Mathematical and Experimental Models for HIV Dynamics

描述（由申请人提供）：本提案中的研究重点是使用数学和统计模型来回答有关使用实验和临床数据影响HIV感染动态的因素的问题。拟议的研究包括定量和生物科学家之间的跨学科互动，并将指导数学模型的开发和分析。 相反，模型结果将指导进一步的实验和数据收集。 我们的调查是基于系统的常微分方程和偏微分方程，将需要复杂的数学和统计分析。在实验室和临床数据模型的开发过程中，对合理统计方法的需求是固有的。 非线性随机效应统计模型的严格计算和随机方法将应用于来自个体聚集群体的各种数据。 目前，由于现有方法的极端计算成本，标准技术仅部分足够。为了克服这个困难，一个新的“整合数据”的方法，用于非线性随机效应模型的参数估计和推断。 具体的实验和临床研究将包括在实验室实验中调查各种艾滋病毒株之间竞争的影响，并分析临床数据，以揭示艾滋病毒感染细胞群体的非线性衰减特性的性质。将根据数学模型设计体外研究，以评估靶细胞群体大小对两种艾滋病毒株动力学的影响。实验室实验将以数学模型为指导，并根据最近开发的培养系统进行，该系统可以控制感染细胞的死亡率，从而可以在更类似于体内条件的环境中进行实验。体内临床分析将表征HAART后HIV-1感染细胞群体的衰变行为。以前的预测-基于线性模型-从感染个体中根除病毒所需的时间在临床观察中尚未实现。 此外，未来对HIV感染者的治疗和管理在很大程度上依赖于对感染细胞群衰变特征的准确理解。 因此，迫切需要更准确地描述受感染细胞群的衰变谱。

DESCRIPTION (provided by applicant): The research in this proposal focuses on using mathematical and statistical models to answer questions about factors that affect the dynamics of HIV infection using both experimental and clinical data. The proposed research consists of interdisciplinary interactions between quantitative and biological scientists and will guide the development and analysis of the mathematical models. Conversely, model outcomes will direct further experiments and data collection. Our investigations are based on systems of ordinary and partial differential equations and will require sophisticated mathematical and statistical analysis. The need for sound statistical methods is inherent in the development of models for laboratory and clinical data. Rigorous computational and stochastic methods for nonlinear random effects statistical models will be applied to a variety of data from aggregate populations of individuals. At present, standard techniques are only partially adequate due to the extreme computational costs of existing methods. To overcome this difficulty, a new "integrated data" method for parameter estimation and inference in nonlinear random effects models will be developed. Specific experimental and clinical research will include investigating the effects of competition between various strains of HIV in laboratory experiments and analysis of clinical data that will reveal the nature of nonlinear decay characteristics of populations of HIV-infected cells. The in vitro study will be designed based on mathematical models to assess the effects of the target-cell population size on the dynamics of two strains of HIV Laboratory experiments will guide and be guided by mathematical models and be conducted based on a recently developed culture system that allows control over the infected cell death rate so that the experiments can be conducted in a setting more similar to the in vivo condition. The in vivo clinical analysis will characterize the decay behavior for populations of HIV-1 infected cells following HAART. Previous predictions---based on linear models---of the time needed for viral eradication from an infected individual have not been realized in clinical observations. Furthermore, future treatment and management of HIV infected individuals relies heavily on an accurate understanding of the decay characteristics of infected cell populations. Thus there is an urgent need to more accurately describe the decay profile of infected cell populations.