一类具有周期治疗和非局部感染的反应扩散多菌株HIV模型的动力学分析  

Threshold Dynamics of a Spatial Heterogeneous Reaction-diffusion HIV Model with Periodic Therapy Nonlocal Infection and Multiply Strains

作　　者：陈龙昊 吴鹏 何泽荣[2] CHEN Longhao;WU Peng;HE Zerong(Zhuoyue Honors College,Hangzhou Dianzi University,Hangzhou 310018,China;School of Sciences,Hangzhou Dianzi University,Hangzhou 310018,China)

机构地区：[1]杭州电子科技大学卓越学院,浙江杭州310018 [2]杭州电子科技大学理学院,浙江杭州310018

出　　处：《应用数学》2025年第2期584-594,共11页Mathematica Applicata

基　　金：国家自然科学基金(12201557);浙江省属高校基本科研业务费专项资金(GK249909299001-020)。

摘　　要：该文建立了一类周期反应扩散多菌株HIV感染模型,并考虑了空间异质性和非局部接触两个重要因素.首先,研究了模型的适定性,其次,通过更新方程推导出模型下一代再生算子R(x)并定义了模型的基本再生数R_(0)为R(x)的谱半径,同时讨论了R_(0)对应特征问题的主特征值之间的等价关系.最后,分析了系统关于阈值R_(0)的动力学行为,即R_(0)<1时无感染周期解是全局渐近稳定的,R_(0)>1时系统是一致持久的.In this paper,we establish a periodic reaction-diffusion model for HIV infection involving multiple strains,and considering two important factors:spatial heterogeneity and nonlocal infection.Firstly,the well-posedness of the system is studied.Secondly,by using the renewal equation,the next generation operator R(x)of the system is derived,and the basic reproduction number R_(0)is defined as the spectral radius of R(x).Meanwhile,the equivalence between R_(0)and the principal eigenvalue of the corresponding eigenvalue problem is discussed.Finally,the dynamical behavior of the system with respect to the threshold R_(0)is analyzed,that is,when R_(0)<1,the infection-free periodic solution is globally attractive,and the system is uniformly persistent when R_(0)>1.

关 键 词：多菌株HIV模型 周期治疗 反应扩散 非局部感染 基本再生数 阈值动力学 

分 类 号：O175[理学—数学]