A dynamical model for stage-specific HIV incidences with application to sub-Saharan Africa

In this paper a deterministic model for HIV epidemic with three stages of disease progression among infected patients is discussed. It is assumed that the patient once infected experiences disease progression up to full-blown AIDS. Using two systems of ordinary differential equations that are coupled through a delay in one of the systems, a compartmental model for the dynamics of the HIV/AIDS epidemic is constructed. The transmission of the disease is considered to be only through heterosexual contact and vertically from an infected mother to her unborn child. Numerical integration of the equations is used for simulating the stage-specific epidemic curves, given the demographic and epidemiological parameters of the model. The simulation results with respect to Uganda's HIV/AIDS epidemic scenario obtained are found to be consistent with the published findings namely that the corresponding prevalence is a non-decreasing function of time for at least 30 years of the epidemic. Furthermore, through simulation it is noted that all the three stage-specific prevalence rate curves also satisfy this condition.