一类具有饱和恢复率的随机传染病模型

A Stochastic Epidemic Model with Saturated Recovery Rate

利用定性分析的方法,研究了一类具有饱和恢复率的随机SIR传染病模型。首先在确定型模型中引入参数的随机扰动,利用Lyapunov方法讨论了随机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I(t)、R(t)趋于零的充分性条件。结果表明,当白噪声足够大时,染病者、治愈者将消失。

By using the method of qualitative analysis,a kind of stochastic SIR epidemic model with saturated recovery rate is studied.First,the random disturbance of the parameters is introduced into the deterministic model,and the existence and uniqueness of the positive solution of the random model are discussed based on the Lyapunov method.Then the Itôformula and the law of strong large numbers are used to obtain the sufficiency conditions of I(t)and R(t)tending to zero.The results show that when the white noise is large enough,the infected and recovered will disappear.