TY - JOUR
ID - 6530
TI - Study of a mathematical model of an epidemic via dynamic programming approach.
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Touffik, Bouremani
AU - Slimani, Yacine
AD - Laboratory of Applied Mathematics, LAMA, Faculty of Technology, Setif-1 Ferhat Abbas University, 19000, Algeria
AD - Laboratory of Intelligent System, LIS, Faculty of Technology, Setif-1 Ferhat Abbas University, 19000, Algeria
Y1 - 2022
PY - 2022
VL - 13
IS - 2
SP - 1649
EP - 1661
KW - Optimal control
KW - Dynamic Programming
KW - Maximum principle
KW - Differential inclusion
KW - Hamiltonian flow
KW - Value function
DO - 10.22075/ijnaa.2022.25802.3131
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_6530.html
L1 - https://ijnaa.semnan.ac.ir/article_6530_ee1f29b5542d840934583365c923f3ed.pdf
ER -