English Abstract Extrapolation of logistic functions fitting current
AIDS incidence data has been used as a prediction tool. We investigate the
mathematical characteristics of these functions and show an application on
the AIDS incidence data of the Amsterdam region. Furthermore, we develop a
deterministic model, explicitly taking into account some main processes
which affect the development and spreading of AIDS. It is assumed that the
processes of incubation and immigration into c.q. withdrawal from the
at-risk population can be modelled in a distributed way. Under various
severe restrictions this model has the logistic function as a solution. The
analytical solution to the model proposed by Birkhead is shown to give
irrealistic results for long term predictions. The linear logistic function
is found to be perfectly suited for calibration of the parameters of the
deterministic model. The advantage of the use of the deterministic model
over the extrapolation of a curve fitting function lies in the possibility
of using parameters sets that vary in time. The possible applicaton of the
presented method as an improved tool for short term AIDS incidence
prediction is discussed.
