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摘要
A class of SIR epidemic model with generalized nonlinear incidence rate is presented in this paper. Temporary immunity and stochastic perturbation are also considered. The existence and uniqueness of the global positive solution is achieved. Sufficient conditions guaranteeing the extinction and persistence of the epidemic disease are established. Moreover, the threshold behavior is discussed, and the threshold value R-0 is obtained. We show that if R-0 < 1, the disease eventually becomes extinct with probability one, whereas if R-0 > 1, then the system remains permanent in the mean.
