具有Logistic增长且含Ornstein-Uhlenbeck过程和心理效应的随机SIRS传染病模型  

A stochastic SIRS infectious disease model with Logistic growth and Ornstein-Uhlenbeck process and psychological effects

作　　者：赵彦军 孙晓辉 苏丽 郝智超 李文轩 ZHAO Yan-jun;SUN Xiao-hui;SU Li;HAO Zhi-chao;LI Wen-xuan(International Business School,Jilin International Studies University,Changchun 130117,China;College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]吉林外国语大学国际商学院,吉林长春130117 [2]吉林大学数学学院,吉林长春130012

出　　处：《东北师大学报（自然科学版）》2024年第4期1-10,共10页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11271154);吉林省教育厅科学技术研究项目(JJKH20231389KJ);吉林省教育科学“十四五”规划2022年度课题(GH22708);吉林外国语大学2024年度国家级大学生创新创业训练计划项目(202410964019)。

摘　　要：研究了一类受环境噪声影响具有Logistic增长且含Ornstein-Uhlenbeck过程和心理效应的随机SIRS传染病模型.通过构造Lyapunov函数并利用Ito公式,证明了全局正解的存在唯一性.给出了决定疾病灭绝和持久的阈值——随机基本再生数R_(0)^(s),当R_(0)^(s)<1时,疾病灭绝;当R_(0)^(s)>1时,疾病持久;当R_(0)^(s)=1时,通过基于停时的方法得到疾病灭绝.通过数值模拟验证了理论分析结果的正确性和疾病对心理效应的依赖性.A stochastic SIRS infectious disease model with Logistic growth and Ornstein-Uhlenbeck process and psychological effects is established.By constructing Lyapunov function and applying Ito's formula,the global existence and uniqueness of positive solution are proved.It is analytically made out the stochastic epidemic threshold R_(0)^(s) which pilots the extinction and permanence in mean of the disease.It is given that the disease extinguishes when R_(0)^(s)<1.Othewise,if R_(0)^(s)>1,then disease is permanent in mean.For the critical case R_(0)^(s)=1,it has shown that disease dies out by using an approach involving some appropriate stopping times.A series of numerical simulations is presented to confirm the correctness of the theoretical analysis results and the dependence of disease on psychological effects.

关 键 词：LOGISTIC增长 ORNSTEIN-UHLENBECK过程 心理效应 灭绝性 持久性 

分 类 号：O175.14[理学—数学]