Optimal control of tuberculosis transmission model with vaccination

Tuberculosis (TB) is a disease that causes many deaths in the world. This paper discusses optimal control strategies of TB transmission with vaccination in newborns and adults. This study aims to minimize the cost of vaccination intervention and reduce infected populations. Using the Pontryagin Principle, we obtained the optimal control characteristics of the model. Then, it transformed from a continuous to a semi-discrete function. It means that vaccination was given only at certain times. Next, numerical simulations were performed to obtain the optimal control interpretation. As a result, vaccination control was more effective in adults than newborns. Vaccination control for adults will be more effective if given every four years because it will minimize the weight cost of vaccination and reduce the infected population's number.