A Mathematical Model for HIV-TB Co-infection: The Effect of Treatment

Abstract. We propose a population model for HIV-TB co-infection dynamics by considering treatments for HIV infection, active tuberculosis and co-infection. The HIV only and TB only models are analyzed separately, as well as full model. The basic reproduction numbers for TB (RT0 ) and HIV (RH0 ) and overall reproduction number for the system R0 = max{R T 0 ,R H 0 } are computed. The equilibria and their stability are studied. We explore the effect of early and late HIV treatment on disease induced death during the TB treatment course. Mathematical analysis of our model shows that successful disease eradication requires treatment of single disease, that is, treatment for HIV only and TB only infected individuals with addition to co-infection treatment.