Optimal Control of an SIR Model with Delay in State and Control Variables. (13th August 2013)

• Record Type: Journal Article
• Authors: Elhia, Mohamed; Rachik, Mostafa; Benlahmar, Elhabib
• Other Names: Ishikawa H. Academic Editor.; Panteleev M. A. Academic Editor.
• Is Part Of: ISRN biomathematics. Volume 2013(2013)
• Publication Date: 2013-08-13
• Subjects: Biomathematics -- Periodicals; Models, Biological; Biometry; Biomathematics; Electronic journals; Periodicals; Periodicals; Fulltext; Internet Resources; Periodicals; 570.151
• DOI: 10.1155/2013/403549
• Languages: English
• ISSNs: 2090-7702

Abstract

Abstract : We will investigate the optimal control strategy of an SIR epidemic model with time delay in state and control variables. We use a vaccination program to minimize the number of susceptible and infected individuals and to maximize the number of recovered individuals. Existence for the optimal control is established; Pontryagin's maximum principle is used to characterize this optimal control, and the optimality system is solved by a discretization method based on the forward and backward difference approximations. The numerical simulation is carried out using data regarding the course of influenza A (H1N1) in Morocco. The obtained results confirm the performance of the optimization strategy.