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

数学物理学报 ›› 2023, Vol. 43 ›› Issue (3): 970-984.

• • 上一篇

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

吴鹏^1,^2,^*(),王秀男³,何泽荣⁴

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

收稿日期:2022-08-03 修回日期:2023-02-12 出版日期:2023-06-26 发布日期:2023-06-01
通讯作者: 吴鹏 E-mail:hzpengwu@163.com
基金资助:
国家自然科学基金(12201557);国家自然科学基金(11871185);浙江省教育厅一般项目(Y202249921)

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

Wu Peng^1,^2,^*(),Wang Xiunan³,He Zerong⁴

¹School of Sciences, Hangzhou Dianzi University, Hangzhou 310018
²School of Data Sciences, Zhejiang University of Finance & Economics, Hangzhou 310018
³Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
⁴Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018

Received:2022-08-03 Revised:2023-02-12 Online:2023-06-26 Published:2023-06-01
Contact: Peng Wu E-mail:hzpengwu@163.com
Supported by:
NSFC(12201557);NSFC(11871185);Foundation of Zhejiang Provincial Education Department(Y202249921)

摘要/Abstract

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.

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

Abstract:

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.

Key words: HIV/AIDS model, Dirichlet boundary condition, Age-space structured, Basic reproduction ratio, Threshold dynamics, Uniform persistence

中图分类号:

O175.1

吴鹏,王秀男,何泽荣. 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[J]. 数学物理学报, 2023, 43(3): 970-984.

Wu Peng,Wang Xiunan,He Zerong. Dynamical Analysis of an Age-Space Structured HIV/AIDS Model with Homogeneous Dirichlet Boundary Condition[J]. Acta mathematica scientia,Series A, 2023, 43(3): 970-984.

图/表 4

图 1

(a) $R_0$ 的值, 其中参数值同式 (6.1), $\gamma_1=5.7, \gamma_2=6.8$ ; (b) $R_0$ 的值, 其中参数值同式 (6.1) 以及 $\gamma_1=7.6, \gamma_2=9$ }"

图 1

图 2

当 $R_0\approxeq 0.927<1$ 时 $U_2(x,t)$ 的演化行为"

图 2

图 3

当 $R_0\approxeq 1.492\gg 1$ 时 $U_2(x,t)$ 的演化行为"

图 3

图 4

扩散系数 $d_n (n=1,2,3)$ 对基本再生数 $R_0$ 的影响. 其他参数值同式 (6.1)"

图 4

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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

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