Stochastic extinction and persistence of a parasite–host epidemiological model

Yuting Liu, Meijing Shan, Xinze Lian and Weiming Wang

Physica A: Statistical Mechanics and its Applications, 2016, vol. 462, issue C, 586-602

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 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.

Keywords: Parasite–host model; Extinction; Persistence; Stationary distribution (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:462:y:2016:i:c:p:586-602

DOI: 10.1016/j.physa.2016.06.022

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