ABSTRACT

This study focuses on investigating the role of stability in the spread and control of HIV within a homosexual population. Although a lot of studies has been reported on the spread and control of HIV, for instance, J.D.MurraYC199O) studied the impact of doubling time for the epidemic on the basic reproductive rate Ro. He reported that the larger the basic reproductive rate Ro, the shorter the doubling time. But much work has not been done to examine the existence of epidemic and its stability on the transmission dynamic of HIV infection. Consequently, we thought of investigating the role of stability in the spread of HIV in a given population. Qualitative analysis of deterministic models for HIV epidemiology was used to achieve this objective. The other feature of this study is the numerical simulation of the basin of attraction of the associated stable equilibrium of the model. Such numerical simulation enables us to predict, (for the stability case) the persistence or eradication of HIV based on the initial sizes of the subpopulations of the model. Our result shows that, controlling the initial sizes of the subpopulation can lead to the elimination of HIV infection in place of persistence.