一类具有饱和恢复率的随机SIR传染病模型的持久性  

Permanence of a Stochastic SIR Epidemic Model with Saturated Recovery Rate

作　　者：刘娟[1] 吴延敏 Liu Juan;Wu Yanmin(Bengbu University,Bengbu 233030,China)

机构地区：[1]蚌埠学院,安徽蚌埠233030

出　　处：《廊坊师范学院学报（自然科学版）》2024年第3期5-8,13,共5页Journal of Langfang Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(12001001);蚌埠学院自然科学研究项目(2022ZR03)。

摘　　要：在确定型模型的基础上,考虑随机因素,得到了一类具有饱和发生率的随机SIR模型。首先给出随机模型的正不变集,进而介绍持久性含义,利用Ito公式及强大数定律得到了疾病流行的充分性条件。结果表明,当白噪声强度满足一定的参数条件时,染病类群体不会消失,这对于控制疾病的蔓延是不利的。On the basis of deterministic models,a class of stochastic SIR models with saturated recovery rate is obtained by considering random factors.Firstly,the positive invariant set of the stochastic model is given,and then the meaning of persistence is introduced.The sufficiency conditions for disease prevalence are obtained by using the Ito formula and the strong law of large numbers.The results indicate that when the white noise intensity meets certain parameter conditions,the infected population will not disappear,which is unfavorable for controlling the spread of diseases.

关 键 词：随机SIR模型 饱和恢复率 正不变集 ITO公式 

分 类 号：O175.12[理学—数学]