  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.
