Modeling Transmission Dynamics of Tuberculosis: Parameter Estimation and Sensitivity Analysis Using Real-World Data

Abstract: Tuberculosis (TB) continues to pose a major public health challenge, particularly in high-burden regions such as Ethiopia, necessitating a more profound understanding of its transmission dynamics. In this study, we developed an SVEITRS compartmental model to investigate the transmission dynamics of TBs, utilizing real data from Ethiopia from 2011-2021. Model parameters were estimated via two methods: nonlinear least squares and maximum likelihood, with maximum likelihood providing more accurate and reliable results, as confirmed by a test case. The model's stability analysis indicated that there is a disease-free equilibrium in areas where the basic reproduction number ($\mathscr{R}_0$) is less than one. The results suggest that optimal conditions could lead to the elimination of TB. On the other hand, there is an endemic equilibrium in areas where $\mathscr{R}_0$ is greater than one, which means that the disease is still present. Sensitivity analysis revealed important factors affecting TB levels: higher natural death rates, vaccination rates, treatment rates, and disease-related death rates lower TB cases, whereas higher recruitment rates, contact rates, infection rates, and loss of vaccine protection increase its spread. These findings highlights to the necessity of enhancing vaccination, treatment, and recovery strategies while addressing drivers of transmission to achieve TB control in Ethiopia. This study provides useful advice for guiding TB control efforts and public health interventions in Ethiopia and similar regions.