A stochastic SIRS epidemic model with infectious force under intervention strategies

Yongli Cai, Yun Kang, Malay Banerjee, Weiming Wang

Research output: Contribution to journalArticlepeer-review

213 Scopus citations


In this paper, we extend a classical SIRS epidemic model with the infectious forces under intervention strategies from a deterministic framework to a stochastic differential equation (SDE) one through introducing random fluctuations. The value of our study lies in two aspects. Mathematically, by using the Markov semigroups theory, we prove that the reproduction number R0S can be used to govern the stochastic dynamics of SDE model. If R0S<1, under mild extra conditions, the SDE system has a disease-free absorbing set which means the extinction of disease with probability one. If R0S>1, under mild extra conditions, it has an endemic stationary distribution which leads to the stochastical persistence of the disease. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics.

Original languageEnglish (US)
Pages (from-to)7463-7502
Number of pages40
JournalJournal of Differential Equations
Issue number12
StatePublished - Dec 15 2015


  • Epidemic model
  • Markov semigroups
  • Reproduction number
  • Stationary distribution

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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