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Study of a mathematical model of an epidemic via dynamic programming approach. | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 132، دوره 13، شماره 2، مهر 2022، صفحه 1649-1661 اصل مقاله (1.15 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.25802.3131 | ||
| نویسندگان | ||
| Bouremani Touffik* 1؛ Yacine Slimani2 | ||
| 1Laboratory of Applied Mathematics, LAMA, Faculty of Technology, Setif-1 Ferhat Abbas University, 19000, Algeria | ||
| 2Laboratory of Intelligent System, LIS, Faculty of Technology, Setif-1 Ferhat Abbas University, 19000, Algeria | ||
| تاریخ دریافت: 14 دی 1400، تاریخ بازنگری: 31 فروردین 1401، تاریخ پذیرش: 25 اردیبهشت 1401 | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Optimal control؛ Dynamic programming؛ Maximum principle؛ Differential inclusion؛ Hamiltonian flow؛ Value function | ||
| مراجع | ||
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