On the complexities of modeling HIV/AIDS in Southern Africa

Abstract

In this paper problems associated with the modeling of HIV/AIDS in Southern Africa are presented. A mathematical model is presented to highlight the three major challenges of modeling HIV/AIDS, i.e condom use, vertical transmission and treatment. The model analysis for the case, where the treatment parameter ñ = 0, is presented in terms of the model reproduction number R and threshold parameters R_T and R_A that show the contribution of vertical transmission. It is shown that if R, R_T, R_A < 1, then the disease free equilibrium point is both locally asymptotically and globally stable. Numerical simulations for the model are presented to determine the role of some key epidemiological parameters of the model.

First Published Online: 14 Oct 2010