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 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.