一类具有空间异质性的HIV非局部扩散模型的时空动力学分析  

Spatio-temporal Dynamics of HIV Infection Model with Nonlocal Dispersal and Spatial Heterogeneity

作　　者：方诚 吴鹏 FANG CHENG;WU PENG(School of Data Sciences,Zhejiang University of Finance&Economics,Hangzhou 310018,China;School of Sciences,Hangzhou Dianzi University,310018,China)

机构地区：[1]浙江财经大学数据科学学院,杭州310018 [2]杭州电子科技大学理学院,杭州310018

出　　处：《应用数学学报》2025年第2期263-279,共17页Acta Mathematicae Applicatae Sinica

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(GK249909299001-20)资助项目。

摘　　要：该文研究了一类具有空间异质性HIV潜伏感染的非局部扩散动力学模型.克服了非局部算子引起的非紧性困难并利用更新方程得到了下一代再生算子R的泛函表达式,进而得到模型基本再生数R0,即下一代再生算子R的谱半径.然后对系统进行阈值动力学分析.具体地,通过构造合适的Lyapunov泛函证明了当R0<1时,未感染平衡态是全局渐近稳定的;利用点耗散系统的一致持久性理论证明了当R0>1时,系统是一致持久的并且系统至少存在一个正平衡态.In this paper,a nonlocal dispersal dynamic model of HIV latent infection with spatial heterogeneity is studied.We overcome the difficulty of non compactness caused by the nonlocal dispersal operator,and obtain the functional expression of the next generation operator R by using the renewal equation.Then,the basic reproduction number R_0 of the model is obtained,which is defined by the spectral radius of the next generation regeneration operator R.Finally,the threshold dynamics of the system is analyzed.Specifically,by constructing appropriate Lyapunov functional,it is proved that the uninfected steady state is globally asymptotically stable when R_0 <1;Applying the consistent persistence theory of point dissipative systems,we prove that the system is uniformly persistent and has at least one positive steady state when R_0> 1.

关 键 词：HIV 潜伏感染 非局部扩散模型 空间异质性 下一代再生算子 阈值动力学 

分 类 号：O175[理学—数学]