Optimal control of an epidemic by vaccination using dynamic programming approach

Bouremani Touffik, Benterki Djamel and Slimani Yacine

International Journal of Mathematics in Operational Research, 2022, vol. 23, issue 3, 372-393

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. (search for similar items in EconPapers)
Date: 2022
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