Modeling, Estimation and Control in HIV Dynamics

描述(申请人提供)：艾滋病毒相关疾病现在和将来仍在继续 是一个重要的临床和公共卫生问题，也是一个国际问题 安全、稳定、发展问题。尽管高度全球化的到来 主动抗逆转录病毒疗法(HAART)显著减少了与艾滋病毒相关的 发病率和死亡率，艾滋病毒感染治疗的进一步进展 个人需要更深入地理解 以及这些强大的治疗方法是如何影响他们的。例如, 个人是否可以通过控制中断或停止治疗 感染是一个重要的临床问题，我们可以对其进行深入的了解。 通过改进对疾病机制的理解。事实上，并不是所有的人 体验同等水平的治疗效果，当务之急是 这些机制在不同个体之间的差异是可以阐明的。数学 常微分方程组和时滞微分方程组的模型， 都被用来描述相互作用的动力学 艾滋病毒和人类免疫系统的不同部分，从而使 理论化的机制，并导致了相当多的最近的洞察力。然而， 只有简化的这种模型已经用临床数据进行了测试；因此， 仍然是数学建模的重要机会 增强了对艾滋病毒感染和相关免疫反应的了解。 调查人员将使用先进的数学模型和相关 开发艾滋病毒、ITS之间相互作用的新模型的统计方法 靶资源(T细胞、巨噬细胞和/或树突状细胞)，以及人类 免疫系统，特别强调在以下基础上建立模型 尽可能提供临床数据。他们将测试和分析非线性 HIV感染动力学和相关免疫的数学机制 使用常微分方程式和偏微分方程式的反应。在某些情况下 其中数据分析表明，模型中的非线性描述 生物学是相关的，它们将执行数值和/或定性 对系统进行分析以识别系统的稳定行为和分叉 数学系统，这反过来又可以提供对 生物系统。 此外，他们将制定和实施正式的统计和 模型中参数估计的计算方法，重点是 解释和探索不同类型的变异性潜在机制 个人。终于来了。他们将使用模型和方法来解决特定的问题 科学问题，包括动态参数的差异分析 基于多种寄主基因型和发展的最优控制 旨在指导艾滋病毒结构化治疗中断的方法学 心理治疗。

DESCRIPTION (provided by applicant): HIV-related illness is and will continue to be an important clinical and public health issue as well an international security, stability, and development issue. Although the advent of Highly Active Anti-Retroviral Therapy (HAART) has significantly reduced HIV-related morbidity and mortality, further advances in the treatment of HIV-infected individuals require a deeper understanding of the underlying mechanisms of the disease and how they are affected by these powerful treatments. For example, whether individuals may interrupt or discontinue treatment with control of infection is an important clinical question, insight into which may be gained by improved understanding of disease mechanisms. Indeed, as not all individuals experience the same level of treatment efficacy, it is imperative that variation in these mechanisms across individuals be elucidated. Mathematical models, in the form of systems of ordinary and delay differential equations, have been used to provide descriptions of the dynamics of the interactions of HIV and various compartments of the human immune system and thus formalize theorized mechanisms and have led to considerable recent insights. However, only simplified such models have been tested with clinical data; thus, there remain significant opportunities for mathematical modeling to contribute to enhanced understanding of HIV infection and associated immune response. The investigators will use advanced mathematical modeling and relevant statistical methods to develop new models for interactions among HIV, its target resources (T-cells, macrophages and/or dendritic cells), and the human immune system, with a particular emphasis on building models on the basis of clinical data wherever possible. They will test for and analyze nonlinear mathematical mechanisms in HIV infection dynamics and associated immune response using both ordinary and partial differential equations. In situations where data analysis suggests that nonlinearities in the models that describe the biology are relevant, they will perform numerical and/or qualitative analysis of the systems to identify stable behavior and bifurcations in the mathematical system, which in turn could provide insight into control of the biological system. Furthermore, they will develop and implement formal statistical and computational methods to estimate parameters in the models with emphasis on accounting for and exploring variability underlying mechanisms across different individuals. Finally. they will use the models and methods to address specific scientific questions, including analysis of differences in dynamic parameters based on a variety of host genotypes and development of optimal control methodologies designed to guide for structured treatment interruptions of HIV therapy.