Dynamics of a stochastic SIR epidemic model with saturated incidence

Qun Liu and Qingmei Chen

Applied Mathematics and Computation, 2016, vol. 282, issue C, 155-166

Abstract: In this paper, the dynamics of a stochastic SIR epidemic model with saturated incidence is investigated. Firstly, we prove that the system has a unique global positive solution with any positive initial value. Then we verify that random effect may lead the disease to extinction under a simple condition. Thirdly, we establish a sufficient condition for persistence in the mean of the disease. Moreover, we show that there is a stationary distribution to the stochastic system under certain parametric restrictions. Finally, some numerical simulations are carried out to confirm the analytical results.

Keywords: Persistence in the mean; Extinction; Stationary distribution; Itô’s formula; Lyapunov functions (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:282:y:2016:i:c:p:155-166

DOI: 10.1016/j.amc.2016.02.022

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