具有非局部扩散和空间异质性的年龄-空间结构HIV潜伏感染模型的动力学分析

数学物理学报 ›› 2025, Vol. 45 ›› Issue (1): 279-294.

具有非局部扩散和空间异质性的年龄-空间结构HIV潜伏感染模型的动力学分析

吴鹏¹,方诚^2,^*()

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

收稿日期:2024-02-26 修回日期:2024-04-30 出版日期:2025-02-26 发布日期:2025-01-08
通讯作者: * 方诚,E-mail:fangcheng12@zufe.edu.cn
基金资助:
国家自然科学基金(12201557);浙江省统计研究项目(23TJQN12);浙江省属高校基本科研业务费专项资金(GK249909299001-20)

Dynamical Analysis of an Age-Structured HIV Latent Model with Nonlocal Dispersal and Spatial Heterogeneity

Wu Peng¹,Fang Cheng^2,^*()

¹School of Sciences, Hangzhou Dianzi University, Hangzhou 310018
²School of Data Sciences, Zhejiang University of Finance and Economics, Hangzhou 310018

Received:2024-02-26 Revised:2024-04-30 Online:2025-02-26 Published:2025-01-08
Supported by:
NSFC(12201557);Statistical Research Project of Zhejiang Province(23TJQN12);Fundamental Research Funds for the Provincial Universities of Zhejiang(GK249909299001-20)

摘要/Abstract

摘要：

空间异质性和感染年龄深刻影响着 HIV 在宿主体内的感染进程. 为了研究空间异质性和感染年龄对 HIV 的感染动力学的影响, 该文提出一个年龄结构的非局部扩散 HIV 潜伏感染模型来描述 HIV 在宿主体内不同器官中的扩散. 首先研究模型解的全局存在性. 其次, 通过建立模型的一般更新方程, 推导出下一代再生算子 $\mathcal{R}$, 继而得出模型基本再生数 $R_0$ 是算子 $\mathcal{R}$ 的谱半径. 作为传染病模型的动力学阈值, $R_0$ 决定着 HIV 感染在宿主体内的消亡和爆发. 最后, 利用 Krasnoselskii 不动点定理证明了系统非平凡解的存在性. 此外, 在特殊情形下证明了系统正平衡态的渐近性质.

关键词: HIV, 非局部扩散, 年龄结构, 空间异质, 基本再生数, 阈值动力学

Abstract:

The spatial heterogeneity and infection age profoundly affect the infection process of HIV in the within-host. In order to investigate the effects of spatial heterogeneity and infection age on the infection dynamics of HIV, in this paper, we propose an age structured and nonlocal diffusion HIV latent infection model to describe the diffusion of HIV in different organs of the within-host. Firstly, we investigate the global existence of the model solution. Secondly, by establishing the general update equation of the model, the next generation regeneration operator $\mathcal{R}$ is derived, and the basic regeneration number $R_0 $ of the model is obtained as the spectral radius of the operator $\mathcal{R}$. As the dynamics threshold of the infectious disease model, $R_0$ determines the extinction and outbreak of HIV infection in the host. Finally, the existence of non trivial solutions for the system was proved by using Krasnoselskii fixed point theorem. In addition, the asymptotic profiles of the positive steady state of the system were proved in special case.

Key words: HIV, nonlocal dispersal, age structure, spatial heterogeneity, basic reproduction number, threshold dynamics

中图分类号:

O175

吴鹏, 方诚. 具有非局部扩散和空间异质性的年龄-空间结构HIV潜伏感染模型的动力学分析[J]. 数学物理学报, 2025, 45(1): 279-294.

Wu Peng, Fang Cheng. Dynamical Analysis of an Age-Structured HIV Latent Model with Nonlocal Dispersal and Spatial Heterogeneity[J]. Acta mathematica scientia,Series A, 2025, 45(1): 279-294.

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