A structured Markov chain model to investigate the effects of pre-exposure vaccines in tuberculosis control

•Endogenous reactivation of tubercle bacilli and exogenous reinfection are incorporated into a new pre-exposure vaccination model.•The mathematical model is analytically studied by using block-structured Markov processes.•In the setting of small communities, the coverage level is a key index in predicting the number of vaccinations in terms of the vaccine effectiveness.•Two peaks of infection are found to occur showing a low degree and a high degree of colonization with tubercle bacilli.