Optimal treatment and vaccination control strategies for the dynamics of pulmonary tuberculosis. (English) Zbl 1359.92075

Summary: In this article we apply optimal control theory to one-strain tuberculosis model that incorporates vaccination and treatment. In this model the control mechanisms associated with chemoprophylaxis of latently infected with TB and education campaign are incorporated in order to reduce the number of latently and actively infected population with TB through application of Pontryagin’s Maximum Principle. Numerical simulations are carried out by using both forward and backward in time fourth order Runge-Kutta schemes. The results show that education campaign control measure alone is more effective in curbing TB transmissions and infections than chemoprophylaxis of latently infected. Furthermore the combination of the two measures has desirable effect of reducing the number of infected individuals with TB than when a single control is used. We suggest that for total eradication of TB from the community, the emphasis of education campaign should be the focal point and chemoprophylaxis of latently infected individuals control strategy has to be paired with treatment of actively infected TB individuals.


92C60 Medical epidemiology
92C50 Medical applications (general)
49N90 Applications of optimal control and differential games
49K15 Optimality conditions for problems involving ordinary differential equations
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