Perelson A S, Kirschner D E, De Boer R
Theoretical Division, Los Alamos National Laboratory, New Mexico.
Math Biosci. 1993 Mar;114(1):81-125. doi: 10.1016/0025-5564(93)90043-a.
We examine a model for the interaction of HIV with CD4+ T cells that considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. Using this model we show that many of the puzzling quantitative features of HIV infection can be explained simply. We also consider effects of AZT on viral growth and T-cell population dynamics. The model exhibits two steady states, an uninfected state in which no virus is present and an endemically infected state, in which virus and infected T cells are present. We show that if N, the number of infectious virions produced per actively infected T cell, is less a critical value, Ncrit, then the uninfected state is the only steady state in the nonnegative orthant, and this state is stable. For N > Ncrit, the uninfected state is unstable, and the endemically infected state can be either stable, or unstable and surrounded by a stable limit cycle. Using numerical bifurcation techniques we map out the parameter regimes of these various behaviors. oscillatory behavior seems to lie outside the region of biologically realistic parameter values. When the endemically infected state is stable, it is characterized by a reduced number of T cells compared with the uninfected state. Thus T-cell depletion occurs through the establishment of a new steady state. The dynamics of the establishment of this new steady state are examined both numerically and via the quasi-steady-state approximation. We develop approximations for the dynamics at early times in which the free virus rapidly binds to T cells, during an intermediate time scale in which the virus grows exponentially, and a third time scale on which viral growth slows and the endemically infected steady state is approached. Using the quasi-steady-state approximation the model can be simplified to two ordinary differential equations the summarize much of the dynamical behavior. We compute the level of T cells in the endemically infected state and show how that level varies with the parameters in the model. The model predicts that different viral strains, characterized by generating differing numbers of infective virions within infected T cells, can cause different amounts of T-cell depletion and generate depletion at different rates. Two versions of the model are studied. In one the source of T cells from precursors is constant, whereas in the other the source of T cells decreases with viral load, mimicking the infection and killing of T-cell precursors.(ABSTRACT TRUNCATED AT 400 WORDS)
我们研究了一个HIV与CD4+ T细胞相互作用的模型，该模型考虑了四个群体：未感染的T细胞、潜伏感染的T细胞、活跃感染的T细胞和游离病毒。利用这个模型，我们表明HIV感染中许多令人困惑的定量特征都可以得到简单的解释。我们还考虑了齐多夫定（AZT）对病毒生长和T细胞群体动态的影响。该模型呈现出两种稳定状态，一种是不存在病毒的未感染状态，另一种是存在病毒和感染T细胞的地方性感染状态。我们表明，如果每个活跃感染的T细胞产生的感染性病毒粒子数量N小于一个临界值Ncrit，那么未感染状态是在非负象限中唯一的稳定状态，并且这个状态是稳定的。对于N > Ncrit，未感染状态是不稳定的，而地方性感染状态可能是稳定的，也可能是不稳定的且被一个稳定的极限环所包围。使用数值分岔技术，我们描绘出了这些不同行为的参数区域。振荡行为似乎位于生物学上现实的参数值区域之外。当地方性感染状态稳定时，与未感染状态相比，其特征是T细胞数量减少。因此，T细胞耗竭是通过建立一个新的稳定状态而发生的。通过数值方法以及准稳态近似法研究了这个新稳定状态建立的动态过程。我们推导了早期动态过程的近似值，在早期自由病毒迅速与T细胞结合，在中间时间尺度上病毒呈指数增长，在第三个时间尺度上病毒生长减缓并接近地方性感染稳定状态。使用准稳态近似法，该模型可以简化为两个常微分方程，它们概括了大部分动态行为。我们计算了地方性感染状态下的T细胞水平，并展示了该水平如何随模型中的参数变化。该模型预测，不同的病毒株，其特征是在感染的T细胞内产生不同数量的感染性病毒粒子，会导致不同程度的T细胞耗竭，并以不同的速率产生耗竭。研究了该模型的两个版本。在一个版本中，来自前体的T细胞来源是恒定的，而在另一个版本中，T细胞来源随着病毒载量的增加而减少，模拟了T细胞前体的感染和杀伤情况。（摘要截选至400字）
