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Optimal control of an epidemic by vaccination using dynamic programming approach

Author

Listed:
  • Bouremani Touffik
  • Benterki Djamel
  • Slimani Yacine

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.

Suggested Citation

  • Bouremani Touffik & Benterki Djamel & Slimani Yacine, 2022. "Optimal control of an epidemic by vaccination using dynamic programming approach," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 23(3), pages 372-393.
    • Handle: RePEc:ids:ijmore:v:23:y:2022:i:3:p:372-393
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