具有治疗、完全Logistic增长和免疫应答延迟的HIV感染模型分析

Analysis of HIV infection model with treatment, complete Logistic growth and delayed immune response

建立具有治疗、完全Logistic增长和免疫应答延迟的HIV感染模型,通过对一些关键参数的分析,证明:如果逆转录酶抑制剂和蛋白酶抑制剂的作用效果满足一定的条件,则在可行域内,无感染平衡点是唯一的稳定状态;如果治疗的效果不足够,则平衡点成为不稳定的,且HIV感染存在。在一定条件下,时滞可以影响免疫耗尽平衡点和感染平衡点的稳定性。数值模拟验证了所得结论。

The model of HIV infection with treatment, complete Logistic growth and delayed immune response is established. Through the analysis of some key parameters, it is shown that if the effect of reverse transcriptase inhibitors and protease inhibitors satisfies certain conditions, then in the feasible region, no infection equilibrium point is the only stable state;if the effect of treatment is not sufficient, the equilibrium point becomes unstable, and HIV infection is present, the time delay can affect the stability of the immune depletion equilibrium point and the infection equilibrium point under certain conditions. The conclusions are verified by digital simulation.