Assessing the Effects of Holling Type-II Treatment Rate on HIV-TB Co-infection

In this paper, a HIV-TB co-infection model is explored which incorporates a non-linear treatment rate for TB. We begin with presenting a HIV-TB co-infection model and analyze both HIV and TB sub-models separately. The basic reproduction numbers corresponding to HIV-only, TB-only and the HIV-TB full model are computed. The disease-free equilibrium point of the HIV sub-model is shown to be locally as well as globally asymptotically stable when its corresponding reproduction number is less than unity. The HIV-only model exhibits a transcritical bifurcation. On the other hand, for the TB sub-model, the disease-free equilibrium point is locally asymptotically stable but may not be globally asymptotically stable. We have also analyzed the full HIV-TB co-infection model. Numerical simulations are performed to investigate the effect of treatment rate in the presence of resource limitation for TB infected individuals, which emphasize the fact that to reduce co-infection from the population programs to accelerate the treatment of TB should be implemented.