一类具有饱和发生率的随机传染病模型的定性分析

Qualitative Analysis of a Stochastic Epidemic Model with Saturated Incidence

利用随机微分方程理论,研究了一类具有饱和发生率的随机SIQS传染病模型。首先引入参数的随机扰动,利用Lyapunov方法讨论了模型正解的存在性及唯一性,进而使用Itô公式及强大数定律得到了系统灭绝的充分性条件。结果表明,当白噪声足够大时,疾病将消失。

Based on the stochastic differential equation theory,this paper studied a stochastic SIQS epidemic model with saturated incidence.First,the stochastic disturbance of the parameters was introduced.Second,the existence and uniqueness of the positive solution of the model were discussed by using the Lyapunov’s method.At last,the sufficient condition for the system's extinction was obtained by using the Itô’s lemma and the strong law of large numbers.The results show that the disease will disappear when the white noise is strong enough.