一类具有空间扩散的SEIAV模型及其阈值动力学研究  

A Class of SEIAV Models with Spatial Diffusion and Its Threshold Dynamics

作　　者：刘一鸣 高建国 LIU Yiming;GAO Jianguo(School of Mathematics and Information Science,North Minzu University,Yinchuan 750021,China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021

出　　处：《应用数学》2023年第1期134-151,共18页Mathematica Applicata

基　　金：国家自然科学基金(61761002)。

摘　　要：本文在现有的模型基础上,考虑无症状感染者、游离病毒的传播及空间扩散等因素的影响,建立了一个扩展的SEAIV模型.在研究模型正解的存在性,并给出作为阈值的基本再生数R_(0)的前提下,对疾病的灭绝及持久的情况进行讨论,得到当R_(0)<1时模型的无病平衡点的稳定性以及R_(0)>1时地方病平衡点的稳定性,同时利用数值模拟进行验证.进一步讨论在R_(0)=1的情况下,模型的无病平衡点的全局吸引性.In this paper,based on the existing models,an extended SEAIV model is established considering the influence of asymptomatic infected persons,the spread of free viruses,spatial diffusion,and other factors.On the premise of studying the existence of the positive solution of the model and giving the basic regeneration number Ras the threshold,the extinction and persistence of the disease are discussed,The stability of the disease-free equilibrium point of the model when R<1 and the stability of the endemic equilibrium point when R> 1 is obtained.At the same time,the numerical simulation is used to verify the stability.The global attractivity of the disease-free equilibrium point of the model when R=1 is further discussed.

关 键 词：稳定性分析 反应扩散模型 基本再生数 阈值动力学 传染病模型 

分 类 号：O29[理学—应用数学]