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.
