Optimal control for a time delay multi-strain tuberculosis fractional model: a numerical approach

In this article, optimal control for a novel fractional multi-strain Tuberculosis model with time delay is presented. The proposed model is governed by a system of fractional delay differential equations, where the fractional derivative is defined in the Caputo sense. Modified parameters are introduced to account for the fractional order. Two delays in the proposed model representing the time delay on the diagnosis and commencement of treatment of individuals with active Tuberculosis infection in two and three strains. Necessary and sufficient conditions that guarantee the existence and the uniqueness of the solution of the resulting systems are given. Two control variables are proposed to minimize the cost of interventions. Two simple numerical methods are used to study the nonlinear fractional delay optimal control problem. The methods are the iterative optimal control method (IOCM) and the generalized Euler method (GEM). Comparative studies are implemented, it is found that the IOCM is better than the GEM.