Optimal Control for the Transmission Dynamics of Tuberculosis

F. El kihal, M. Al hia, I. Abouelkheir, M. Rachik

Abstract: the subject of this work is the application of optimal control for the system of ordinary differential equation modeling a tuberculosis (TB) dis- ease with exogenous reinfection. A TB model that considers the existence of a new class (mainly in the african context) is considered the lost to follow up individuals. Seeking to reduce the infections group by the re- duction of the contact between infections, lost and susceptible individuals, and to reduce the number of lost to follow up, we use control representing the prevention of exogenous reinfection. The Pontryagins maximum prin- ciple is used to characterize the optimal control. An optimality system is derived and solved numerically.

Keywords: Optimal control, exogenous reinfection, Tuberculosis, TB model with exogenous reinfection