关键词: 随机SIR传染病模型, 饱和发生率, It公式, 灭绝性, 持久性

Abstract: We considered a class of stochastic SIR epidemic model with saturated incidence and psychological effect by white noise  in the environment. By constructing Lyapunov function and applying Ito formula, the global existence and uniqueness of the positive solution was obtained. We prove that when stochastic basic reproduction number R*≤1, the disease-free equilibrium is stochastically asymptotical stability, which means the disease will be extinction; if R*>1, the disease will be existence stochastically. The numerical simulation results verify the correctness of the theoretical results.

Key words: stochastic SIR epidemic model, saturated incidence, Ito formula, extinction, persistence