Abstract
Abstract 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 R 0 S : if R 0 S 1 , under mild extra conditions, the disease goes to extinction with probability one and the disease-free dynamics occurs; while R 0 S > 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 R 0 S ; (3) The noise perturbations can be beneficial to control the spread of disease on average.
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