A stochastic SIR model on a graph with epidemiological and population dynamics occurring over the same time scale

Pierre Montagnon

Published 2018-05-14Version 1

We define and study an open stochastic SIR model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same time scale. Entries are assumed to be density-dependent with a constant component, the amplitude of which determines the overall scale of the population process. Standard branching approximation results for the epidemic process are first given, along with a numerical computation method for the probability of a major epidemic outbreak. This procedure is illustrated using real data on trade-related cattle movements from a densely populated livestock faming region in western France (Finist\`ere) and epidemiological parameters corresponding to an infectious epizootic disease. In a second time, we exhibit an exponential lower bound for the total size of the epidemic in the stable endemic case as a scaling parameter goes to infinity using the Freidlin-Wentzell theory of large deviations from a dynamical system.