Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2012, Article ID 318150, 10 pages
http://dx.doi.org/10.1155/2012/318150
Research Article

Analysis of an SEIS Epidemic Model with a Changing Delitescence

Institute of Mathematics and Computer Science, Fuzhou University, Fuzhou, FuJian 350002, China

Received 17 May 2012; Accepted 26 July 2012

Academic Editor: Allan Peterson

Copyright © 2012 Jinghai Wang. 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. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. R. M. Anderson and R. M. May, “Population biology of infectious diseases: part 1,” Nature, vol. 280, pp. 361–367, 1979. View at Google Scholar
  4. L. Q. Gao, J. Mena-Lorca, and H. W. Hethcote, “Four SEI endemic models with periodicity and separatrices,” Mathematical Biosciences, vol. 128, no. 1-2, pp. 157–184, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. Z. Ma, Y. Zhou, W. Wang, and Z. Jin, Mathematical Ecology, Springer, New York, NY, USA, 1990.
  6. 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
  7. 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
  8. W. M. Liu, H. W. Hethcote, and S. A. Levin, “Dynamical behavior of epidemiological models with nonlinear incidence rates,” Journal of Mathematical Biology, vol. 25, no. 4, pp. 359–380, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. A. d'Onofrio, “Stability properties of pulse vaccination strategy in SEIR epidemic model,” Mathematical Biosciences, vol. 179, no. 1, pp. 57–72, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. S. Liao, “On the homotopy analysis method for nonlinear problems,” Applied Mathematics and Computation, vol. 147, no. 2, pp. 499–513, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. Y. R. Shi, X. J. Xu, Z. X. Wu et al., “Application of the homotopy analysis method to solving nonlinear evolution equations,” Acta Physica Sinica, vol. 55, no. 4, pp. 1555–1560, 2006. View at Google Scholar · View at Zentralblatt MATH
  12. J. Hui and D. Zhu, “Global stability and periodicity on SIS epidemic models with backward bifurcation,” Computers & Mathematics with Applications, vol. 50, no. 8-9, pp. 1271–1290, 2005. View at Publisher · View at Google Scholar
  13. J. Li and Z. Ma, “Qualitative analyses of SIS epidemic model with vaccination and varying total population size,” Mathematical and Computer Modelling, vol. 35, no. 11-12, pp. 1235–1243, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. L.-I. Wu and Z. Feng, “Homoclinic bifurcation in an SIQR model for childhood diseases,” Journal of Differential Equations, vol. 168, no. 1, pp. 150–167, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. C. Jeffries, V. Klee, and P. van den Driessche, “When is a matrix sign stable?” Canadian Journal of Mathematics, vol. 29, no. 2, pp. 315–326, 1977. View at Google Scholar · View at Zentralblatt MATH