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 constantrate and incorporates time lags for one to become infective and the otherto become fully blown. A complete qualitative analysis of the model,including the boundedness and positivity of the solutions, local stabilityof the equilibrium points is done. We applly the next generation matrixto determine the disease reproduction number R0. The Model is shownto be completely determined by the reproduction number. The modelis numerically analysed to asses the effects of the delay on the dynamicsof HIV/AIDS and the demographic impact of the epidemic using thedemographic and epidemiological parameters for Kenya.