we analyze screening data reported by Santé Publique France over 13 metropolitan French regions between 1st of December 2021 and the 30th of January 2022. During the investigated period, the delta variant was replaced by omicron in all metropolitan regions in approximately three weeks. The analysis conducted retrospectively allows us to consider the whole replacement time window and compare regions with different times of omicron introduction and baseline levels of variants' transmission potential. As large uncertainties regarding cross-immunity among variants persist, uncertainty analyses were carried out to assess its impact on our estimations. RESULTS: Assuming that 80% of the population was immunized against delta, a cross delta/omicron cross-immunity of 25% and an omicron generation time of 3.5 days, the relative strength of omicron to delta, expressed as the ratio of their respective reproduction rates, [Formula: see text], was found to range between 1.51 and 1.86 across regions. Uncertainty analysis on epidemiological parameters led to [Formula: see text] ranging from 1.57 to 2.34 on average over the metropolitan French regions, weighted by population size. CONCLUSIONS: Upon introduction, omicron spread rapidly through the French territory and showed a high fitness relative to delta. We documented considerable geographical heterogeneities on the spreading dynamics. The historical reconstruction of variant emergence dynamics provide valuable ground knowledge to face future variant emergence events.

Predicting veal-calf trading events in France.

Global trade has been ranked as one of the top five drivers of infectious disease threat events. More specifically, livestock trade is known to increase the speed at which infectious diseases circulate and to facilitate their dissemination over large distances Therefore, predicting animal movements arising from trade is crucial for assessing epidemic risk and the impact of preventive measures. In this study, we developed a statistical framework for predicting trading events using predictors accessible from routinely collected data. We focused on veal calves, a category of animals with significant commercial value; the dataset considered the veal calf trade in France between January 2011 and June 2019. A subset of farms with consistent trade behaviour over time was built to be used throughout the study. To predict sale or purchase event occurrences, our predictive framework was based on random forests as a binary classification tool, an approach that allows a large number of potential predictors. We explored the robustness of model predictions with respect to the delay in data acquisition and prediction lag time. Overall, sales were more accurately predicted than purchasing events. Unsurprisingly, a delay in data acquisition led to a decrease in the performance of indicators, whereas prediction lag time had little impact. Sale-related predictors mostly reflected past trading events, whereas purchase-related predictors were associated with past trading events, farm management and general farm characteristics. The model outputs also suggested that the veal calf trading network is driven by sales rather than by purchases. Regardless of the length of the delay in data acquisition and prediction lag, the random forest approach fitted on data with municipality as trading unit and a 28-day trading period provided better performance scores (F1-score, positive predictive value and negative predictive value) than scenarios with finer temporal and spatial aggregation units. Predicted trade events can therefore be used to reconstruct the entire veal calf trading network and transfers between selling and purchasing units for each period. This predicted network could be further used to simulate the spread of pathogens via animal trade.

Inference in Gaussian state-space models with mixed effects for multiple epidemic dynamics.

The estimation from available data of parameters governing epidemics is a major challenge. In addition to usual issues (data often incomplete and noisy), epidemics of the same nature may be observed in several places or over different periods. The resulting possible inter-epidemic variability is rarely explicitly considered. Here, we propose to tackle multiple epidemics through a unique model incorporating a stochastic representation for each epidemic and to jointly estimate its parameters from noisy and partial observations. By building on a previous work for prevalence data, a Gaussian state-space model is extended to a model with mixed effects on the parameters describing simultaneously several epidemics and their observation process. An appropriate inference method is developed, by coupling the SAEM algorithm with Kalman-type filtering. Moreover, we consider here incidence data, which requires to develop a new version of the filtering algorithm. Its performances are investigated on SIR simulated epidemics for prevalence and incidence data. Our method outperforms an inference method separately processing each dataset. An application to SEIR influenza outbreaks in France over several years using incidence data is also carried out. Parameter estimations highlight a non-negligible variability between influenza seasons, both in transmission and case reporting. The main contribution of our study is to rigorously and explicitly account for the inter-epidemic variability between multiple outbreaks, both from the viewpoint of modeling and inference with a parsimonious statistical model.

