Fitting and projecting HIV epidemics: Data, structure and parsimony
  Understanding historical trends in the epidemic of HIV is important for assessing current and projecting future trends in prevalence, incidence and mortality and for evaluating the impact and cost-effectiveness of control measures. In generalized epidemics the available data are of variable quality among countries and limited mainly to trends in the prevalence of HIV among women attending ante-natal clinics. In concentrated epidemics one needs, at the very least, time trends in the prevalence of HIV among different risk groups, including intravenous drug users, men-who-have-sex-with-men, and commercial sex workers as well as the size of each group and the degree of overlap between them. Here we focus on the comparatively straight forward problems presented by generalized epidemics. We fit data from Kenya to a susceptible-infected model and then successively add structure to the model, drawing on our knowledge of the natural history of HIV, to explore the effect that different structural aspects of the model have on the fits and the projections.   Both heterogeneity in risk and changes in behaviour over time are important but easily confounded. Using a Weibull rather than exponential survival function for people infected with HIV, in the absence of treatment, makes a significant difference to the estimated trends in incidence and mortality and to the projected trends. Allowing for population growth has a small effect on the fits and the projections but is easy to include. Including details of the demography adds substantially to the complexity of the model, increases the run time by several orders of magnitude, but changes the fits and projections only slightly and to an extent that is less than the uncertainty inherent in the data. We make specific recommendations for the kind of model that would be suitable for understanding and managing HIV epidemics in east and southern Africa. 
Brian G. Williams
q-bio.QM