一类随机SIQS传染病模型的持久性

Persistence of a Class of Stochastic SIQS Infectious Disease Models

给出了具有随机干扰的SIQS传染病模型的正不变集,研究了该模型中染病群体的持久性。由持久性定义、Itô公式和强大数定律导出了疾病流行的充分性条件,并得出以下结论:当白噪声较小时,疾病会持续存在,这说明微小的随机扰动不能抑制疾病的蔓延。

The positive invariant set of SIQS epidemic model with random interference was given,and the persistence of the infected population in the model was studied.Based on the definition of persistence,Itô formula and the strong law of large numbers,the sufficiency conditions of disease epidemic were derived.It is concluded that when the white noise is small,the disease will continue to exist,which shows that the small stochastic perturbation cannot inhibit the spread of the disease.