, Dynamics of a stochastic epidemic model with Markov switching and general incidence rate

Abstract

In this paper, the stochastic SIR epidemic model with Markov switching and general incidence rate is investigated. We classify the model by introducing a threshold value λ. To be more specific, we show that if λ < 0 then the disease-free is globally asymptotic stable i.e., the disease will eventually disappear while the epidemic is strongly stochastically permanent provided that λ > 0. We also give some of numerical examples to illustrate our results.