The African swine fever modelling challenge: Model comparison and lessons learnt.

Robust epidemiological knowledge and predictive modelling tools are needed to address challenging objectives, such as: understanding epidemic drivers; forecasting epidemics; and prioritising control measures. Often, multiple modelling approaches can be used during an epidemic to support effective decision making in a timely manner. Modelling challenges contribute to understanding the pros and cons of different approaches and to fostering technical dialogue between modellers. In this paper, we present the results of the first modelling challenge in animal health - the ASF Challenge - which focused on a synthetic epidemic of African swine fever (ASF) on an island. The modelling approaches proposed by five independent international teams were compared. We assessed their ability to predict temporal and spatial epidemic expansion at the interface between domestic pigs and wild boar, and to prioritise a limited number of alternative interventions. We also compared their qualitative and quantitative spatio-temporal predictions over the first two one-month projection phases of the challenge. Top-performing models in predicting the ASF epidemic differed according to the challenge phase, host species, and in predicting spatial or temporal dynamics. Ensemble models built using all team-predictions outperformed any individual model in at least one phase. The ASF Challenge demonstrated that accounting for the interface between livestock and wildlife is key to increasing our effectiveness in controlling emerging animal diseases, and contributed to improving the readiness of the scientific community to face future ASF epidemics. Finally, we discuss the lessons learnt from model comparison to guide decision making.

Dynamic resource allocation for controlling pathogen spread on a large metapopulation network.

To control the spread of an infectious disease over a large network, the optimal allocation by a social planner of a limited resource is a fundamental and difficult problem. We address this problem for a livestock disease that propagates on an animal trade network according to an epidemiological-demographic model based on animal demographics and trade data. We assume that the resource is dynamically allocated following a certain score, up to the limit of resource availability. We adapt a greedy approach to the metapopulation framework, obtaining new scores that minimize approximations of two different objective functions, for two control measures: vaccination and treatment. Through intensive simulations, we compare the greedy scores with several heuristics. Although topology-based scores can limit the spread of the disease, information on herd health status seems crucial to eradicating the disease. In particular, greedy scores are among the most effective in reducing disease prevalence, even though they do not always perform the best. However, some scores may be preferred in real life because they are easier to calculate or because they use a smaller amount of resources. The developed approach could be adapted to other epidemiological models or to other control measures in the metapopulation setting.

A mechanistic and data-driven reconstruction of the time-varying reproduction number: Application to the COVID-19 epidemic.

The effective reproduction number Reff is a critical epidemiological parameter that characterizes the transmissibility of a pathogen. However, this parameter is difficult to estimate in the presence of silent transmission and/or significant temporal variation in case reporting. This variation can occur due to the lack of timely or appropriate testing, public health interventions and/or changes in human behavior during an epidemic. This is exactly the situation we are confronted with during this COVID-19 pandemic. In this work, we propose to estimate Reff for the SARS-CoV-2 (the etiological agent of the COVID-19), based on a model of its propagation considering a time-varying transmission rate. This rate is modeled by a Brownian diffusion process embedded in a stochastic model. The model is then fitted by Bayesian inference (particle Markov Chain Monte Carlo method) using multiple well-documented hospital datasets from several regions in France and in Ireland. This mechanistic modeling framework enables us to reconstruct the temporal evolution of the transmission rate of the COVID-19 based only on the available data. Except for the specific model structure, it is non-specifically assumed that the transmission rate follows a basic stochastic process constrained by the observations. This approach allows us to follow both the course of the COVID-19 epidemic and the temporal evolution of its Reff(t). Besides, it allows to assess and to interpret the evolution of transmission with respect to the mitigation strategies implemented to control the epidemic waves in France and in Ireland. We can thus estimate a reduction of more than 80% for the first wave in all the studied regions but a smaller reduction for the second wave when the epidemic was less active, around 45% in France but just 20% in Ireland. For the third wave in Ireland the reduction was again significant (>70%).

