Table of Contents
ISRN Applied Mathematics
Volume 2013, Article ID 706848, 4 pages
http://dx.doi.org/10.1155/2013/706848
Research Article

Optimal Control Strategy for SEIR with Latent Period and a Saturated Incidence Rate

1Department of Mathematics and Computer Science, Faculty of Sciences El Jadida, Chouaib Doukkali University, P.O. Box 20, El Jadida, Morocco
2Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, P.O. Box 7955, Sidi Othman, Casablanca, Morocco

Received 24 April 2013; Accepted 22 May 2013

Academic Editors: Q. Song and Y. Wang

Copyright © 2013 Abta Abdelhadi and Laarabi Hassan. 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.

Abstract

We propose an SEIR epidemic model with latent period and a modified saturated incidence rate. This work investigates the fundamental role of the vaccination strategies to reduce the number of susceptible, exposed, and infected individuals and increase the number of recovered individuals. The existence of the optimal control of the nonlinear model is also proved. The optimality system is derived and then solved numerically using a competitive Gauss-Seidel-like implicit difference method.