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 goes to extinction with probability one and the disease-free dynamics occurs; while 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.