The role of mathematical models in the study of HIV transmission and the epidemiology of AIDS.

The role of mathematical models in the study of human immunodeficiency virus (HIV) transmission, the epidemiology and demographic impact of acquired immune deficiency syndrome (AIDS), and the course of infection within an individual is reviewed. Attention is focused on the part models can play in short-term prediction, parameter estimation, the interpretation of observed patterns, and the identification of areas in which knowledge is inadequate. Methods for short-term predictions, over 1-3 years, have proved reliable and can take account of distributed delays in the interval between reporting and diagnosis. Parametric and nonparametric methods have been developed for estimating summary statistics (e.g., means) for the distributed incubation period of AIDS. Current estimates, based on cohort or transfusion-associated AIDS cases, lie in the range of 7-10 years. Transmission models for longer-term prediction are less reliable at present given the many uncertainties concerning key epidemiological parameters. Theoretical studies highlight the need for quantitative data on temporal changes in the distribution of rates of sexual partner change and fluctuations in viral abundance in serum, secretions, and excretions (i.e., infectiousness) throughout the long and variable incubation period of the disease.