# Analysis and optimal control of a fractional MSD model

Document Type : Research Article

Authors

1 Department of Mathematics, Fasa Branch, Islamic Azad University, Fasa, Iran.

2 Department of Mathematics, Faculty of sciences, University of Gonabad, Gonabad, Iran.

Abstract

In this research, we aim to analyze a mathematical model of Maize streak virus disease as a problem of fractional optimal control. For dynamical analysis, the boundedness and uniqueness of solutions have been investi-gated and proven. Also, the basic reproduction number is obtained, and local stability conditions are given for the equilibrium points of the model. Then, an optimal control strategy is proposed for the purpose of examining the best strategy to fight the maize streak disease. We solve the fractional optimal control problem by a forward-backward sweep iterative algorithm. In this algorithm, the state variable is obtained in a forward and co-state variable by a backward method where an explicit Runge-Kutta method is used to solve differential equations arising from fractional optimal control problems. Some comparative results are presented in order to verify the model and show the efficacy of the fractional optimal control treatments.

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