Introduction

The natural history of HIV infection has been viewed as a staged process since the early years of the epidemic. The Walter Reed staging system was devised in 1986 (Redfield et al. 1986), and a number of other staging systems have been used since then. A staged Markov model is a natural mathematical device for modeling such a process. The Markov model has been used in five basic areas of HIV/AIDS research:

1. To describe the natural history of HIV infection (Longini et al. 1989a,b, Longini 1990, Longini et al 1991);

2. to evaluate the effect of covariates on stage-specific progression rates, such as therapy (Longini et al. 1993);

3. to predict the stage-specific course of the HIV epidemic in selected populations (Longini et al. 1992) and in the USA as a whole (CDC 1992, Brookmeyer 1991);

4. to estimate HIV incidence from infection surveys (Satten and Longini 1994);

5. to provide estimates for HIV transmission models used to estimate transmission probabilities (Longini et al. 1989b) and to investigate the dynamics of the HIV epidemic (Hethcote et al.1991a,b, Jacquez et ah 1988, Koopman et al 1991).

The purpose of this paper is to review the progress that has been made in areas 1-3, and to describe further refinements of the Markov modeling approach.