We formulate a mathematical model to explore the impact ofvaccination and treatment on the transmission dynamics oftuberculosis (TB). We develop a technique to prove that the basicreproduction number is the threshold of global stability of thedisease-free and endemic equilibria. We then incorporate a controlterm and evaluate the cost of control strategies, and then performan optimal control analysis by Pontryagin's maximum principle. Ournumerical simulations suggest that the maximum vaccination strategyshould be enforced regardless of its efficacy.
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Yang et al. (2016) studied this question.
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