基于T细胞和巨噬细胞的HIV感染模型研究

Study on the HIV Infection Model Based on T-Cell and Macrophage

摘要: 本文在HIV感染过程中，考虑两类靶细胞：整合速度快的CD⁺₄ T细胞和整合速度慢的巨噬细胞，建立基于两类靶细胞的HIV感染模型。该模型主要包括感染细胞转化成正常细胞的恢复阶段。首先，定义模型的基本再生数，进而得到无病平衡点E0以及感染平衡点E^*，并理论推导得到模型在两类平衡点的局部渐近稳定性。进一步地，通过利用Lasalle不变原理以及构造Lyapunov函数，得出，当R₀ < 1时，无病平衡点E₀是全局渐近稳定的。最后，通过查阅文献确定参数的实际范围，对模型进行数值模拟，验证稳定性理论的正确性。

Abstract: During the infection process, we consider two types of target cells: CD⁺₄ T cells with a fast integration rate and macrophages with a slow integration rate, and establish an HIV infection model based on the two types of target cells. The main features of this model include the recovery phase of the transformed cells from infected cells into normal cells. We obtain the basic reproduction number R₀, disease-free equilibrium point E₀ and infection equilibrium point E^* of the model, and theoretically derive the local asymptotic stability of the model at the two types of equilibrium points. Furthermore, by using Lasalle’s invariance principle and the Lyapunov function, we obtain that when R₀ < 1, the disease-free equilibrium point E₀ is globally asymptotically stable. Finally, the actual range of parameters is determined by consulting the literature, and the model is numerically simulated to verify the correctness of the stability theory.