具有饱和发生率的随机多群体SIS传染病动力学性态研究  

Dynamic behavior of stochastic multigroup SIS infectious disease with saturated incidence rate

作　　者：田雪宏 刘茂省 TIAN Xuehong;LIU Maoxing(School of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,太原030051

出　　处：《黑龙江大学自然科学学报》2022年第6期631-639,共9页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(12071445,12001501);山西省自然科学基金资助项目(201901D211275);山西省“1331”重点创新团队。

摘　　要：基于环境白噪声带来的影响,考虑了一类具有饱和发生率的随机多群体SIS传染病模型。通过构造合适的Lyapunov函数,对系统全局正解的存在唯一性进行了分析,证明了当满足一定条件时,系统存在唯一的平稳分布并得出了疾病灭绝的充分条件。结果表明,减少半饱和常数的值有利于控制传染病的传播。Based on the influence of environmental white noise,a stochastic multigroup SIS infectious disease model with saturated incidence rate is considered.By constructing suitable Lyapunov functions,the existence and uniqueness of the global positive solution is analyzed.It is proved that when certain conditions are satisfied,the system has a unique stationary distribution,and the sufficient conditions for the extinction of the disease are derived.The results show that reducing the value of the half saturation constant are beneficial for controlling the spread of infectious diseases.

关 键 词：随机传染病模型 饱和发生率 多群体 平稳分布 疾病灭绝 

分 类 号：O211.63[理学—概率论与数理统计]