Model fitting and projection of the AIDS epidemic

Previously it was possible to fit detailed models to incidence data (for example, of AIDS) only by trial and error and good judgment; the large number of parameters obstructed optimization of, for example, the (approximate) likelihood. Here, we analyze a model for the spread of AIDS in a homosexual population and identify a minimal set of primary components that dictate the dynamics of the Model: the initial growth rate theta, the basic reproductive ratio R0, and the heterogeneity coefficient S. It is then shown that it is sufficient to maximize the likelihood over these three primary components; further maximization over the remaining secondary parameters does not produce a significant improvement in the fit or affect the projection of the epidemic. This method also allows construction of confidence limits for the projected incidence curve, allowing us to quantify the uncertainties associated with such model fitting procedures. The method is tested on simulation data to analyze how the accuracy of estimates and projections changes as we gain more data.