一类具有Dirichlet边界条件的年龄-空间结构HIV/AIDS传染病模型的动力学分析  

Dynamical Analysis of an Age-Space Structured HIV/AIDS Model with Homogeneous Dirichlet Boundary Condition

作　　者：吴鹏 王秀男 何泽荣[4] Wu Peng;Wang Xiunan;He Zerong(School of Sciences,Hangzhou Dianzi University,Hangzhou 310018;School of Data Sciences,Zhejiang University of Finance&Economics,Hangzhou 310018;Department of Mathematics,University of Tennessee at Chattanooga,Chattanooga,TN 37403,USA;Institute of Operational Research and Cybernetics,Hangzhou Dianzi University,Hangzhou 310018)

机构地区：[1]杭州电子科技大学理学院,杭州310018 [2]浙江财经大学数据科学学院,杭州310018 [3]美国田纳西大学查塔努加分校数学系,查塔努加田纳西州37403 [4]杭州电子科技大学运筹与控制研究所,杭州310018

出　　处：《数学物理学报（A辑）》2023年第3期970-984,共15页Acta Mathematica Scientia

基　　金：国家自然科学基金(12201557,11871185);浙江省教育厅一般项目(Y202249921)。

摘　　要：为了探讨个体扩散、感染年龄和Dirichlet边界环境对HIV/AIDS时空传播动力学的影响,该文构建了一类具有齐次Dirichlet边界条件的年龄空间结构HIV/AIDS传染病动力学模型.首先,应用特征线方法,作者将模型转化为一个积分反应扩散方程模型.其次,作者给出模型基本再生数R_(0)的泛函表达式,并研究了以R_(0)为阈值的模型解的动力学行为.具体地,当R_(0)<1时,HIV/AIDS在人群中可以被消除;而当R_(0)>1时,HIV感染在人群中会持续存在.最后,在二维空间区域中作者通过数值模拟验证了文中理论结果.In order to explore the impact of human movement,infection age,and a hostile boundary environment on the HIV/AIDS spatiotemporal transmission dynamics,we construct an age-space structure model with homogeneous Dirichlet boundary condition.Applying the method of characteristics,we transform the model into a system of a reaction-diffusion equation and an integral equation.We derive the basic reproduction ratio R_(0)and investigate the threshold dynamics in terms of R_(0).Out theoretical results show that,under appropriate conditions,the disease can be eliminated when R_(0)<1 and the infection is uniformly persistent among the population when R_(0)>1.We verify the theoretical result by numerical simulations in a two-dimensional spatial domain.

关 键 词：HIV/AIDS 模型 DIRICHLET 边界条件 年龄-空间结构 基本再生数 阈值动力学 一致持久性 

分 类 号：O175.1[理学—数学]