A multi‐group SEIRI epidemic model with logistic population growth under discrete Markov switching: Extinction, persistence, and positive recurrence

Abstract

This paper is concerned with the stochastic dynamics of a multi‐group stochastic SEIRI epidemic model with logistic population growth, standard incidence rate, and Markovian switching. For this purpose, we first show that the solution of the stochastic system is positive and global. Then we obtain sufficient conditions for the extinction of disease. In addition, the persistence in the mean of disease is proved. Specifically, by constructing suitable stochastic Lyapunov functions, we find a domain that is positive recurrence for the solution of stochastic system. Finally, numerical simulations are employed to verify our analytical results.