Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213220220701Study of a mathematical model of an epidemic via dynamic programming approach.16491661653010.22075/ijnaa.2022.25802.3131ENBouremani TouffikLaboratory of Applied Mathematics, LAMA, Faculty of Technology, Setif-1 Ferhat Abbas University, 19000, AlgeriaYacine SlimaniLaboratory of Intelligent System, LIS, Faculty of Technology, Setif-1 Ferhat Abbas University, 19000, AlgeriaJournal Article20220104We 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.https://ijnaa.semnan.ac.ir/article_6530_ee1f29b5542d840934583365c923f3ed.pdf