Stochastic extinction and persistence of a parasite–host epidemiological model

In this paper, we investigate the stochastic extinction and persistence of a parasite–host epidemiological model. We show that the global dynamics of the stochastic model can be governed by the basic reproduction number R0S: if R0S 1, under mild extra conditions, the disease persists and endemic dynamics occurs almost surely, the solutions of the stochastic model fluctuate around the steady state of the deterministic model, and a unique stationary distribution can be found. Based on realistic parameters of Daphnia-microparasite system, numerical simulations have been performed to verify/extend our analytical results. Epidemiologically, we find that: (1) Large environment fluctuations can suppress the outbreak of disease; (2) The distributions are governed by R0S; (3) The noise perturbations can be beneficial to control the spread of disease on average.

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