Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2014, Article ID 426456, 7 pages
http://dx.doi.org/10.1155/2014/426456
Research Article

The Effect of Impulsive Vaccination on Delayed SEIRS Epidemic Model Incorporating Saturation Recovery

1Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, Henan 450002, China
2School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China

Received 24 September 2013; Accepted 17 February 2014; Published 25 March 2014

Academic Editor: Ryusuke Kon

Copyright © 2014 Yongfeng Li 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.

Linked References

  1. Z. Agur, L. Cojocaru, G. Mazor, R. M. Anderson, and Y. L. Danon, “Pulse mass measles vaccination across age cohorts,” Proceedings of the National Academy of Sciences of the United States of America, vol. 90, no. 24, pp. 11698–11702, 1993. View at Publisher · View at Google Scholar · View at Scopus
  2. D. D. Bainov and P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific & Technical, New York, NY, USA, 1993.
  3. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
  4. Y. Li, J. Cui, and X. Song, “Dynamics of a predator-prey system with pulses,” Applied Mathematics and Computation, vol. 204, no. 1, pp. 269–280, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. X. Song and Y. Li, “Dynamic complexities of a Holling II two-prey one-predator system with impulsive effect,” Chaos, Solitons & Fractals, vol. 33, no. 2, pp. 463–478, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. X. Liu, “Impulsive stabilization and applications to population growth models,” Rocky Mountain Journal of Mathematics, vol. 25, no. 1, pp. 381–395, 1995. View at Google Scholar · View at Zentralblatt MATH
  7. A. Lakmeche and O. Arino, “Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment,” Dynamics of Continuous, Discrete and Impulsive Systems Series B, vol. 7, no. 2, pp. 265–287, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. W. Wang, “Global behavior of an SEIRS epidemic model with time delays,” Applied Mathematics Letters, vol. 15, no. 4, pp. 423–428, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. J. Hui and L.-S. Chen, “Impulsive vaccination of sir epidemic models with nonlinear incidence rates,” Discrete and Continuous Dynamical Systems. Series B, vol. 4, no. 3, pp. 595–605, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. S. Gao, L. Chen, J. J. Nieto, and A. Torres, “Analysis of a delayed epidemic model with pulse vaccination and saturation incidence,” Vaccine, vol. 24, no. 35-36, pp. 6037–6045, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. S. Ruan and W. Wang, “Dynamical behavior of an epidemic model with a nonlinear incidence rate,” Journal of Differential Equations, vol. 188, no. 1, pp. 135–163, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. W.-M. Liu, S. A. Levin, and Y. Iwasa, “Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models,” Journal of Mathematical Biology, vol. 23, no. 2, pp. 187–204, 1985. View at Google Scholar · View at Scopus
  13. Y. Li and J. Cui, “The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, pp. 2353–2365, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. Y. Li, C. Ma, and J. Cui, “The effect of constant and mixed impulsive vaccination on SIS epidemic models incorporating media coverage,” Rocky Mountain Journal of Mathematics, vol. 38, no. 5, pp. 1437–1455, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  15. J. Cui, X. Mu, and H. Wan, “Saturation recovery leads to multiple endemic equilibria and backward bifurcation,” Journal of Theoretical Biology, vol. 254, no. 2, pp. 275–283, 2008. View at Publisher · View at Google Scholar · View at Scopus
  16. K. L. Cooke and P. Van Den Driessche, “Analysis of an SEIRS epidemic model with two delays,” Journal of Mathematical Biology, vol. 35, no. 2, pp. 240–260, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  17. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Digo, Calif, USA, 1993.