A HIV/AIDS model in a homogeneous population with time lags in the transmission

Abstract

We investigate a simple HIV/AIDS epidemic model in a heterosexual population by by modifying a Susceptible-Infective-Removed (SIR) model. The model considers sexual transmission of HIV where individuals are being recruited into sexually matured age group at a constant rate and incorporates time lags for one to become infective and the other to become fully blown. A complete qualitative analysis of the model, including the boundedness and positivity of the solutions, local stability of the equilibrium points is done. We applly the next generation matrix to determine the disease reproduction number R0. The Model is shown to be completely determined by the reproduction number. The model is numerically analysed to asses the effects of the delay on the dynamics of HIV/AIDS and the demographic impact of the epidemic using the demographic and epidemiological parameters for Kenya.