Mathematical Analysis of Optimal Control of Human Immunodeficiency Virus (HIV) Co-infection with Tuberculosis (TB)

The co-occurrence of Human Immunodeficiency Virus (HIV) and Tuberculosis (TB) poses a significant global health challenge, affecting an estimated 1.4 million individuals worldwide. The synergistic progression of these diseases contributes to elevated morbidity and mortality rates. Recognizing the substantial public health burden they impose, this study introduces fifteen (15) compartmental models to discern optimal control strategies for treating HIV-TB co-infection. Initial consideration is given to sub-models for HIV and TB individually, followed by the comprehensive HIV-TB co-infection model. The research quantitatively analyzes the existence and uniqueness of HIV and TB models, examining the stability of equilibrium points for disease-free and endemic states. The Basic Reproduction Number (R0) is computed using the Next Generation Matrix method. Optimal control strategies are evaluated to determine the preferred sequence for treating co-infection. Employing MAPLE software with the differential transformation method, numerical simulations underscore the importance of epidemiological features in the dynamic spread of HIV-TB co-infection. The results emphasize the efficacy of simultaneous treatment for both diseases, coupled with immune system support, compared to sequential treatment of one disease.