Banks H T, Bortz D M, Holte S E
Center for Research in Scientific Computation, Box 8205, North Carolina State University, Raleigh, NC 27695-8205, USA.
Math Biosci. 2003 May;183(1):63-91. doi: 10.1016/s0025-5564(02)00218-3.
We consider classes of functional differential equation models which arise in attempts to describe temporal delays in HIV pathogenesis. In particular, we develop methods for incorporating arbitrary variability (i.e., general probability distributions) for these delays into systems that cannot readily be reduced to a finite number of coupled ordinary differential equations (as is done in the method of stages). We discuss modeling from first principles, introduce several classes of non-linear models (including discrete and distributed delays) and present a discussion of theoretical and computational approaches. We then use the resulting methodology to carry out simulations and perform parameter estimation calculations, fitting the models to a set of experimental data. Results obtained confirm the statistical significance of the presence of delays and the importance of including delays in validating mathematical models with experimental data. We also show that the models are quite sensitive to the mean of the distribution which describes the delay in viral production, whereas the variance of this distribution has relatively little impact.
我们考虑在试图描述HIV发病机制中的时间延迟时出现的泛函微分方程模型类别。特别地，我们开发了一些方法，用于将这些延迟的任意变异性（即一般概率分布）纳入那些不易简化为有限个耦合常微分方程的系统中（如同在阶段法中那样）。我们从第一原理讨论建模，引入几类非线性模型（包括离散延迟和分布延迟），并对理论和计算方法进行讨论。然后，我们使用所得方法进行模拟并执行参数估计计算，将模型拟合到一组实验数据。获得的结果证实了延迟存在的统计显著性以及在使用实验数据验证数学模型时纳入延迟的重要性。我们还表明，模型对描述病毒产生延迟的分布均值相当敏感，而该分布的方差影响相对较小。
