Bezier Curve Parameterization Methods for Solving Optimal Control Problems of SIR Model

In this paper the optimal control strategies with two control variable of an SIR (susceptible-infected-recovered) epidemic model are introduced. The effect of dispersion of the population in a bounded habitat has been taken into consideration. The aim of this work is to minimize the infective and susceptible individuals and to maximize the total number of recovered individuals by using the possible control variables. To solve optimal control problem we use direct and indirect methods, Bernstein-Bezier parametrisation of control variable and invasive weed optimization of objective function, and adaptive critic design with echo state networks, respectively. Our results indicate that these two methods are able to solve optimal control problems.