Stationary distribution of stochastic SIRS epidemic model with standard incidence

Zhao, Yanan and Lin, Yuguo and Jiang, Daqing and Mao, Xuerong and Li, Yong (2016) Stationary distribution of stochastic SIRS epidemic model with standard incidence. Discrete and Continuous Dynamical Systems - Series B, 21 (7). pp. 2363-2378. ISSN 1531-3492

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    Abstract

    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.