Drug resistance remains a major problem for the treatment of HIV. Resistance can occur due to mutations that were present before treatment starts or due to mutations that occur during treatment. The relative importance of these two sources is unknown. We study three different situations in which HIV drug resistance may evolve: starting triple-drug therapy, treatment with a single dose of nevirapine and interruption of treatment. For each of these three cases good data are available from literature, which allows us to estimate the probability that resistance evolves from standing genetic variation. Depending on the treatment we find probabilities of the evolution of drug resistance due to standing genetic variation between 0 and 39%. For patients who start triple-drug combination therapy, we find that drug resistance evolves from standing genetic variation in approximately 6% of the patients. We use a population-dynamic and population-genetic model to understand the observations and to estimate important evolutionary parameters. We find that both, the effective population size of the virus before treatment, and the fitness of the resistant mutant during treatment, are key-parameters that determine the probability that resistance evolves from standing genetic variation. Importantly, clinical data indicate that both of these parameters can be manipulated by the kind of treatment that is used.
Mathematical analysis and potential therapeutic implications of a novel HIV-1 model of basal and activated transcription in T-cells and macrophages
HIV-1影响着全世界数千万人。目前的治疗通常涉及抗逆转录病毒药物的鸡尾酒，这在减少病毒和延长寿命方面是有效的。然而，目前还没有FDA批准的HIV-1转录抑制剂。此外，只有少数尝试模拟HIV-1的转录过程。在这项工作中，我们扩展了DeMarino et al.（2020）中引入的一种新的HIV-1转录三态模型，该模型已根据实验数据开发和验证。在将该模型拟合到体外数据之后，已经观察到HIV-1在T细胞和巨噬细胞中的转录过程的显著差异。特别是，T细胞中HIV-1启动子的激活似乎随着Tat蛋白接近临界阈值而迅速发生。相比之下，同样的过程在巨噬细胞中发生得更顺利。在这项工作中，我们进行了系统的数学分析的模型，以补充实验数据拟合和敏感性分析较早进行。我们推导出该模型的显式解，得到原模型的精确转录过程衰减率，然后研究非线性对系统行为的影响，包括正平衡的存在性和局部及全局稳定性.我们能够显示的稳定性的积极的稳定状态在有限的情况下，在一般情况下的全球稳定性仍然是一个悬而未决的问题。通过对转录抑制药物治疗的效果进行建模，我们为它有效降低病毒载量提供了一个重要的条件。此外，我们的数值模拟和分析指出，转录抑制剂的效果可以通过与标准治疗同步来增强，例如联合抗逆转录病毒治疗，以减少总剂量和毒性。
Combination interventions for Hepatitis C and Cirrhosis reduction among people who inject drugs: An agent-based, networked population simulation experiment
