具有蛋白酶抑制剂治疗的HIV病毒的传染病模型分析

An Epidemic Model Analysis of HIV Virus with Protease Inhibitor Treatment

建立了T细胞以胸腺和自身有丝分裂进行增殖且具有蛋白酶抑制剂治疗的HIV传染病模型.通过分析该传染病模型,得到蛋白酶抑制剂失效的临界阈值σ和平衡点存在的条件,证明了在不同参数范围内的稳定性.通过对模型的理论分析和数值模拟,发现当σ<σ,无病平衡点是全局渐近稳定的,即疾病消失.当σ>σ,正平衡点是全局渐近稳定的,即HIV病毒流行.且得到σ的值越低,基本再生数R_0的值也越低,即当蛋白酶抑制剂的有效率越高,使得艾滋病患者的免疫功能提高.降低被感染T细胞的死亡率,也使病毒的输入率降低,从而更有利的控制病毒的传播.

In this paper, we consider a HIV model with T cells produced from thymus and proliferation through mitosis and protease inhibitor drugs treatment. It is obtained that the threshold of failure rate of protease inhibitor σ, and the existence conditions of the equilibria of the model. By theoretical analysis and numerical simulation, we find that the disease-free equilibrium is global asymptotically stable when σσ, i.e., the HIV infection disappear.If σσ, the positive equilibrium is global asymptotically stable, i.e., the HIV infection persists. We found the basic reproduction number R_0 will be decreased with parameter σ.It means that HIV patients＇ immune force will be improved when the effective rate of PI is higher. If the mortality of infected T cells will be reduced, then the recruitment rate of HIV virus will be decreased, too. Thus, it is better to control the spread of virus.