Optimal control strategies of a tuberculosis model with exogenous reinfection

Abstract

For the tuberculosis (TB) model with exogenous reinfection, we study the impact of two control strategies: chemoprophylaxis and treatment. We focus primarily on controlling the disease using an objective function based on a combination of minimizing the number of TB infections and minimizing the cost of control strategies. By using Pontryagin's Maximum Principle, we derive the optimal levels of the two controls. Numerical simulations of the optimal system indicate that the strategies should be improved as the exogenous reinfection transmission coefficient increasing. © 2012 Springer-Verlag.