Ciupe M S, Bivort B L, Bortz D M, Nelson P W
Los Alamos National Lab, MS K710, Los Alamos, NM 87545, United States.
Department of Molecular and Cellular Biology, Harvard University, 7 Divinity Avenue, Cambridge, MA 02138, United States.
Math Biosci. 2006 Mar;200(1):1-27. doi: 10.1016/j.mbs.2005.12.006. Epub 2006 Feb 9.
The dynamics of HIV-1 infection consist of three distinct phases starting with primary infection, then latency and finally AIDS or drug therapy. In this paper we model the dynamics of primary infection and the beginning of latency. We show that allowing for time delays in the model better predicts viral load data when compared to models with no time delays. We also find that our model of primary infection predicts the turnover rates for productively infected T cells and viral totals to be much longer than compared to data from patients receiving anti-viral drug therapy. Hence the dynamics of the infection can change dramatically from one stage to the next. However, we also show that with the data available the results are highly sensitive to the chosen model. We compare the results using analysis and Monte Carlo techniques for three different models and show how each predicts rather dramatic differences between the fitted parameters. We show, using a chi(2) test, that these differences between models are statistically significant and using a jackknifing method, we find the confidence intervals for the parameters. These differences in parameter estimations lead to widely varying conclusions about HIV pathogenesis. For instance, we find in our model with time delays the existence of a Hopf bifurcation that leads to sustained oscillations and that these oscillations could simulate the rapid turnover between viral strains and the appropriate CTL response necessary to control the virus, similar to that of a predator-prey type system.
HIV-1感染的动态过程包括三个不同阶段，始于初次感染，接着是潜伏期，最后是艾滋病期或药物治疗期。在本文中，我们对初次感染的动态过程以及潜伏期的开始进行建模。我们表明，与无时滞模型相比，模型中考虑时滞能更好地预测病毒载量数据。我们还发现，我们的初次感染模型预测，与接受抗病毒药物治疗的患者数据相比，高效感染T细胞和病毒总量的周转率要长得多。因此，感染的动态过程在从一个阶段到下一个阶段时会发生显著变化。然而，我们也表明，根据现有数据，结果对所选模型高度敏感。我们使用分析和蒙特卡罗技术对三种不同模型的结果进行比较，并展示每种模型如何预测拟合参数之间相当显著的差异。我们使用卡方检验表明，模型之间的这些差异具有统计学意义，并且使用刀切法，我们找到了参数的置信区间。参数估计的这些差异导致关于HIV发病机制的结论差异很大。例如，我们发现在我们具有时滞的模型中存在霍普夫分岔，这会导致持续振荡，并且这些振荡可以模拟病毒株之间的快速周转以及控制病毒所需的适当CTL反应，类似于捕食者 - 猎物类型系统。