Accounting for farmers' control decisions in a model of pathogen spread through animal trade.

Accounting for individual decisions in mechanistic epidemiological models remains a challenge, especially for unregulated endemic animal diseases for which control is not compulsory. We propose a new integrative model by combining two sub-models. The first one for the dynamics of a livestock epidemic on a metapopulation network, grounded on demographic and animal trade data. The second one for farmers' behavior regarding the adoption of a control measure against the disease spread in their herd. The measure is specified as a protective vaccine with given economic implications, and the model is numerically studied through intensive simulations and sensitivity analyses. While each tested parameter of the model has an impact on the overall model behavior, the most important factor in farmers' decisions is their frequency, as this factor explained almost 30% of the variation in decision-related outputs of the model. Indeed, updating frequently local health information impacts positively vaccination, and limits strongly the propagation of the pathogen. Our study is relevant for the understanding of the interplay between decision-related human behavior and livestock epidemic dynamics. The model can be used for other structures of epidemic models or different interventions, by adapting its components.

Minimizing the number of origins in batches of weaned calves to reduce their risks of developing bovine respiratory diseases.

Bovine respiratory diseases (BRD) are a major concern for the beef cattle industry, as beef calves overwhelmingly develop BRD symptoms during the first weeks after their arrival at fattening units. These cases occur after weaned calves from various cow-calf producers are grouped into batches to be sold to fatteners. Cross-contaminations between calves from different origins (potentially carrying different pathogens), together with increased stress because of the process of batch creation, can increase their risks of developing BRD symptoms. This study investigated whether reducing the number of different origins per batch is a strategy to reduce the risk of BRD cases. We developed an algorithm aimed at creating batches with as few origins as possible, while respecting constraints on the number and breed of the calves. We tested this algorithm on a dataset of 137,726 weaned calves grouped into 9701 batches by a French organization. We also computed an index assessing the risks of developing BRD because of the batch composition by considering four pathogens involved in the BRD system. While increasing the heterogeneity of batches in calf bodyweight, which is not expected to strongly impact the performance, our algorithm successfully decreased the average number of origins in the same batch and their risk index. Both this algorithm and the risk index can be used as part of decision tool to assess and possibly minimize BRD risk at batch creation, but they are generic enough to assess health risk for other production animals, and optimize the homogeneity of selected characteristics.

Neighbourhood contacts and trade movements drive the regional spread of bovine viral diarrhoea virus (BVDV).

To explore the regional spread of endemic pathogens, investigations are required both at within and between population levels. The bovine viral diarrhoea virus (BVDV) is such a pathogen, spreading among cattle herds mainly due to trade movements and neighbourhood contacts, and causing an endemic disease with economic consequences. To assess the contribution of both transmission routes on BVDV regional and local spread, we developed an original epidemiological model combining data-driven and mechanistic approaches, accounting for heterogeneous within-herd dynamics, animal movements and neighbourhood contacts. Extensive simulations were performed over 9 years in an endemic context in a French region with high cattle density. The most uncertain model parameters were calibrated on summary statistics of epidemiological data, highlighting that neighbourhood contacts and within-herd transmission should be high. We showed that neighbourhood contacts and trade movements complementarily contribute to BVDV spread on a regional scale in endemically infected and densely populated areas, leading to intense fade-out/colonization events: neighbourhood contacts generate the vast majority of outbreaks (72%) but mostly in low immunity herds and correlated to a rather short presence of persistently infected animals (P); trade movements generate fewer infections but could affect herds with higher immunity and generate a prolonged presence of P. Both movements and neighbourhood contacts should be considered when designing control or eradication strategies for densely populated region.

Controlling bovine paratuberculosis at a regional scale: Towards a decision modelling tool.

