Exploring the Dynamics of Tuberculosis Epidemics Model Using Computational Approaches: A Comparative Study

Tuberculosis (TB) is a contagious disease caused by Mycobacterium tuberculosis that primarily affects the lungs and spreads through airborne transmission. The TB epidemic model simulates disease spread by tracking various compartments to assess transmission rates and the impact of control measures. In this study, a system of equations governing the TB transmission model is considered and solved using three computational approaches. The total population of TB epidemics model under investigation was segmented into five categories: susceptible [Formula: see text], infected [Formula: see text], diagnosed [Formula: see text], treated [Formula: see text], and recovered [Formula: see text]. Approximate analytical solutions are derived using the differential transform method (DTM), Shehu transformation-Akbari–Ganji’s-Pade approximation method (SAGPM), and the Daftardar–Jafari method (DJM). A numerical simulation was conducted using an innovative Python-Jupyter notebook framework and validated against approximate analytical solutions, demonstrating exceptional precision and reliability. All methods performed effectively across the specified time intervals, with the SAGPM exhibiting outstanding accuracy. Furthermore, a sensitivity analysis of [Formula: see text] and the impact of various key parameters within the TB model were explored to understand the influence and dynamic behavior of the proposed model. This analysis assists in better understanding the spread and inhibition of tuberculosis by emphasizing the significance of the model parameters.