An age-structured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells
An age-structured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells
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DOI：
10.3934/mbe.2004.1.267
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发表时间：
2004-09-01
影响因子：
2.6
通讯作者：
Perelson, AS
中科院分区：
文献类型：
--
作者：
Nelson, PW;Gilchrist, MA;Perelson, AS
HIV-1感染的数学模型可以帮助解释药物治疗实验，并提高我们对HIV-1和免疫系统之间相互作用的理解。我们开发并分析了一个年龄结构的HIV-1感染模型，该模型允许生产性感染的T细胞的死亡率和病毒颗粒的产生率随T细胞被感染的时间长短而变化。我们表明，这个模型是一个推广的标准微分方程和延迟模型以前用于描述HIV-1感染，并提供了一种手段，探索病毒的生产和死亡的基本问题。我们表明，该模型有未感染和感染的稳定状态，跨临界分岔连接。我们进行了局部稳定性分析的非平凡平衡解，并提供了一个一般的稳定性条件，模型的年龄结构。然后，我们使用数值方法来研究我们的模型的解决方案，侧重于分析原发性HIV感染。我们表明，血液中达到峰值病毒水平的时间不仅取决于初始条件，而且还取决于病毒产生的方式。如果病毒产量缓慢上升，我们发现与使用标准（恒定病毒产量）HIV感染模型获得的结果相比，达到病毒载量峰值的时间延迟。我们发现，病毒载量随时间变化的数据是不够的，以确定功能指定的病毒生产率或受感染的细胞死亡率受感染的细胞年龄的依赖性。这些功能必须通过新的定量实验来确定。
Mathematical models of HIV-1 infection can help interpret drug treatment experiments and improve our understanding of the interplay between HIV-1 and the immune system. We develop and analyze an age-structured model of HIV-1 infection that allows for variations in the death rate of productively infected T cells and the production rate of viral particles as a function of the length of time a T cell has been infected. We show that this model is a generalization of the standard differential equation and of delay models previously used to describe HIV-1 infection, and provides a means for exploring fundamental issues of viral production and death. We show that the model has uninfected and infected steady states, linked by a transcritical bifurcation. We perform a local stability analysis of the nontrivial equilibrium solution and provide a general stability condition for models with age structure. We then use numerical methods to study solutions of our model focusing on the analysis of primary HIV infection. We show that the time to reach peak viral levels in the blood depends not only on initial conditions but also on the way in which viral production ramps up. If viral production ramps up slowly, we find that the time to peak viral load is delayed compared to results obtained using the standard (constant viral production) model of HIV infection. We find that data on viral load changing over time is insufficient to identify the functions specifying the dependence of the viral production rate or infected cell death rate on infected cell age. These functions must be determined through new quantitative experiments.