Wang Jinliang, Dong Xiu
School of Mathematical Science, Heilongjiang University, Harbin 150080, China.
Math Biosci Eng. 2018 Jun 1;15(3):569-594. doi: 10.3934/mbe.2018026.
There is a growing interest to understand impacts of latent infection age and infection age on viral infection dynamics by using ordinary and partial differential equations. On one hand, activation of latently infected cells needs specificity antigen, and latently infected CD4+ T cells are often heterogeneous, which depends on how frequently they encountered antigens, how much time they need to be preferentially activated and quickly removed from the reservoir. On the other hand, infection age plays an important role in modeling the death rate and virus production rate of infected cells. By rigorous analysis for the model, this paper is devoted to the global dynamics of an HIV infection model subject to latency age and infection age from theoretical point of view, where the model formulation, basic reproduction number computation, and rigorous mathematical analysis, such as relative compactness and persistence of the solution semiflow, and existence of a global attractor are involved. By constructing Lyapunov functions, the global dynamics of a threshold type is established. The method developed here is applicable to broader contexts of investigating viral infection subject to age structure.
人们越来越有兴趣通过使用常微分方程和偏微分方程来理解潜伏感染年龄和感染年龄对病毒感染动态的影响。一方面，潜伏感染细胞的激活需要特异性抗原，并且潜伏感染的CD4+ T细胞通常是异质性的，这取决于它们遇到抗原的频率、优先激活所需的时间以及从储存库中快速清除所需的时间。另一方面，感染年龄在模拟被感染细胞的死亡率和病毒产生率方面起着重要作用。通过对该模型的严格分析，本文从理论角度致力于研究一个受潜伏年龄和感染年龄影响的HIV感染模型的全局动态，其中涉及模型构建、基本再生数计算以及严格的数学分析，如解半流的相对紧性和持续性以及全局吸引子的存在性。通过构造李雅普诺夫函数，建立了阈值类型的全局动态。这里开发的方法适用于研究受年龄结构影响的病毒感染的更广泛背景。