Johne's disease (paratuberculosis), a worldwide enzootic disease of cattle caused by Mycobacterium avium subsp. paratuberculosis (Map), mainly introduced into farms by purchasing infected animals, has a large economic impact for dairy producers. Since diagnostic tests used in routine are poorly sensitive, observing Map spread in the field is hardly possible, whereas there is a need for evaluating control strategies. Our objective was to provide a modelling framework to compare the efficacy of regional control strategies combining internal biosecurity measures and testing of traded animals, against Map spread in a metapopulation of dairy cattle herds. We represented 12,857 dairy herds located in Brittany (France), based on data from 2005 to 2013, used to calibrate herd sizes and demographic rates and to define trade events in a multiscale model of Map infection dynamics. By clustering and categorical descriptive analysis of intensive simulations of this model, based on a numerical experimental design, a large panel of control measures was explored. Their efficacy was assessed on model outputs such as the prevalence and probability of extinction at the metapopulation level. In addition, we proposed a scoring for the effort required to implement control measures and prioritized control strategies based on their theoretical epidemiological efficacy. Our results clearly indicate that eradication cannot be achieved on the mid term using available control measures. However, we identified relevant combinations of measures that lead to the control of Map spread with realistic level of implementation and coverage. The study highlights the challenge of controlling paratuberculosis in an endemically infected region as related to the poor test characteristics and frequent trade movements. Our model lays the foundations for a flexible and efficient tool to help collective animal health managers in defining relevant control strategies at a regional scale, accounting for local specificities in terms of contact network and farms' characteristics.

Spread of Coxiella burnetii between dairy cattle herds in an enzootic region: modelling contributions of airborne transmission and trade.

Q fever, a worldwide zoonotic disease caused by Coxiella burnetii, is a looming concern for livestock and public health. Epidemiological features of inter-herd transmission of C. burnetii in cattle herds by wind and trade of cows are poorly understood. We present a novel dynamic spatial model describing the inter-herd regional spread of C. burnetii in dairy cattle herds, quantifying the ability of airborne transmission and animal trade in C. burnetii propagation in an enzootic region. Among all the new herd infections, 92% were attributed to airborne transmission and the rest to cattle trade. Infections acquired following airborne transmission were shown to cause relatively small and ephemeral intra-herd outbreaks. On the contrary, disease-free herds purchasing an infectious cow experienced significantly higher intra-herd prevalence. The results also indicated that, for short duration, both transmission routes were independent from each other without any synergistic effect. The model outputs applied to the Finistère department in western France showed satisfactory sensitivity (0.71) and specificity (0.80) in predicting herd infection statuses at the end of one year in a neighbourhood of 3 km around expected incident herds, when compared with data. The model developed here thus provides important insights into the spread of C. burnetii between dairy cattle herds and paves the way for implementation and assessment of control strategies.

Market analyses of livestock trade networks to inform the prevention of joint economic and epidemiological risks.

Conventional epidemiological studies of infections spreading through trade networks, e.g., via livestock movements, generally show that central large-size holdings (hubs) should be preferentially surveyed and controlled in order to reduce epidemic spread. However, epidemiological strategies alone may not be economically optimal when costs of control are factored in together with risks of market disruption from targeting core holdings in a supply chain. Using extensive data on animal movements in supply chains for cattle and swine in France, we introduce a method to identify effective strategies for preventing outbreaks with limited budgets while minimizing the risk of market disruptions. Our method involves the categorization of holdings based on position along the supply chain and degree of market share. Our analyses suggest that trade has a higher risk of propagating epidemics through cattle networks, which are dominated by exchanges involving wholesalers, than for swine. We assess the effectiveness of contrasting interventions from the perspectives of regulators and the market, using percolation analysis. We show that preferentially targeting minor, non-central agents can outperform targeting of hubs when the costs to stakeholders and the risks of market disturbance are considered. Our study highlights the importance of assessing joint economic-epidemiological risks in networks underlying pathogen propagation and trade.

Estimation of parameters related to vaccine efficacy and dengue transmission from two large phase III studies.

