Abstract
The aim of this paper is to study the stochastic SIS epidemic model with general incidence functional response under regime-switching. We derive a sufficient and almost necessary condition for the extinction and permanence of the epidemic system. Moreover, the rate of all convergences of the solution are also established. Our work generalizes and improves many existing results. Precisely, we obtain sharper results for a more general model by introducing a novel technique, which can be used systematically for other systems. Moreover, it is also shown, interestingly, that switching can make extinction become persistence but it can also reverse persistence to extinction. A number of numerical examples are given to illustrate our results.
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