Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO, 80403, USA.
J Math Biol. 2024 Feb 28;88(3):34. doi: 10.1007/s00285-024-02056-1.
We consider a deterministic model of HIV infection that involves macrophages as a long-term active reservoir to describe all three stages of the disease process: the acute stage, chronic infection, and the transition to AIDS. The proposed model is shown to retain crucial properties, such as the positivity of solutions, regardless of variations in model parameters. A dynamical analysis is performed to identify the local stability properties of the viral clearance steady state. This analysis illustrates how chronically infected macrophages can explain the progression to AIDS and provoke viral explosion, while previous models do not. We further demonstrate that the infected T-cell population, even if not responsible for the majority of new infections that lead to viral explosion, may contribute significantly to the transition amongst the three stages of infection. Moreover, we explore the implications of the model for the administration of antiretroviral therapy (ART) and provide quantitative estimates that emphasize the time sensitive nature of treatment initiation and the level of drug efficacy. Finally, we study the effects of treatment interruption on the disease dynamics predicted by the model and elucidate the influence of both interruption time and duration.
我们考虑了一个涉及巨噬细胞作为长期活跃储库的 HIV 感染确定性模型，以描述疾病过程的所有三个阶段：急性阶段、慢性感染和向艾滋病的转变。所提出的模型被证明保留了关键性质，例如解决方案的正定性，而不管模型参数的变化。进行了动力学分析以确定病毒清除稳定状态的局部稳定性性质。该分析说明了慢性感染的巨噬细胞如何能够解释艾滋病的进展并引发病毒爆发，而以前的模型则不能。我们进一步证明，受感染的 T 细胞群体即使不是导致病毒爆发的大多数新感染的原因，也可能对感染的三个阶段之间的转变产生重大影响。此外，我们探讨了该模型对抗逆转录病毒疗法 (ART) 管理的意义，并提供了定量估计，强调了治疗开始的时间敏感性和药物疗效的水平。最后，我们研究了治疗中断对模型预测的疾病动力学的影响，并阐明了中断时间和持续时间的影响。
