A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data.
A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data.
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DOI：
10.1016/j.mbs.2011.11.002
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发表时间：
2012-01
影响因子：
4.3
通讯作者：
Rong L
中科院分区：
文献类型：
--
作者：
Pawelek KA;Liu S;Pahlevani F;Rong L
数学模型为我们理解艾滋病毒的动力学做出了巨大贡献。在HIV模型中引入时间延迟通常会给模型的数学分析以及模型预测与患者数据的比较带来挑战。在本文中，我们将两个延迟，一个是感染细胞在病毒进入后产生病毒体所需的时间，另一个是适应性免疫反应出现以控制病毒复制所需的时间，纳入HIV-1模型。我们开始模型分析证明的正性和有界的解决方案，局部稳定的无感染和感染的稳定状态，和一致持久的系统。通过发展几个李雅普诺夫泛函，我们得到的条件，确保全局稳定的平衡态。我们还拟合模型，包括两个延迟的病毒载量数据从10例患者在原发性HIV-1感染和估计参数值。虽然延迟模型比没有延迟的模型更适合患者数据（实现数据和建模预测之间的更小误差），但我们无法从统计学角度确定哪一个更好。这突出表明，当我们将时间延迟纳入数学模型来研究病毒动力学时，需要更多的数据集进行模型验证和选择。
Mathematical models have made considerable contributions to our understanding of HIV dynamics. Introducing time delays to HIV models usually brings challenges to both mathematical analysis of the models and comparison of model predictions with patient data. In this paper, we incorporate two delays, one the time needed for infected cells to produce virions after viral entry and the other the time needed for the adaptive immune response to emerge to control viral replication, into an HIV-1 model. We begin model analysis with proving the positivity and boundedness of the solutions, local stability of the infection-free and infected steady states, and uniform persistence of the system. By developing a few Lyapunov functionals, we obtain conditions ensuring global stability of the steady states. We also fit the model including two delays to viral load data from 10 patients during primary HIV-1 infection and estimate parameter values. Although the delay model provides better fits to patient data (achieving a smaller error between data and modeling prediction) than the one without delays, we could not determine which one is better from the statistical standpoint. This highlights the need of more data sets for model verification and selection when we incorporate time delays into mathematical models to study virus dynamics.
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DOI：
10.1084/jem.190.6.841
发表时间：
1999-09-20
期刊：
The Journal of experimental medicine
影响因子：
--
作者：
Little SJ;McLean AR;Spina CA;Richman DD;Havlir DV
通讯作者：
Havlir DV
DOI：
10.1073/pnas.94.24.13193
发表时间：
1997-11-25
影响因子：
11.1
作者：
Chun, TW;Stuyver, L;Fauci, AS
通讯作者：
Fauci, AS
影响因子：
3.5
作者：
Li, Michael Y.;Shu, Hongying
通讯作者：
Shu, Hongying
影响因子：
1.9
作者：
Liu, Shengqiang;Beretta, Edoardo
通讯作者：
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影响因子：
82.9
作者：
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