基于比率依赖的HIV-1模型的数学分析

Mathematical analysis for a ratio-dependent model of HIV-1 infection

构造和分析了一个基于比率依赖的模型,此模型包括细胞内部的时滞,综合反转病毒疗法,具有感染性的T细胞和不具感染性的T细胞.细胞内部的时滞由Γ分布来模拟,这样可以将一般的泛函微分方程(FDE)系统转化为常微分方程(ODE)系统或离散微分方程(DDE)系统.本文讨论了这两种特殊情况下平衡点的稳定性.当时滞是弱时滞时FDE模型可转化成ODE模型,并且得到了FDE模型平衡点的稳定性条件.

This paper develops and analyzes a ratio-dependent model that includes an intracellular delays, combination antiretrovial therapy and the dynamics of both infected and uninfected T-cells. The intracellular delay is modelled by a gamma distribution, which can lead the general model (FDE) to the ODE model or the DDE model as special cases. Stability is discussed for the two special cases. The FDE model can be converted into an ODE model when the delay kernel is the weak delay. The stability for the FDE model is obtained under appropriate conditions.