Bézier curve parametrisation and echo state network methods for solving optimal control problems of SIR model

In this work, we introduce an optimal control problem with two control variables of the SIR (susceptible-infected-recovered) epidemic model to minimise the infective and susceptible individuals. To solve the control problem, we use direct Bernstein-Bézier parametrisation of the control variables and metaheuristic optimisation methods of an objective function, and indirect methods, adaptive critic design (ACD) with echo state networks (ESNs) and Pontryagin's maximum principle. We propose Bernstein-Bézier parametrisation and ESNs based algorithms to solve optimal control problems for systems governed by differential equations. We use ACD with ESNs to approximate co-state equations. Our simulations have shown that the proposed two methods are able to solve optimal control problems.