Optimal control of an epidemic by vaccination using dynamic programming approach
by Bouremani Touffik; Benterki Djamel; Slimani Yacine
International Journal of Mathematics in Operational Research (IJMOR), Vol. 23, No. 3, 2022

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.

Online publication date: Thu, 01-Dec-2022

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