Title: Optimal control of an epidemic by vaccination using dynamic programming approach

Authors: Bouremani Touffik; Benterki Djamel; Slimani Yacine

Addresses: Laboratory of Applied Mathematics (LAMA), Faculty of Technology, Setif-1 Ferhat Abbas University, 19000, Algeria ' Laboratory of Fundamental and Numerical Mathematics (LMFN), Department of Mathematics, Faculty of Sciences, Setif-1 Ferhat Abbas University, 19000, Algeria ' Laboratory of Intelligent Systems (LIS), Faculty of Technology, Setif-1 Ferhat Abbas University, 19000, Algeria

Abstract: In this paper, we are interested in solving a SIR epidemic model which can be reformulated as a control problem. We use some recent developments of the dynamics programming method to obtain a rigorous solution of the optimal control problem formulated in Trélat (2019). We use some refinement of Cauchy's method of characteristics for stratified Hamilton-Jacobi equations to describe a large set of admissible trajectories and identify a domain on which the value function exists and is generated by some admissible controlsm, and their optimality is justified by using one of the well-known verification theorems as an argument for sufficient optimality conditions.

Keywords: optimal control; differential inclusion; Pontryagin's maximum principle; dynamic programming; Hamiltonian flow; value function; verification theorem.

DOI: 10.1504/IJMOR.2022.127379

International Journal of Mathematics in Operational Research, 2022 Vol.23 No.3, pp.372 - 393

Received: 20 Apr 2021
Accepted: 30 Jun 2021
Published online: 01 Dec 2022 *

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