Dynamics of HIV-TB co-infection with detection as optimal intervention strategy

Abstract

In this paper, a HIV/AIDS and TB co-infection model has been explored, which incorporates detection and treatment for both diseases. We begin with presenting a co-infection model and then start analyzing both the HIV and the TB sub-models separately. The basic reproduction numbers corresponding to both HIV and TB are computed. Both the HIV/AIDS and the TB sub-models have been shown to exhibit two equilibrium points, namely, the disease-free equilibrium point and the unique endemic equilibrium point. For both sub-models, the disease-free equilibrium point is locally as well as globally asymptotically stable when their corresponding reproduction number is less than unity. The endemic equilibrium point for both sub-models exists, when their corresponding reproduction numbers is greater than one. We also analyze the full HIV-TB co-infection model. With the aim of minimizing infectives and the cost of applying effort towards the detection and the treatment, optimal control analysis is performed for the full model using the Pontryagin’s maximum principle. Numerical simulations with different combinations of efforts are then performed to explore the effect of detection in the presence of treatment for both diseases. Numerical simulations emphasize the fact that to reduce co-infection from the population, programs to accelerate the detection of both diseases are also required along with the treatment.