School of Science and Technology, Zhejiang International Studies University, Hangzhou, Zhejiang, People's Republic of China.
College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, People's Republic of China.
J Biol Dyn. 2021 Dec;15(1):367-394. doi: 10.1080/17513758.2021.1950224.
In this paper, with eclipse stage in consideration, we propose an HIV-1 infection model with a general incidence rate and CTL immune response. We first study the existence and local stability of equilibria, which is characterized by the basic infection reproduction number and the basic immunity reproduction number . The local stability analysis indicates the occurrence of transcritical bifurcations of equilibria. We confirm the bifurcations at the disease-free equilibrium and the infected immune-free equilibrium with transmission rate and the decay rate of CTLs as bifurcation parameters, respectively. Then we apply the approach of Lyapunov functions to establish the global stability of the equilibria, which is determined by the two basic reproduction numbers. These theoretical results are supported with numerical simulations. Moreover, we also identify the high sensitivity parameters by carrying out the sensitivity analysis of the two basic reproduction numbers to the model parameters.
在本文中，我们考虑到蚀变阶段，提出了一个具有一般发病率和 CTL 免疫反应的 HIV-1 感染模型。我们首先研究了平衡点的存在性和局部稳定性，其特征在于基本感染繁殖数 和基本免疫繁殖数 。局部稳定性分析表明平衡点发生了跨越临界分岔。我们分别以传播率和 CTL 的衰减率作为分叉参数，确认了无病平衡点和感染免疫自由平衡点的分岔。然后，我们应用李雅普诺夫函数的方法来建立平衡点的全局稳定性，其由两个基本繁殖数决定。这些理论结果得到了数值模拟的支持。此外，我们还通过对模型参数进行两个基本繁殖数的敏感性分析，确定了高敏感参数。
