Mathematical Analysis of Transmission Dynamics of HIV/TB Co-Infection in the Presence of Treatment

Abstract

Abstract In this study we analyze a mathematical model for the HIV and TB co-infection for different treatment strategies. We analyze the TB and HIV/AIDS sub-models, we presented conditions for positivity and boundedness of solution. The HIV-only model is shown to have asymptotically stable equilibrium and we established conditions of the existence of the endemic equilibrium in terms of the reproduction number associated with the disease-free equilibrium. The TB-only model shows behavior of backward bifurcation, where the stable disease-free equilibrium exists with a stable endemic equilibrium when the associated reproduction number. We further analyze the full HIV/TB model to incorporate the treatment to the both diseases. A numerical simulation of the models is performed to investigate the effect certain parameters on the spread of the diseases.