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Discrete Dynamics in Nature and Society
Volume 2009, Article ID 979217, 17 pages
http://dx.doi.org/10.1155/2009/979217
Research Article

Stability Analysis of a Delayed SIR Epidemic Model with Stage Structure and Nonlinear Incidence

Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China

Received 28 April 2009; Accepted 21 August 2009

Academic Editor: Antonia Vecchio

Copyright © 2009 Xiaohong Tian and Rui Xu. 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. Ma, Y. Zhou, W. Wang, and Z. Jin, Mathematical Modeling and Research of Epidemic Dynamical System, Science Press, Beijing, China, 2004.
  2. E. Beretta, T. Hara, W. Ma, and Y. Takeuchi, “Global asymptotic stability of an SIR epidemic model with distributed time delay,” Nonlinear Analysis: Theory, Methods & Applications, vol. 47, no. 6, pp. 4107–4115, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Z. Jin, Z. E. Ma, and S. L. Yuan, “A SIR epidemic model with varying population size,” Journal of Engineering Mathematics, vol. 20, no. 3, pp. 93–98, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. G. Pang and L. Chen, “A delayed SIRS epidemic model with pulse vaccination,” Chaos, Solitons & Fractals, vol. 34, no. 5, pp. 1629–1635, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. 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
  6. Y. Takeuchi, W. Ma, and E. Beretta, “Global asymptotic properties of a delay SIR epidemic model with finite incubation times,” Nonlinear Analysis: Theory, Methods & Applications, vol. 42, no. 6, pp. 931–947, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. W. Wang, G. Mulone, F. Salemi, and V. Salone, “Permanence and stability of a stage-structured predator-prey model,” Journal of Mathematical Analysis and Applications, vol. 262, no. 2, pp. 499–528, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Y. Xiao and L. Chen, “Modeling and analysis of a predator-prey model with disease in the prey,” Mathematical Biosciences, vol. 171, no. 1, pp. 59–82, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Y. Xiao, L. Chen, and F. ven den Bosch, “Dynamical behavior for a stage-structured SIR infectious disease model,” Nonlinear Analysis: Real World Applications, vol. 3, no. 2, pp. 175–190, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. C. D. Yuan and B. A. Hu, “A SI epidemic model with two-stage structure,” Acta Mathematicae Applicatae Sinica, vol. 25, no. 2, pp. 193–203, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. T. Zhang and Z. Teng, “Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence,” Chaos, Solitons & Fractals, vol. 37, no. 5, pp. 1456–1468, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. V. Capasso and G. Serio, “A generalization of the Kermack-McKendrick deterministic epidemic model,” Mathematical Biosciences, vol. 42, no. 1-2, pp. 43–61, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. D. Xiao and S. Ruan, “Global analysis of an epidemic model with nonmonotone incidence rate,” Mathematical Biosciences, vol. 208, no. 2, pp. 419–429, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, vol. 191 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1993. View at MathSciNet
  15. R. Xu and Z. Ma, “The effect of dispersal on the permanence of a predator-prey system with time delay,” Nonlinear Analysis: Real World Applications, vol. 9, no. 2, pp. 354–369, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. X. Song and L. Chen, “Optimal harvesting and stability for a two-species competitive system with stage structure,” Mathematical Biosciences, vol. 170, no. 2, pp. 173–186, 2001. View at Publisher · View at Google Scholar · View at MathSciNet