Tuberculosis and HIV/AIDS co-dynamics: a mathematical model and sensitivity analysis

Abstract

The study’s aim is to investigate the role of treatment at any stage of infection in reducing the expansion of both Tuberculosis and HIV infection in the community. For this, we formulate and analyze a new non-linear compartmental system to study the dynamic of the diseases. The results indicate that the endemic equilibrium point for sub-models is locally and globally asymptotically stable whenever the basic reproduction number is over than 1 and unstable otherwise. A sensitivity analysis is performed in order to discover the parameters having an important impact on the reproduction number. Finally, the effect of variable transmission probalities, treatment rates, and the stability of the co-infection endemic equilibrium point are indicated through a numerical simulation of the full model via MATLAB.