The dynamic nature of interactions between the Human Immunodeficiency Virus (HIV) and the human immune system is complex and remains poorly understood in spite of recent important findings about the kinetic of viral and T-cell replication and clearance and the identification of cell- surface co-receptors for HIV entry. Developing accurate descriptions and a deeper understanding of the interactions between HIV and the immune system during the acute and early stages of Hiv infection is critical to the evaluation of new, promising therapeutic regimens. Mathematical models, in the form of systems of deterministic or stochastic rate equations, provide the most natural and convenient framework for formal descriptions of interactions between HIV and various compartments of the human immune system. Various simplified biological models for these interactions have been translated into such mathematical models and published by numerous research groups. Most of these models have focused on descriptions of the long-term course rather than the acute/early stage of HIV infection. There has been no serious and systematic study of the mathematical and probabilistic properties of these models. These models have typically been fit to data from few, select patients using statistical models and methods that give virtually no serious attention to assessing sources of variability across patients. Finally, there has been no careful and comprehensive comparative study of these models with respect ot their ability to accurately describe systematic patterns in longitudinally collected virological and immunological data and to predict subsequent clinical outcomes. We propose to perform a systematic assessment of mathematical models for interactions between HIV and the human immune system with a particular emphasis on the utility of these models for describing acute and early stages of HIV infection. We will refine the formulation of these mathematical models and derive from them statistical models that acknowledge important sources of variation in observable analogs of model variables. We will develop and implement formal statistical methods to fit these models to data from clinical studies of acute/early HIV infection and perform a data-based comparative study of the models. Through existing and ongoing collaborations with clinical researchers, er will use the models and methods to address specific scientific questions that are posed in the context of clinical studies.
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