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When an infectious animal disease is managed by individual farmers, without collective coordination, individual and often heterogeneous control decisions can have a significant impact on the epidemic dynamics. However, decision processes and epidemic processes are often modelled and analysed separately. In this study, we developed a unified modelling framework to jointly represent the dynamics of the spread of an animal disease between farms via the animal trade network and the adaptive control decisions made by each agent (farmer). The proposed algorithm makes the decision process depend on each agent's own situation, its previous decisions and the decisions of their trading partners, reflecting a stochastic behaviour combining imitation and learning. This framework allows the impact of individual livestock vaccination decisions on large-scale epidemic dynamics to be assessed. It is generic and can be adapted to other livestock intervention modalities.

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(A) Schematic of the stochastic integrative model at the farm level, including the epidemiological and decision-making components, as well as a cost function evaluation step and a decision implementation. (B) Temporal dynamics of vaccination decisions for two different values (upper and lower panels) of the parameter reflecting the sensitivity of farmers to their own costs and used in the decision component. Results corresponding to a realisation of the stochastic integrative model schematised in (A). NV (non-vaccination), V (vaccination). Each colour represents a different vaccination scheme, defined by the sequence of vaccination decisions at each of the six decision instants. For example, the pattern [NV1, NV2, V3, V4, V5, V6] refers to farms that do not vaccinate their animals at the first two decision points and always vaccinate afterwards. Each vertical line represents a decision point in time and the width of the flows between two such points in time is proportional to the frequency in the population of farmers who have chosen a given vaccination scheme.