%0 Journal Article
%T Study of a mathematical model of an epidemic via dynamic programming approach.
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Touffik, Bouremani
%A Slimani, Yacine
%D 2022
%\ 07/01/2022
%V 13
%N 2
%P 1649-1661
%! Study of a mathematical model of an epidemic via dynamic programming approach.
%K Optimal control
%K Dynamic Programming
%K Maximum principle
%K Differential inclusion
%K Hamiltonian flow
%K Value function
%R 10.22075/ijnaa.2022.25802.3131
%X 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.
%U https://ijnaa.semnan.ac.ir/article_6530_ee1f29b5542d840934583365c923f3ed.pdf