| Titre : | Stochastic Modelling and Optimal Control of Epidemic Models |
| Auteurs : | Habib Nadjet, Auteur ; Mekkaoui Imen, Directeur de thèse |
| Type de document : | texte manuscrit |
| Editeur : | [S.l.] : Université de Saida - Dr Moulay Tahar. Faculté des Sciences. Département de Mathématiques., 2024/2025 |
| Format : | 83 ص |
| Accompagnement : | CD |
| Langues: | Anglais |
| Index. décimale : | BUC-M 003779 |
| Catégories : |
Master Mathématiques Specialization: Stochastic Statistical Analysis of Processes and Applications |
| Résumé : |
Abstract
This work considers some mathematical methods for formulation and numerical simulation of stochastic epidemic models. Specifically, models are formulated by stochastic differential equations. Some well-known examples are used for illustration such as a SIR epidemic model. An optimal control analysis of a dynamical system of optimal control is presented. The stochastic and deterministic control systems are studied. For the deterministic optimal control problem the Pontryagins Maximum Principle is used. The stochastic optimal control problem is performed by using Stochastic Maximum Principle. The comparative results are obtained numerically through simulation, with a specific application to influenza using the Susceptible-Infected-Recovered (SIR) model. The results highlight the advantages of stochastic optimal control in mitigating Epidemics outbreaks, offering insights for policymakers on resource allocation and intervention strategies in the presence of uncertainty. Key words: Epidemic models, Optimal control theory, Pontryagins Maximum Principle, Stochastic Maximum Principle, Numerical simulations, Stochastic Differential Equations. |
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Documents numériques (1)
BUC-M 003779 Adobe Acrobat PDF |
