Stability Analysis of the Mathematical Model on the Control of HIV/AIDS Pandemic in a Heterogeneous Population

Abstract

HIV/AIDS is a dreaded disease which has over the years claimed the life of so many people both female and male, adult and children in the whole continents or the globe. In this paper, a mathematical model on the control of HIV/AIDS was formulated using; vaccine, condom, therapeutic dose and public health campaign as control measures. The dynamic analysis of the model was carried out and the effective reproduction number R0 obtained. The local and global stability analyses were conducted. From the analysis carried out, we got that R0>1, which shows that HIV/AIDS is endemic. Furthermore, the Maple software was applied to obtain the eigenvalues which validate the asymptotically stable nature of the disease equilibrium position. Matlab was used to simulate various submodels from the main model using numerical values of the parameters. Results obtained were discussed which extends some results in literature.