SEIR MODELING OF TUBERCULOSIS TRANSMISSION WITH VACCINATION: ESTIMATING THE MINIMUM COVERAGE REQUIRED FOR ELIMINATION IN NORTH SUMATERA

Abstract

Tuberculosis (TB) remains one of the most significant public health challenges in Indonesia, particularly in North Sumatra Province, which records a relatively high prevalence rate. e–Exposed–Infectious–Recovered) A framework to analyze TB's transmission dynamics and evaluate vaccination's effectiveness as an intervention strategy. The primary objective of this research is to estimate the minimum vaccination coverage required to eliminate TB from the population. The model was built by incorporating vaccination rate parameters into the SEIR mathematical model and applied using regional epidemiological data obtained from the North Sumatra Central Bureau of Statistics. A deterministic approach is employed to simulate the system and derive the basic reproduction number ( ), which serves as an indicator of disease persistence across various levels of vaccination coverage. The results of numerical simulations performed using 4th-Order Runge Kutta indicate the existence of a critical vaccination threshold required to reduce below the one-condition that theoretically represents the possibility of disease elimination from the population. These findings provide a quantitative basis for formulating more targeted, data-driven vaccination policies. Calculations based on real-world data reveal that the current R₀ value in North Sumatra remains above one ( ), suggesting that TB continues to pose a risk of remaining endemic. Simulations were also conducted by varying the vaccination coverage while assuming a constant transmission rate, indicating that a minimum of 87.5% vaccination coverage is required to suppress R₀ below the critical threshold. This study underscores the importance of employing mathematical modeling as a decision-support tool in public health policy. The findings deepen the understanding of TB transmission dynamics and offer a robust quantitative foundation for setting vaccination targets for disease elimination in endemic areas such as North Sumatra.