Optimal control strategy for a discrete time epidemic models of mycobacterium tuberculosis infections

Abstract

In this paper, our aim is to study the optimal control strategy of a mathematical model of the tuberculosis transmission in the discrete case, and to investigate, in discrete time, optimal control strategy in which the controls are: vaccination and treatment and sensibilisation. The studied population is divided into five compartments SL1IL2R. Our objective is to find the best strategy to reduce the number of S, L1, I and L2. So, the Pontryagin’s maximum principle, in discrete time, is used to characterize the optimal control. The numerical simulation is carried out using MATLAB. The obtained results confirm the performance of the optimization strategy.