使用T-20治疗HIV-1患者的不同策略的数学建模与研究

通过建立数学模型,描述了HIV-1感染者使用抗病毒治疗药物——融合酶抑制剂(T-20)的治疗效果.使用脉冲微分方程描述了T-20的使用过程,并考虑了两种不同的药物消除动力学:一级消除动力学与米-曼(Michaelis-Menten)消除动力学.此模型是个非自治微分方程系统,主要关注其无病平衡态,并研究当接受治疗者在服药完全依从的治疗过程中无病平衡态的稳定性.分别针对药物剂量与服药间隔得到了使得无病平衡态稳定的阈值条件.此外,还研究了间歇治疗的效果.研究表明,间歇治疗的效果甚至可以比完全不治疗还要糟糕.     

Modelling two different therapy strategies for drug T-20 on HIV-1 patients

A mathematical model describing the antiretroviral therapy of Enfuvirtide on HIV-1 patients is developed. The effect of Enfuvirtide (formerly called T-20) by impulsive differential equations is modeled by two different drug elimination kinetics, the first-order elimination kinetics and the Michaelis-Menten elimination kinetics. The model is a non-autonomous system of differential equations. For a time-dependent system, the disease-free equilibrium is mainly studied. Its stability, when the therapy is taken with perfect adherence, is obtained. To ensure the disease-free equilibrium remains stable, the analytical thresholds for dosage and dosing intervals are determined. The effects of supervised treatment interruption are also explored. It is shown that the supervised treatment interruption can be worse than no therapy at all.