Mathematical models have shed light on the dynamics of HIV- 1 infection in vivo. In this paper, we generalize continuous mathematical models of drug therapy for HIV-1 by Perelson et al. (Science 271:1582–1586, 1996) and Perelson and Nelson (SIAM Rev 41:3–44, 1999) on time scales, i.e., a nonempty closed subset of real numbers in order to derive new discrete models that predict the total concentration of plasma virus as a function of time. One of our main goals is to compare discrete mathematical models with the continuous model in Perelson et al. (1996) where HIV infected patients were given protease inhibitors and sampled frequently thereafter. For the comparison, we use experimental data collected in Perelson et al. (1996) and estimate the parameters such as the virion clearance rate and the rate of loss of infected cells by fitting the total concentration of plasma virus to this data set. Our results show that discrete systems describe the best fit. In the previous models of this study, the efficacy of protease inhibitor is assumed to be perfect. Motivated by Perelson and Nelson (1999), we end the paper with a mathematical model of imperfect protease inhibitor and reverse transcriptase (RT) inhibitor combination therapy of HIV-1 infection on time scales with its stability analysis.

数学模型阐明了体内HIV-1感染的动态。在本文中，我们归纳了Perelson等人对HIV-1药物治疗的连续数学模型。（Science 271：1582–1586，1996）和Perelson and Nelson（SIAM Rev 41：3–44，1999）的时间尺度，即实数的非空封闭子集，以便得出可预测总浓度的新离散模型血浆病毒随时间的变化。我们的主要目标之一是将Perelson等人的离散数学模型与连续模型进行比较。（1996年），那里的HIV感染患者被给予蛋白酶抑制剂，此后经常取样。为了进行比较，我们使用Perelson等人收集的实验数据。（1996年），并通过将血浆病毒的总浓度拟合到该数据集来估计诸如病毒体清除率和感染细胞的损失率之类的参数。我们的结果表明，离散系统描述了最佳拟合。在本研究的先前模型中，蛋白酶抑制剂的功效被认为是完美的。受Perelson和Nelson（1999）的启发，我们以不完整的蛋白酶抑制剂和逆转录酶（RT）抑制剂联合治疗HIV-1感染的时间模型为模型，并对其稳定性进行了分析。