Abstract: Based on a saturated infection rate and the mechanism of Human Immunodeficiency Virus（HIV） inducing the apoptosis in CD4+ T cells, a modified anti-HIV infection treatment model is proposed. This model has an infection-free equilibrium point and an endemic infection equilibrium point. It shows that if the model’s basic reproductive number[R0] less than 1, then the infection-free equilibrium point of the model is globally asymptotically stable, if the model’s[R0] greater than 1, then the endemic infection equilibrium point of the model is locally asymptotically stable. Based on the clinical data from HIV drug resistance database of Stanford University, it uses the proposed model to simulate the dynamics of a group patients’ anti-HIV infection treatment and make long-term prediction for the group’s anti-HIV infection treatment. Numerical simulations suggest that the anti-HIV infection treatment cannot control HIV inducing the apoptosis of CD4+ T cells, when the drug resistance appears, the resistance may get stronger if nothing changes in anti-HIV infection treatment, the anti-HIV infection treatment of the group patients is failed eventually.

Key words: Human Immunodeficiency Virus（HIV） infection model, globally asymptotically stable, basic reproductive number, numerical simulation

摘要： 基于饱和发生率和艾滋病病毒（HIV）诱导CD4+ T细胞凋亡的机制，提出了一个改进的抗HIV感染治疗模型。新模型有病毒清除平衡点和持续带毒平衡点。证明了若模型的基本再生数[R0]小于1，则病毒清除平衡点全局渐近稳定;若模型的[R0]大于1，则持续带毒平衡点局部渐近稳定。基于斯坦福大学HIV耐药性数据库，用新模型模拟一组患者抗HIV感染治疗并做疗效的长期预测。数值模拟结果说明抗病毒治疗无法抑制HIV诱导CD4+ T细胞凋亡;HIV耐药性出现后若不及时更换治疗方案，耐药性会增强;长期预测表明该组患者的抗HIV感染治疗以失败告终。

关键词: 艾滋病病毒（HIV）感染模型, 全局渐近稳定, 基本再生数, 数值模拟