具有水平传播和环境传播的反应扩散传染病模型研究  

Analysis of a Reaction-Diffusion Epidemic Model with Horizontal Transmission and Environmental Transmission

作　　者：胡振祥 聂麟飞[1] Hu Zhenxiang;Nie Linfei(School of Mathematics and System Sciences,Xinjiang University,Urumqi 830017)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830017

出　　处：《数学物理学报（A辑）》2022年第6期1849-1860,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(11961066);新疆维吾尔自治区自然科学基金(2021D01E12,2021D01C070)。

摘　　要：该文提出一类具有水平传播和环境传播的反应扩散传染病模型,讨论模型的适定性,包括解的全局存在性和一致有界性.进一步,通过下一代算子的谱半径定义给出基本再生数R0的精确表达式,并利用单调动力系统理论和一致持续性理论研究模型的阈值动力学.In this paper,a reaction-diffusion epidemic model with horizontal transmission and environmental transmission is proposed.The well posedness of this model is investigated,including the global existence and uniform boundedness of the solution.Furthermore,the basic reproduction number R0 is defined by the spectral radius of the next generation operator.The threshold dynamics of the model is studied by using monotone dynamical systems theory and uniform persistence theory.

关 键 词：反应扩散模型 环境传播与水平传播 标准发生率 基本再生数 一致持续性 

分 类 号：O175.21[理学—数学]