About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 454073, 7 pages
http://dx.doi.org/10.1155/2012/454073
Research Article

Stochastically Perturbed Epidemic Model with Time Delays

School of Science, Chang’an University, Xi’an 710064, China

Received 3 November 2012; Accepted 4 December 2012

Academic Editor: Junli Liu

Copyright © 2012 Tailei Zhang. 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. J. Zhen, Z. Ma, and M. Han, “Global stability of an SIRS epidemic model with delays,” Acta Mathematica Scientia Series B, vol. 26, no. 2, pp. 291–306, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. E. Beretta, V. Capasso, and F. Rinaldi, “Global stability results for a generalized Lotka-Volterra system with distributed delays: applications to predator-prey and to epidemic systems,” Journal of Mathematical Biology, vol. 26, no. 6, pp. 661–688, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. K. L. Cooke, “Stability analysis for a vector disease model,” The Rocky Mountain Journal of Mathematics, vol. 9, no. 1, pp. 31–42, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. E. Beretta and Y. Takeuchi, “Global stability of an SIR epidemic model with time delays,” Journal of Mathematical Biology, vol. 33, no. 3, pp. 250–260, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. 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
  6. W. Ma, M. Song, and Y. Takeuchi, “Global stability of an SIR epidemic model with time delay,” Applied Mathematics Letters, vol. 17, no. 10, pp. 1141–1145, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. V. B. Kolmanovskiĭ and V. R. Nosov, Stability of Functional-Differential Equations, vol. 180 of Mathematics in Science and Engineering, Academic Press, London, UK, 1986.
  8. E. Beretta, V. Kolmanovskii, and L. Shaikhet, “Stability of epidemic model with time delays influenced by stochastic perturbations,” Mathematics and Computers in Simulation, vol. 45, no. 3-4, pp. 269–277, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. L. E. Shaĭkhet, “Stability in probability of nonlinear stochastic systems with delay,” Mathematical Notes, vol. 57, no. 1-2, pp. 103–106, 1995.
  10. L. Shaĭkhet, “Stability in probability of nonlinear stochastic hereditary systems,” Dynamic Systems and Applications, vol. 4, no. 2, pp. 199–204, 1995. View at Zentralblatt MATH