# American Institute of Mathematical Sciences

September  2016, 21(7): 2363-2378. doi: 10.3934/dcdsb.2016051

## Stationary distribution of stochastic SIRS epidemic model with standard incidence

 1 College of Mathematic, Jilin University, Changchun 130012, Jilin, China, China 2 College of Mathematics, Beihua University, Jilin 132013, Jilin, China 3 College of Science, China University of Petroleum(East China), Qingdao 266580, Shandong, China 4 Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26, Richmond Street, Glasgow G1 1XH

Received  December 2014 Revised  September 2015 Published  August 2016

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 $L^1$. This shows the system is ergodic. The presented results are demonstrated by numerical simulations.
Citation: Yanan Zhao, Yuguo Lin, Daqing Jiang, Xuerong Mao, Yong Li. Stationary distribution of stochastic SIRS epidemic model with standard incidence. Discrete & Continuous Dynamical Systems - B, 2016, 21 (7) : 2363-2378. doi: 10.3934/dcdsb.2016051
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