BACKGROUND: A tetravalent dengue vaccine was shown to be efficacious against symptomatic dengue in two phase III efficacy studies performed in five Asian and five Latin American countries. The objective here was to estimate key parameters of a dengue transmission model using the data collected during these studies. METHODS: Parameter estimation was based on a Sequential Monte Carlo approach and used a cohort version of the transmission model. Serotype-specific basic reproduction numbers were derived for each country. Parameters related to serotype interactions included duration of cross-protection and level of cross-enhancement characterized by differences in symptomaticity for primary, secondary and post-secondary infections. We tested several vaccine efficacy profiles and simulated the evolution of vaccine efficacy over time for the scenarios providing the best fit to the data. RESULTS: Two reference scenarios were identified. The first included temporary cross-protection and the second combined cross-protection and cross-enhancement upon wild-type infection and following vaccination. Both scenarios were associated with differences in efficacy by serotype, higher efficacy for pre-exposed subjects and against severe dengue, increase in efficacy with doses for naïve subjects and by a more important waning of vaccine protection for subjects when naïve than when pre-exposed. Over 20 years, the median reduction of dengue risk induced by the direct protection conferred by the vaccine ranged from 24% to 47% according to country for the first scenario and from 34% to 54% for the second. CONCLUSION: Our study is an important first step in deriving a general framework that combines disease dynamics and mechanisms of vaccine protection that could be used to assess the impact of vaccination at a population level.

Modelling of paratuberculosis spread between dairy cattle farms at a regional scale.

Mycobacterium avium subsp. paratuberculosis (Map) causes Johne's disease, with large economic consequences for dairy cattle producers worldwide. Map spread between farms is mainly due to animal movements. Locally, herd size and management are expected to influence infection dynamics. To provide a better understanding of Map spread between dairy cattle farms at a regional scale, we describe the first spatio-temporal model accounting simultaneously for population and infection dynamics and indirect local transmission within dairy farms, and between-farm transmission through animal trade. This model is applied to Brittany, a French region characterized by a high density of dairy cattle, based on data on animal trade, herd size and farm management (birth, death, renewal, and culling) from 2005 to 2013 for 12,857 dairy farms. In all simulated scenarios, Map infection highly persisted at the metapopulation scale. The characteristics of initially infected farms strongly impacted the regional Map spread. Network-related features of incident farms influenced their ability to contaminate disease-free farms. At the herd level, we highlighted a balanced effect of the number of animals purchased: when large, it led to a high probability of farm infection but to a low persistence. This effect was reduced when prevalence in initially infected farms increased. Implications of our findings in the current enzootic situation are that the risk of infection quickly becomes high for farms buying more than three animals per year. Even in regions with a low proportion of infected farms, Map spread will not fade out spontaneously without the use of effective control strategies.

Epidemics in markets with trade friction and imperfect transactions.

Market trade-routes can support infectious-disease transmission, impacting biological populations and even disrupting trade that conduces the disease. Epidemiological models increasingly account for reductions in infectious contact, such as risk-aversion behaviour in response to pathogen outbreaks. However, responses in market dynamics clearly differ from simple risk aversion, as are driven by other motivation and conditioned by "friction" constraints (a term we borrow from labour economics). Consequently, the propagation of epidemics in markets of, for example livestock, is frictional due to time and cost limitations in the production and exchange of potentially infectious goods. Here we develop a coupled economic-epidemiological model where transient and long-term market dynamics are determined by trade friction and agent adaptation, and can influence disease transmission. The market model is parameterised from datasets on French cattle and pig exchange networks. We show that, when trade is the dominant route of transmission, market friction can be a significantly stronger determinant of epidemics than risk-aversion behaviour. In particular, there is a critical level of friction above which epidemics do not occur, which suggests some epidemics may not be sustained in highly frictional markets. In addition, friction may allow for greater delay in removal of infected agents that still mitigates the epidemic and its impacts. We suggest that policy for minimising contagion in markets could be adjusted to the level of market friction, by adjusting the urgency of intervention or by increasing friction through incentivisation of larger-volume less-frequent transactions that would have limited effect on overall trade flow. Our results are robust to model specificities and can hold in the presence of non-trade disease-transmission routes.

