Optimal control for a nonlinear mathematical model of tumor under immune suppression: A numerical approach

Abstract

SummaryIn this paper, optimal control for a novel nonlinear mathematical model of tumor under immune suppression is presented. The proposed model is governed by a system of fractional differential equations, where the fractional derivative is defined in the Caputo sense. Modified parameters are introduced to account for the fractional order. Necessary and sufficient conditions that guarantee the existence and the uniqueness of the solution of the control problem are given. Two control 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 generalized Euler method and the nonstandard generalized Euler method. The stability analysis and the truncation error of the nonstandard generalized Euler method are given. Comparative studies are implemented.