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Global stability and optimal control for a tuberculosis model with vaccination and treatment

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  • We formulate a mathematical model to explore the impact of vaccination and treatment on the transmission dynamics of tuberculosis (TB). We develop a technique to prove that the basic reproduction number is the threshold of global stability of the disease-free and endemic equilibria. We then incorporate a control term and evaluate the cost of control strategies, and then perform an optimal control analysis by Pontryagin's maximum principle. Our numerical simulations suggest that the maximum vaccination strategy should be enforced regardless of its efficacy.
    Mathematics Subject Classification: Primary: 34D20, 34H05; Secondary: 49J15.


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