Population dynamics and epidemic processes on a trade network

Abstract : This thesis discusses the mathematical modelling of population dynamics on cattle trade networks coupled with epidemic processes.We first consider metapopulation models taking into account local demographic dynamics (immigration, births, deaths and animal movements due to trade between the nodes of the network). Recurrence and ergodicity criteria are stated for Markovian models with deterministic local dynamics and stochastic inter-nodal transferts, for a multitype branching process with immigration and for a jump process with logistic rates on a finite state space. In these last two cases, we study scaling limits of processes over finite time intervals and their stability over time scales that are exponentials of the scaling parameter.In a second part, we define a coupling of the jump population models considered with an SIR (Susceptible --- Infected --- Removed) epidemic dynamics. The resulting process accounts for local infectious contacts and pathogen propagation on the network due to movements of infective animals. We approximate the epidemic process by a multitype branching process on finite time intervals, then provide an iterative method to compute the probability of a emph{major epidemic outbreak}, defined as the event of survival of the approximating branching process. We then show that conditionally on a major epidemic outbreak and under a stability condition for an endemic equilibrium of the associated dynamical system, the extinction time and final size of the epidemic grow at least exponentially with respect to the scaling parameter of the model.We finally perform a numerical application of the theoretical results obtained on the SIR model coupled with logistic population dynamics. Calibrating the demographical model parameters on the 2015 Finistère cattle trade network, we compute indicators of the epidemic vulnerability of the network induced by individual holdings. We detail a protocol to assess the relative efficiency of three types of control strategies (screening at importation, isolation and vaccination) targeting the holdings identified as critical for the computed indicators.
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Pierre Montagnon. Population dynamics and epidemic processes on a trade network. Probability [math.PR]. Université Paris-Saclay, 2019. English. ⟨NNT : 2019SACLX025⟩. ⟨tel-02272853⟩

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