具有感染年龄结构的CD4^＋T-细胞感染HIV病毒模型分析

Analysis of an Age-structured Model of HIV Infection of CD4^+T-cells

本文建立和研究一类具有感染年龄结构的CD4^+T-细胞感染HIV病毒的动力学模型.得到决定该模型的未感染平衡点和感染平衡点的存在性和局部渐近稳定性条件,即当一个感染细胞在其整个感染期间产生病毒的总数不超过某一个阈值时,系统总存在局部渐近稳定的未感染平衡点;当一个感染细胞在其整个感染期间产生病毒的总数超过这一阈值时,未感染平衡点不稳定,此时存在局部渐近稳定的感染平衡点.

In this paper, we formulate and analyze the dynamics behavior of an agestructured model of HIV infection of CD4^＋ T-cells. A threshold parameter is given, which determine the existence and stability of the uninfected and the infected steady state. That is, when the total number of virus produced by an infected cell is less than the threshold, the system exists only an uninfected steady state and it is locally asymptotically stable, when the total number of virus produced by an infected cell is greater than the threshold, the uninfected steady state is unstable, and the system exists an infected steady state, which is locally asymptotically stable.