Bai Ning, Xu Rui
Complex Systems Research Center, Shanxi University, Taiyuan 030006, China.
Math Biosci Eng. 2021 Feb 5;18(2):1689-1707. doi: 10.3934/mbe.2021087.
In this paper, an in-host HIV infection model with latent reservoir, delayed CTL immune response and immune impairment is investigated. By using suitable Lyapunov functions and LaSalle's invariance principle, it is shown that when time delay is equal to zero, the immunity-inactivated reproduction ratio is a threshold determining the global dynamics of the model. By means of the persistence theory for infinite dimensional systems, it is proven that if the immunity-inactivated reproduction ratio is greater than unity, the model is permanent. Choosing time delay as the bifurcation parameter and analyzing the corresponding characteristic equation of the linearized system, the existence of a Hopf bifurcation at the immunity-activated equilibrium is established. Numerical simulations are carried out to illustrate the theoretical results and reveal the effects of some key parameters on viral dynamics.
本文研究了一个具有潜伏库、延迟细胞毒性T淋巴细胞（CTL）免疫反应和免疫损伤的宿主体内HIV感染模型。通过使用合适的Lyapunov函数和LaSalle不变性原理，结果表明当时间延迟为零时，免疫失活繁殖率是决定模型全局动态的一个阈值。借助无穷维系统的持久性理论，证明了如果免疫失活繁殖率大于1，则模型是持久的。选择时间延迟作为分岔参数并分析线性化系统的相应特征方程，建立了在免疫激活平衡点处存在Hopf分岔的结论。进行了数值模拟以说明理论结果并揭示一些关键参数对病毒动态的影响。
