Abstract
This paper deals with the problem of optimal control of a deterministic model of tuberculosis (abbreviated as TB for tubercle bacillus). We first present and analyze an uncontrolled tuberculosis model which incorporates the essential biological and epidemiological features of the disease. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with one or more stable endemic equilibria when the associated basic reproduction number is less than the unity. Based on this continuous model, the tuberculosis control is formulated and solved as an optimal control problem, indicating how control terms on the chemoprophylaxis and detection should be introduced in the population to reduce the number of individuals with active TB. Results provide a framework for designing the cost-effective strategies for TB with two intervention methods.
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