Stability and Asymptotic Behavior of a Regime-Switching SIRS Model with Beddington–DeAngelis Incidence Rate

A regime-switching SIRS model with Beddington–DeAngelis incidence rate is studied in this paper. First of all, the property that the model we discuss has a unique positive solution is proved and the invariant set is presented. Secondly, by constructing appropriate Lyapunov functionals, global stochastic asymptotic stability of the model under certain conditions is proved. Then, we leave for studying the asymptotic behavior of the model by presenting threshold values and some other conditions for determining disease extinction and persistence. The results show that stochastic noise can inhibit the disease and the behavior will have different phenomena owing to the role of regime-switching. Finally, some examples are given and numerical simulations are presented to confirm our conclusions.