Basic properties of models for the spread of HIV/AIDS

[摘要] ENGLISH ABSTRACT: While research and population surveys in HIV/AIDS are well established indeveloped countries, Sub-Saharan Africa is still experiencing scarce HIV/AIDSinformation. Hence it depends on results obtained from models. Due to thisdependence, it is important to understand the strengths and limitations ofthese models very well.In this study, a simple mathematical model is formulated and then extendedto incorporate various features such as stages of HIV development, time delayin AIDS death occurrence, and risk groups. The analysis is neither purelymathematical nor does it concentrate on data but it is rather an exploratoryapproach, in which both mathematical methods and numerical simulationsare used.It was found that the presence of stages leads to higher prevalence levels ina short term with an implication that the primary stage is the driver of thedisease. Furthermore, it was found that time delay changed the mortalitycurves considerably, but it had less effect on the proportion of infectives. Itwas also shown that the characteristic behaviour of curves valid for mostepidemics, namely that there is an initial increase, then a peak, and then a decrease occurs as a function of time, is possible in HIV only if low riskgroups are present.It is concluded that reasonable or quality predictions from mathematicalmodels are expected to require the inclusion of stages, risk groups, timedelay, and other related properties with reasonable parameter values.

[发布机构] Stellenbosch University