A stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching

In this paper, we propose and discuss a stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching. First of all, we show that there is a unique positive solution, which is a prerequisite for analyzing the long-term behavior of the stochastic model. Then, a threshold dynamic determined by the basic reproduction number $$ is established: the disease can be eradicated almost surely if $$ and under mild extra conditions, whereas if $$ the densities of the distributions of the solution can converge in L ¹ to an invariant density by using the Markov semigroups theory. Finally, based on realistic parameters obtained from previous literatures, numerical simulations have been performed to verify our analytical results.