A New Model for Tuberculosis, Hepatitis B, and Hepatitis C Propagation in HIV Patients: Stability and Sensitivity Analysis

Co-infections with tuberculosis (TB), hepatitis B virus (HBV), and hepatitis C virus (HCV) pose a significant risk to people infected with HIV. TB remains a serious worldwide health concern, intensified by the HIV epidemic, which significantly increases morbidity and mortality rates worldwide. HIV, HBV, and HCV have similar transmission routes, which allow them to coexist at a considerably higher rate in the same host. The originality of this work lies in the concurrent mathematical modeling of the three major HIV-associated co-infections—TB, HCV, and HBV—within a unified analytical framework, which allows for a comprehensive examination of their dynamic interactions within a population. To do this, we build and examine a compartmental model based on ordinary differential equations to analyze the dynamics of co-infections between HIV and TB, HIV and HBV, and HIV and HCV. We examine the model by demonstrating the existence of a disease-free equilibrium solution. We determine the basic reproduction number of the model and create a Lyapunov–Lasalle candidate function to study the global asymptotic stability of the disease-free equilibrium solution. A sensitivity analysis is conducted to assess the significance of model parameters in the disease dynamics. Ultimately, numerical simulations conducted using MATLAB demonstrate the stability of the co-infection endemic equilibrium and the overall model, as well as the impacts of fluctuating treatment rates and transmission probabilities.