Department of Mathematics and Institute of Applied Mathematics, University of British Columbia, Vancouver, British Columbia, Canada.
PLoS Comput Biol. 2011 Apr;7(4):e1002033. doi: 10.1371/journal.pcbi.1002033. Epub 2011 Apr 28.
Motivated by viral persistence in HIV+ patients on long-term anti-retroviral treatment (ART), we present a stochastic model of HIV viral dynamics in the blood stream. We consider the hypothesis that the residual viremia in patients on ART can be explained principally by the activation of cells latently infected by HIV before the initiation of ART and that viral blips (clinically-observed short periods of detectable viral load) represent large deviations from the mean. We model the system as a continuous-time, multi-type branching process. Deriving equations for the probability generating function we use a novel numerical approach to extract the probability distributions for latent reservoir sizes and viral loads. We find that latent reservoir extinction-time distributions underscore the importance of considering reservoir dynamics beyond simply the half-life. We calculate blip amplitudes and frequencies by computing complete viral load probability distributions, and study the duration of viral blips via direct numerical simulation. We find that our model qualitatively reproduces short small-amplitude blips detected in clinical studies of treated HIV infection. Stochastic models of this type provide insight into treatment-outcome variability that cannot be found from deterministic models.
受长期抗逆转录病毒治疗 (ART) 患者中 HIV 持续存在的启发，我们提出了血液中 HIV 病毒动力学的随机模型。我们考虑了这样一种假设，即在开始接受 ART 之前，HIV 潜伏感染的细胞的激活可以解释接受 ART 的患者中残留的病毒血症，并且病毒爆发（临床上观察到的可检测病毒载量的短暂时期）代表了均值的大偏差。我们将系统建模为连续时间、多类型分支过程。为了推导出概率生成函数的方程，我们使用了一种新的数值方法来提取潜伏储库大小和病毒载量的概率分布。我们发现潜伏储库灭绝时间分布强调了考虑储库动力学不仅仅是半衰期的重要性。我们通过计算完整的病毒载量概率分布来计算爆发幅度和频率，并通过直接数值模拟研究病毒爆发的持续时间。我们发现我们的模型定性地再现了在治疗后 HIV 感染的临床研究中检测到的短期小幅度爆发。这种类型的随机模型提供了从确定性模型中无法找到的治疗结果可变性的见解。
