Abstract
In this paper, a stochastic SIRS epidemic model with general incidence rate under regime switching is investigated. First of all, by applying the Markov semigroups theory, we establish sufficient condition RT0*>0 for the densities of the distributions of solution converge in L1 to an invariant density. Then, we prove the extinction of disease under the condition of RT0*<0. Finally, numerical simulations for two special cases of response function are carried out to illustrate the theoretical results.
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