Approximation of epidemic models by diffusion processes and their statistical inference.

Multidimensional continuous-time Markov jump processes [Formula: see text] on [Formula: see text] form a usual set-up for modeling [Formula: see text]-like epidemics. However, when facing incomplete epidemic data, inference based on [Formula: see text] is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating [Formula: see text]. First, previous results on the approximation of density-dependent [Formula: see text]-like models by diffusion processes with small diffusion coefficient [Formula: see text], where [Formula: see text] is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number [Formula: see text] of observations, which corresponds to the epidemic context, and for [Formula: see text]. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as [Formula: see text] (the basic reproduction number), [Formula: see text], [Formula: see text] are investigated on simulations. Two models, [Formula: see text] and [Formula: see text], corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an analytical approach requires only the classical optimization steps.

Characteristics of the spatio-temporal network of cattle movements in France over a 5-year period.

A good knowledge of the specificities of the animal trade network is highly valuable to better control pathogen spread on a large regional to transnational scale. Because of their temporal dynamical nature, studying multi-annual datasets is particularly needed to investigate whether structural patterns are stable over the years. In this study, we analysed the French cattle movement network from 2005 to 2009 for different spatial granularities and temporal windows, with the three-fold objective of exploring temporal variations of the main network characteristics, computing proxies for pathogen spread on this network, which accounts for its time-varying properties and identifying specificities related to the main types of animals and farms (dairy versus beef). Network properties did not qualitatively vary among different temporal and spatial granularities. About 40% of the holdings and 80% of the communes were directly interconnected. The width of the aggregation time window barely impacted normalised distributions of indicators. A period of 8-16 weeks would suffice for robust estimation of their main trends, whereas longer periods would provide more details on tails. The dynamic nature of the network could be seen through the small overlap between consecutive networks with 65% of common active nodes for only 3% of common links over 2005-2009. To control pathogen spread on such a network, by reducing the largest strongly connected component by more than 80%, movements should be prevented from 1 to 5% of the holdings with the highest centrality in the previous year network. The analysis of breed-wise and herd-wise subnetworks, dairy, beef and mixed, reveals similar trends in temporal variation of average indicators and their distributions. The link-based backbones of beef subnetworks seem to be more stable over time than those of other subnetworks. At a regional scale, node reachability accounting for time-respecting paths, as proxy of epidemic burden, is greater for a dairy region than for a beef region. This highlights the importance of considering local specificities and temporal dynamics of animal trade networks when evaluating control measures of pathogen spread.

Dairy goat demography and Q fever infection dynamics.

Between 2007 and 2009, the largest human Q fever epidemic ever described occurred in the Netherlands. The source was traced back to dairy goat farms, where abortion storms had been observed since 2005. Since one putative cause of these abortion storms is the intensive husbandry systems in which the goats are kept, the objective of this study was to assess whether these could be explained by herd size, reproductive pattern and other demographic aspects of Dutch dairy goat herds alone. We adapted an existing, fully parameterized simulation model for Q fever transmission in French dairy cattle herds to represent the demographics typical for Dutch dairy goat herds. The original model represents the infection dynamics in a herd of 50 dairy cows after introduction of a single infected animal; the adapted model has 770 dairy goats. For a full comparison, herds of 770 cows and 50 goats were also modeled. The effects of herd size and goat versus cattle demographics on the probability of and time to extinction of the infection, environmental bacterial load and abortion rate were studied by simulation. The abortion storms could not be fully explained by demographics alone. Adequate data were lacking at the moment to attribute the difference to characteristics of the pathogen, host, within-herd environment, or a combination thereof. The probability of extinction was higher in goat herds than in cattle herds of the same size. The environmental contamination was highest within cattle herds, which may be taken into account when enlarging cattle farming systems.