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.