# Cattle Shipments and Disease Spread Modeling

Sammanfattning: Spread of transboundary animal diseases can have large impact on animal welfare, public health and economy. The effects of this include economic losses in terms of lower milk production, lower weight gain and culling due to welfare concerns. Disease preparedness is therefore important to be prepared for a possible outbreak, and policies need to be in place in order to take appropriate actions in case of an outbreak. It is also important to be able to take preventive actions to lessen the risk and size of an outbreak. For this, mathematical models are useful to describe the effects of an outbreak and to facilitate informed policy decisions.Mathematical models of spread of animal diseases, implicitly or explicitly, model the route of infection. One route of particular concern is the shipment of livestock animals since animal shipments have the possibility to move infected animals over long distances and introduce disease in previously unaffected areas. It is therefore important to have underlying data to use as input to models in order to consider possible future scenarios. Such data may however be sparse and not readily available. Based on observed (and sometimes incomplete) data, the underlying process that determines the probabilities of livestock shipments’ origins and destinations can be modeled. By using Bayesian statistics and Markov Chain Monte Carlo methods, it is possible to obtain distributions of the underlying parameters in the model, which in turn allow posterior predictive sets of shipments to be generated. These can further be used in a disease simulation to analyze the course of a potential outbreak. Given a large number of scenarios of interest and substantial stochastic effects, implementation of such models requires fast algorithms to facilitate execution of a sufficient number of replicated simulations, which may be infeasible under naive methods. The topics of this thesis are models of live cattle shipment, the problems of lack of shipment data and the computational challenges of modeling and simulating spread of infectious animal diseases.In Paper I, the spatio-temporal variations in distance dependence of cattle shipments in Sweden were studied by using real shipment data, Bayesian statistics and Markov Chain Monte Carlo methods. The main results were that the spatial as well as the temporal aspect are important when modeling networks of cattle shipments in Sweden. The spatial variations distance dependence were analyzed at county, land (Norrland, Svealand and Götaland) and national level (i.e. no spatial variation). Similarly, the temporal aspect were investigated at three levels of granularity, using monthly-, quarterly- and annual variations (i.e no temporal variation). The level of granularity at which the spatio-temporal variations in distance dependence was captured better, in terms of Deviance Information Criterion, was identified at the county and quarter level. This results shows that such variations should be acknowledged when modeling networks of cattle shipments in Sweden.Paper II considered cattle shipments in the U.S. It addressed the problem of intrastate shipments being absent in available data and included responses from a survey taken by experts to estimate the proportion of shipments moving intrastate. The results showed that data from experts had minor effects on the estimations of proportion of intrastate shipments, mainly because of disparate estimates provided by the experts. This paper also investigated three types of functional forms of the distance dependence, and it was shown that the type used in Paper I, was the least preferred of the three. The preferred functional form had a plateau-shape at short distances as well as a fat tail, describing high probability of long-distance shipments.Paper III addressed the computational challenges of simulating spread of livestock diseases. In Paper III, infections were modeled to spread locally from farm to farm without modeling§ each pathway individually (this may include pathways such as airborne spread, wildlife etc.). To avoid evaluating infection probability of all pairs of infected and susceptible premises, spread of disease was simulated by partitioning the landscape into grids and thereby letting farms belong to a specific cell in this grid. An algorithm was introduced that make use of overestimations of the probability of infection to discard entire cells from further consideration as they are considered as uninfected in the current time frame. Despite introducing estimations of probabilities, the algorithm does not introduce estimations to the spread of disease, and does not compromise the integrity of the simulation. This algorithm was compared to the naive algorithm of evaluating the farms pairwise as well as to two other published algorithms developed for increased computational efficiency. It was shown that the algorithm presented in Paper III was as fast as or faster than other considered methods.Paper IV expanded the methods of Paper II and used the methodology from Paper III to simulate spread of disease via cattle shipments and via local spread across the U.S. In Paper IV, additional data at state- and county level were included that aimed at capturing shipment patterns related to the infrastructure of the production system not captured by the distance dependence. The model also considered three types of premises: farm, feedlot and market. This approach allows for different parameters across premises types, acknowledging their different roles in the production system. The result showed that these types of data were important to include when modeling the system and increased model performance in terms of WAIC, suggesting that industry structure should be accounted for when modeling cattle shipments. The spread of disease simulation included control scenarios such as culling of specific premises and also included a SEIR-model to model the infection status of each premises, referred to as partial transition. The results showed that while the inclusion of partial transition slowed the outbreak, the spatial pattern of the outbreak did not change.This thesis provides insights to what factors are important when predicting animal shipments networks for usage in spread of disease simulations and how these factors can be modeled. It also stresses the importance of efficient algorithms when using simulations and presents an algorithm suited for simulating spread of disease between farms where pathways of the pathogen are not modeled explicitly. How to accurately estimate the spread of disease via shipments and how to simulate a large number of outbreak scenarios within reasonable time are two major challenges a modeler faces when trying to predict the impact of a potential outbreak.

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