On the optimal control for fractional multi-strain TB model

In this paper, optimal control of a general nonlinear multi-strain tuberculosis (TB) model that incorporates three strains drug-sensitive, emerging multi-drug resistant and extensively drug-resistant is presented. The general multi-strain TB model is introduced as a fractional order multi-strain TB model. The fractional derivatives are described in the Caputo sense. An optimal control problem is formulated and studied theoretically using the Pontryagin maximum principle. Four controls variables are proposed to minimize the cost of interventions. Two simple-numerical methods are used to study the nonlinear fractional optimal control problem. The methods are the iterative optimal control method and the generalized Euler method. Comparative studies are implemented, and it is found that the iterative optimal control method is better than the generalized Euler method. Copyright © 2016 John Wiley & Sons, Ltd.