Table of Contents
ISRN Biomathematics
Volume 2013 (2013), Article ID 403549, 7 pages
Research Article

Optimal Control of an SIR Model with Delay in State and Control Variables

Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University Mohammedia, BP 7955, Sidi Othman, Casablanca, Morocco

Received 30 May 2013; Accepted 11 July 2013

Academic Editors: H. Ishikawa and M. A. Panteleev

Copyright © 2013 Mohamed Elhia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.