Using sigmoid functions for modelling South African gold production

Abstract

Sigmoid functions were used to approximate the cumulative gold production curve of Southern Africa and to extrapolate them into the future. Southern Africa was chosen because one third of the historic global world gold production comes from the Witwatersrand basin area, and also because the peak gold point was already reached in 1970. All models give a good agreement with reality, when the negative effects of World War II and the positive effects of the apartheid boom 1950 - 1970 are compensated for. From today's viewpoint the Gompertz function was found to give the best model, although this model implies the peak occurred 10 years earlier and due to the apartheid boom was about 300 tons higher. It also shows that the production could possibly rise again in the future to a level of 400 or even 500 metric tons a year. Hence, a biomodal production curve with at least two peak points could be observed in the future. Mathematical results are discussed in respect to the political and economic history of this country.