Ren Jian, Xu Rui, Li Liangchen
Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, P. R. China.
Institute of Applied Mathematics, Army Engineering University, Shijiazhuang 050003, Hebei, P. R. China.
Math Biosci Eng. 2020 Nov 19;18(1):57-68. doi: 10.3934/mbe.2021003.
In this paper, we consider an HIV infection model with saturated infection rate, intracellular delay and saturated cytotoxic T lymphocyte (CTL) immune response. By calculation, we obtain immunity-inactivated reproduction number $\mathscr{R}_0$ and immunity-activated reproduction number $\mathscr{R}_1$. By analyzing the distribution of roots of the corresponding characteristic equations, we study the local stability of an infection-free equilibrium, an immunity-inactivated equilibrium and an immunity-activated equilibrium of the model. By constructing suitable Lyapunov functionals and using LaSalle's invariance principle, we show that if $\mathscr{R}_0 < 1$, the infection-free equilibrium is globally asymptotically stable; If $\mathscr{R}1 < 1 < \mathscr{R}_0$, the immunity-inactivated equilibrium is globally asymptotically stable; If $\mathscr{R}_1>1$, the immunity-activated equilibrium is globally asymptotically stable. Sensitivity analyses are carried out to show the effects of parameters on the immunity-activated reproduction number $\mathscr{R}{1}$ and the viral load.
在本文中，我们考虑一个具有饱和感染率、细胞内延迟和饱和细胞毒性T淋巴细胞（CTL）免疫反应的HIV感染模型。通过计算，我们得到免疫失活繁殖数$\mathscr{R}_0$和免疫激活繁殖数$\mathscr{R}_1$。通过分析相应特征方程根的分布，我们研究了该模型无感染平衡点、免疫失活平衡点和免疫激活平衡点的局部稳定性。通过构造合适的Lyapunov泛函并使用LaSalle不变性原理，我们证明如果$\mathscr{R}_0 < 1$，无感染平衡点是全局渐近稳定的；如果$\mathscr{R}1 < 1 < \mathscr{R}_0$，免疫失活平衡点是全局渐近稳定的；如果$\mathscr{R}_1>1$，免疫激活平衡点是全局渐近稳定的。进行了敏感性分析以显示参数对免疫激活繁殖数$\mathscr{R}{1}$和病毒载量的影响。
