Human Immunodeficiency Virus (HIV) and Tuberculosis (TB) represent a synergistic syndemic where immunocompromising HIV infection significantly escalates the risk of active TB reactivation and progression. We developed and analysis a co-infection compartmental model which incorporates features such as treatment, vaccination, disease progression, and modification parameters to capture the interaction between single and coinfections.The basic reproduction numbers for the HIV and TB sub-models are derived using the next generation matrix method, and stability analysis shows that the disease-free equilibrium is stable when the reproduction number is less than unity. Sensitivity analysis identifies transmission rates and modification parameters as key drivers of disease spread, while treatment and control measures reduce infection levels. Numerical simulations confirm the analytical results and demonstrate that the interaction between HIV and TB significantly increases the overall disease burden. The findings highlight the importance of integrated intervention strategies for effective disease control.
Keywords: HIV, Intervention, TB, basic reproduction., sensitivity
