A stochastic SIRS epidemic model with nonlinear incidence rate

Yongli Cai, Yun Kang, Weiming Wang

Research output: Contribution to journalArticlepeer-review

203 Scopus citations


In this paper, we investigate the global dynamics of a general SIRS epidemic model with a ratio-dependent incidence rate and its corresponding stochastic differential equation version. For the deterministic model, we show that the basic reproduction number R0 determines whether there is an endemic outbreak or not: if R0<1, the disease dies out; while if R0>1, the disease persists. For the stochastic model, we show that its related reproduction number R0S can determine whether there is a unique disease-free stationary distribution or a unique endemic stationary distribution. In addition, we provide analytic results regarding the stochastic boundedness and permanence/extinction. One of the most interesting findings is that random fluctuations introduced in our stochastic model can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics.

Original languageEnglish (US)
Pages (from-to)221-240
Number of pages20
JournalApplied Mathematics and Computation
StatePublished - Jul 15 2017


  • Basic reproduction number
  • Epidemic model
  • Global stability
  • Permanence
  • Stationary distribution

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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