Stationary distribution of stochastic SIRS epidemic model with standard incidence

Yanan Zhao, Yuguo Lin, Daqing Jiang, Xuerong Mao, Yong Li

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We study stochastic versions of a deterministic SIRS (Susceptible, Infective, Recovered, Susceptible) epidemic model with standard incidence. We study the existence of a stationary distribution of stochastic system by the theory of integral Markov semigroup. We prove the distribution densities of the solutions can converge to an invariant density in L1. This shows the system is ergodic. The presented results are demonstrated by numerical simulations.
Original languageEnglish
Pages (from-to)2363-2378
Number of pages16
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number7
Early online date31 Aug 2016
Publication statusPublished - 30 Sep 2016


  • stationary distribution
  • diffusion process
  • Markov semigroups
  • asymptotic stability
  • epidemic model
  • SIRS

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