Abstract
In this paper, the threshold behavior of a susceptible–infected–recovered (SIR) epidemic model with stochastic perturbation is investigated. Firstly, it is obtained that the system has a unique global positive solution with any positive initial value. Random effect may lead to disease extinction under a simple condition. Subsequently, sufficient condition for persistence has been established in the mean of the disease. Finally, some numerical simulations are carried out to confirm the analytical results.
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