Die impak van MIV op die Suid-Afrikaanse bevolking : 'n wiskundige model

Abstract

The first case of HIV-infection in South Africa was reported in 1985. Since then the rapid increase in the number of HIV+ individuals has led to an international pandemic affecting people of all races, nationalities and ethnic backgrounds. In attempts to make people more aware of the destructive impact of HIV, a great number of resources have been allocated in efforts to control the spread of the pandemic. Focused research can play a very important role in this regard. In this study we use mathematical tecniques to try and ascertain and predict the prevalence of HIV-infection. Mathematical models are developed that describe the changes in given subsets of the South African population. The incorporation of social factors into the modelling process contributes to the accuracy and applicability of the models. Throughout the process of developing models, the results are tested and verified by applying the models to relevant statistics with regards to HIV-related deaths. For each model the error between the model and the data is minimised by using a numerical optimisation technique. The process by which reliable data was obtained, is discussed and in this regard reference is made to numerous obstacles that were encountered. Realistic assumptions are made to ensure that the data used during the fitting of the models is accurate.