The Effectiveness of BCG Vaccination Using SEIR Mathematical Model of Tuberculosis Transmission

Abstract

Tuberculosis (TB) is an airborne contagious disease that poses a threat to the human population around the world. In 2022, an estimated 10.6 million people fell ill with TB worldwide, making it the common cause of death globally. Although the implementation of the BCG vaccination program has started since a decade, the vaccine itself offers limited protection. As immunity wanes over time, re-infection will occur even in vaccinated individuals. This paper discussed the effectiveness of BCG vaccination to control the spread of the disease. The SEIR mathematical model of TB transmission is constructed by considering the re-infection of vaccinated individuals. A brief analysis on the existence and local stability of the equilibria is conducted along with the basic reproduction number. The results showed that the value of R₀ is 1.46 in the absence of vaccination, while R₀ = 1.06 when the vaccination rate is at v = 0.55. However, as v ≥ 0.63, the value of R₀ is less than 1, indicating that the disease dies out. The numerical simulation proved the effectiveness of higher vaccination rates in order to eradicate the TB disease from the population. The study’s findings can contribute to the advancement of public health policy to control the spread of the disease.