脉冲输注免疫因子的HIV治疗模型的稳定性分析

Stability Analysis of an HIV Therapy Model with Impulsive Infusing Immune Factors

考虑了一类脉冲输注免疫因子治疗HIV感染的脉冲微分方程模型,分析了有无脉冲输注两种情况下平衡点的稳定性,得到了未感染平衡点全局渐近稳定和两个感染平衡点局部渐近稳定以及具脉冲输注模型的无病周期解全局渐近稳定性的充分条件,进一步对脉冲输注免疫因子的时间间隔给出了一个合理的估计.最后,通过数值模拟验证了所获理论结果的正确性.

In this paper,we consider a class of impulsive differential equation model with impulsive infusing immune factors to treat HTV infection,and then analyze the stability of the equilibrium points in both cases that presence or absence of pulse immune responses.Then we obtain the sufficient conditions for the global stability of the infection-free equilibrium and the local stability of the other two infection equilibrias,and give a sufficient condition for the global stability of disease-free periodic solution with pulse immune response.Further more we give a reasonable estimate of the time interval to infuse immune factors.Finally,some numerical simulation are carried to verify the effectiveness of the theoretical results obtained.