具有Logistic增长和心理作用的随机SIRS传染病模型定性分析  

Qualitative Analysis of Stochastic SIRS Epidemic Model with Logistic Growth and Psychological Effect

作　　者：赵彦军 苏丽 孙晓辉 李文轩 ZHAO Yanjun;SU Li;SUN Xiaohui;LI Wenxuan(International Business School,Jilin International Studies University,Changchun 130117;College of Mathematics,Jilin University,Changchun 130012)

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

出　　处：《工程数学学报》2024年第3期469-480,共12页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(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).

摘　　要：基于流行病受环境噪声和心理作用的影响,建立了一类具有Logistic增长和心理作用的随机SIRS传染病模型,目的在于讨论Logistic增长和心理作用对模型全局动力学的影响。首先,通过构造Lyapunov函数并利用Itˆo公式,证明了该模型全局正解的存在唯一性;然后,在适当的条件下,利用随机Lyapunov函数方法,应用LaSalle不变性原理得到该模型正解存在遍历平稳分布的充分条件。结果表明:环境和心理变化在一定条件下会对疾病起抑制作用。最后,通过数值模拟验证了理论结果的正确性。Based on the fact that epidemics are affected by environmental noise and psychological effects,a stochastic SIRS epidemic model with Logistic growth and psychological effects is established to discuss the effects of Logistic growth and psychological effects on the global dynamics of the model.Firstly,by constructing the Lyapunov function and using the Itˆo formula,the existence and uniqueness of the global positive solution of the model are proved,and then,under appropriate conditions,by using the random Lyapunov function method,the sufficient conditions for the existence of ergodic stationary distribution of the positive solution of the model are obtained by using the LaSalle invariance principle.The results show that environmental and psychological change can inhibit the disease under certain conditions.Finally,the correctness of the theoretical results is verified by numerical simulation.

关 键 词：SIRS传染病模型 LOGISTIC增长 心理作用 平稳分布 遍历性 

分 类 号：O175[理学—数学]