Study of a mathematical model of an epidemic via dynamic programming approach.

Document Type : Research Paper


1 Laboratory of Applied Mathematics, LAMA, Faculty of Technology, Setif-1 Ferhat Abbas University, 19000, Algeria

2 Laboratory of Intelligent System, LIS, Faculty of Technology, Setif-1 Ferhat Abbas University, 19000, Algeria


We use some recent developments in Dynamics Programming Method to obtain a rigorous solution of the epidemic model formulated in E. Trélat [Controle optimal: théorie et applications, (online version 2020)] as an unsolved problem. In fact, this problem is proposed in the context of using Pontryagin’s Maximum Principle. We use a certain 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 a certain admissible control. The optimality is justified by using of one of the well-known verification theorems as an argument for sufficient optimality conditions.


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Volume 13, Issue 2
July 2022
Pages 1649-1661
  • Receive Date: 04 January 2022
  • Revise Date: 20 April 2022
  • Accept Date: 15 May 2022