Modeling the effects of vaccine efficacy and rate of vaccination on the transmission of pulmonary tuberculosis

Numerous prevention intervention strategies have been developed to curtail the spread of pulmonary tuberculosis to susceptible populations. However, pulmonary tuberculosis continues to claim many lives worldwide. In this paper, a deterministic mathematical model incorporating an asymptomatic infectious population, considering vaccine efficacy, and vaccination rate, has been formulated. The model includes asymptomatic infectious individuals since they spread infections incessantly to susceptible populations without being noticed, thus contributing to the high transmission rate. Sensitivity and numerical analysis have been conducted to investigate the impact of varying vaccine efficacy and vaccination rates on the transmission of pulmonary tuberculosis infections from the asymptomatic infectious population. The sensitivity and numerical results show that an increase in vaccine efficacy reduces the asymptomatic infectious population and subsequently lowers the transmission rate of infections. Moreover, an increase in vaccine efficacy was shown to reduce the control reproduction number due to asymptomatic infectious individuals, thereby decreasing the transmission of pulmonary tuberculosis to susceptible populations. Further results indicate that an increase in vaccination rate reduces the control reproduction number due to asymptomatic infectious individuals, consequently lowering the rate of infection transmission. These findings emphasize the need to develop a vaccine of higher efficacy to reduce infection transmission to susceptible populations by the asymptomatic infectious individuals. Additionally, the results underscore the importance of increasing vaccination rates to eradicate pulmonary tuberculosis from the population.