一类具有非线性发生率的随机SIRS传染病模型研究  

A Study on a Stochastic SIRS Epidemic Model with Nonlinear Incidence

作　　者：曹虹[1,2] 樊小琳[1] 聂麟飞[2] CAO Hong;FAN Xiao-lin;NIE Lin-fei(School of Mathematics and Physics,Xinjiang Institute of Engineering,Urumqi 830000,China;College of Mathematics and System Science,Xinjiang University,Urumqi 830046,China)

机构地区：[1]新疆工程学院数理学院,新疆乌鲁木齐830000 [2]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《数学的实践与认识》2024年第10期144-151,共8页Mathematics in Practice and Theory

基　　金：随机传染病模型的动力学行为研究(2015xgy161712);新疆常发传染病的动力学模型及控制策略研究(2022D01A246);新疆维吾尔自治区自然科学基金(2021D01E12)。

摘　　要：研究一类具有非线性发生率的随机SIRS传染病模型.首先证明模型全局正解的存在唯一性;然后讨论在确定性模型的无病平衡点和地方性平衡点附近随机模型的渐近行为,分析随机干扰对传染病传播的影响,结果表明扰动强度的强弱在一定条件下会影响疾病的暴发.In this paper,we study a stochastic SIRS epidemic model with nonlinear incidence.First,the existence and uniqueness of the global positive solution of the model are proved.Then,we discuss the asymptotic behavior of the stochastic model near the diseasefree equilibrium and the endemic equilibrium of the deterministic model,analyzing the effect of stochastic disturbances on the spread of infectious diseases.The results show that the strength of disturbance intensity affects the disease outbreak under certain conditions.

关 键 词：SIRS模型 全局正解 灭绝性 持久性 

分 类 号：O211.6[理学—概率论与数理统计] R181[理学—数学]