Improvement of Short Term AIDS Incidence Predictions by Relating the LogisticFunctions Used for Curve Fitting Actual Data with a Deterministic Model Describing the AIDS Epidemic

摘要

Extrapolation of logistic functions fitting current AIDS incidence data has beenused as a prediction tool. The authors investigate the mathematical characteristics of these functions and show an application on the AIDS incidence data of the Amsterdam region. Furthermore, they 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 the 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 parameter sets that vary in time. The possible application of the presented method as an improved tool for short term AIDS incidence predictions is discussed.