具有饱和发生率的SAIRS传染病模型的定性分析  

Qualitative Analysis of the SAIRS Infectious Disease Model with Saturated Incidence

作　　者：蔡钧如 孙福芹[1] 

机构地区：[1]天津职业技术师范大学理学院,天津

出　　处：《理论数学》2024年第5期92-103,共12页Pure Mathematics

摘　　要：本文建立了一类具有饱和发生率和无症状感染的SAIRS传染病模型。计算了模型的基本再生数R0,并推导出了模型的无病平衡点X0和地方病平衡点X*。进一步地,对模型在饱和发生率的条件下平衡点的稳定性通过解得有界性和构造合适Lyapunov函数方法进行了研究。We have established a class of SAIRS infectious disease models with saturated incidence and asymptomatic infection. The basic reproduction number R0 of the model has been calculated, and the disease-free equilibrium point X0 and endemic equilibrium point X* have been derived. Furthermore, we conducted a qualitative analysis of the stability of equilibrium points under saturated incidence conditions using methods involving boundedness and constructing suitable Lyapunov functions.

关 键 词：饱和发生率 SAIRS模型 稳定性 

分 类 号：O17[理学—数学]