Table of Contents
ISRN Applied Mathematics
Volume 2013, Article ID 706848, 4 pages
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.

Linked References

  1. H. W. Hethcote, H. W. Stech, and P. van den Driessche, “Periodicity and stability in epidemic models: a survey,” in Differential Equations and Applications in Ecology, Epidemics, and Population Problems, S. N. Busenberg and K. L. Cooke, Eds., p. 6582, Academic Press, New York, NY, USA, 1981. View at Google Scholar
  2. A. Kaddar, A. Abta, and H. T. Alaoui, “A comparison of delayed SIR and SEIR epidemic models,” Nonlinear Analysis: Modelling and Control, vol. 16, no. 2, pp. 181–190, 2011. View at Google Scholar · View at Scopus
  3. A. Abta, A. Kaddar, and H. T. Alaoui, “Global stability for delay SIR and SEIR epidemic models with saturated incidence rates,” Electronic Journal of Differential Equations, vol. 2012, no. 23, pp. 1–13, 2012. View at Google Scholar · View at Scopus
  4. D. L. Lukes, Differential Equations: Classical to Controlled, vol. 162 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1982.
  5. W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer, New York, NY, USA, 1975.
  6. I. K. Morton and L. S. Nancy, Dynamics Optimization the Calculus of Variations and Optimal Control in Economics and Management, Elsevier Science, Amsterdam, The Netherlands, 2000.
  7. A. B. Gumel, P. N. Shivakumar, and B. M. Sahai, “A mathematical model for the dynamics of HIV-1 during the typical course of infection,” in Proceedings of the 3rd World Congress of Nonlinear Analysts, vol. 47, pp. 2073–2083, 2001.