具有疫苗接种和暂时性免疫随机延迟的SIR传染病模型

Stochastic delayed SIR epidemic with vaccination model and temporary immunity

本文研究具有疫苗接种和暂时性免疫随机延迟的SIR(Susceptible-Infective-Removed)传染病模型的动力学行为.首先,研究具有任意正初值的系统全局正解的存在唯一性;然后,得到保证疾病平均持久和灭绝的充分条件.同时得到,不管基本再生数R_0的值怎样,大噪声都可以抑制疾病的流行.所得结果表明,时滞对疾病的持久性和灭绝性具有重要的影响.

In this paper, we discuss the dynamics of a stochastic delayed SIR epidemic model with vaccination and temporary immunity. Firstly, we study the existence and uniqueness of the global positive solution with any positive initial value. Then we establish sufficient conditions for persistence in the mean and extinction of the epidemic. Moreover, we obtain that large noise will suppress the disease from prevailing regardless of the value of the basic reproduction number R0. Results show that time delays have important effects on the persistence and extinction of the epidemic.