About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 586867, 9 pages
http://dx.doi.org/10.1155/2013/586867
Research Article

Dynamical Model about Rumor Spreading with Medium

1National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan, Shanxi 030051, China
2Laboratory of Instrumentation Science and Dynamic Measurement, Ministry of Education, North University of China, Taiyuan, Shanxi 030051, China

Received 13 December 2012; Accepted 22 January 2013

Academic Editor: Yanbin Sang

Copyright © 2013 Xiaxia Zhao and Jianzhong 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. K. Kawachi, M. Seki, H. Yoshida, Y. Otake, K. Warashina, and H. Ueda, “A rumor transmission model with various contact interactions,” Journal of Theoretical Biology, vol. 253, no. 1, pp. 55–60, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  2. J. Kostka, Y. A. Oswald, and R. Wattenhofer, “Word of mouth: rumor dissemination in social networks,” in Structural Information and Communication Complexity, vol. 5058 of Lecture Notes in Computer Science, pp. 185–196, Springer, Berlin, Germany, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  3. Z. L. Zhang and Z. Q. Zhang, “An interplay modal for rumour spreadingand emergency development,” Physica A, vol. 388, no. 19, pp. 4159–4166, 2009. View at Publisher · View at Google Scholar
  4. M. Kosfeld, “Rumours and markets,” Journal of Mathematical Economics, vol. 41, no. 6, pp. 646–664, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. L. J. Zhao, Q. Wang, J. J. Cheng et al., “The impact of authorities' media and rumor dissemination on theevolution of emergency,” Physica A, vol. 391, no. 15, pp. 3978–3987, 2012. View at Publisher · View at Google Scholar
  6. L. J. Zhao, J. J. Wang, Y. C. Chen et al., “SIHR rumor spreading model in socialnetworks,” Physica A, vol. 391, no. 7, pp. 2444–2453, 2012. View at Publisher · View at Google Scholar
  7. A. Sudbury, “The proportion of the population never hearing a rumour,” Journal of Applied Probability, vol. 22, no. 2, pp. 443–446, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. K. Kawachi, “Deterministic models for rumor transmission,” Nonlinear Analysis: Real World Applications, vol. 9, no. 5, pp. 1989–2028, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. Rapoport, “Spread of information through a population with socio-structural bias. I. Assumption of transitivity,” Bulletin of Mathematical Biophysics, vol. 15, pp. 523–533, 1953. View at Zentralblatt MATH · View at MathSciNet
  10. A. Rapoport, “Spread of information through a population with socio-structural bias. II. Various models with partial transitivity,” Bulletin of Mathematical Biophysics, vol. 15, pp. 535–546, 1953. View at MathSciNet
  11. A. Rapoport and L. I. Rebhun, “On the mathematical theory of rumor spread,” Bulletin of Mathematical Biophysics, vol. 14, pp. 375–383, 1952. View at MathSciNet
  12. D. J. Daley and D. G. Kendall, “Epidemics and rumours,” Nature, vol. 204, article 1118, 1964. View at Publisher · View at Google Scholar
  13. D. P. Maki and M. Thompson, Mathematical Models and Applications, Prentice-Hall, Englewood Cliffs, NJ, USA, 1973. View at MathSciNet
  14. B. Pittel, “On a Daley-Kendall model of random rumours,” Journal of Applied Probability, vol. 27, no. 1, pp. 14–27, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  15. C. Lefèvre and P. Picard, “Distribution of the final extent of a rumour process,” Journal of Applied Probability, vol. 31, no. 1, pp. 244–249, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. J. Gu, W. Li, and X. Cai, “The effect of the forget-remember mechanism onspreading,” European Physical Journal B, vol. 62, no. 2, pp. 247–255, 2008. View at Publisher · View at Google Scholar
  17. L. A. Huo, P. Q. Huang, and X. Fang, “An interplay model for authorities' actions and rumor spreading in emergency event,” Physica A, vol. 390, no. 20, pp. 3267–3274, 2011. View at Publisher · View at Google Scholar
  18. L. J. Zhao, Q. Wang, J. J. Cheng, Y. C. Chen, J. J. Wang, and W. Huang, “Rumor spreading model with consideration of forgetting mechanism: a case of online blogging live journal,” Physica A, vol. 390, no. 13, pp. 2619–2625, 2011. View at Publisher · View at Google Scholar
  19. 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 · View at MathSciNet
  20. Y. Wang, Z. Jin, Z. M. Yang, Z. K. Zhang, T. Zhou, and G. Q. Sun, “Global analysis of an SIS model with an infective vector on complex networks,” Nonlinear Analysis: Real World Applications, vol. 13, no. 2, pp. 543–557, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. G. Q. Sun, L. Li, Z. Jin, and B. L. Li, “Effect of noise on the pattern formation in an epidemic model,” Numerical Methods for Partial Differential Equations, vol. 26, no. 5, pp. 1168–1179, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. M. Krstić, “The effect of stochastic perturbation on a nonlinear delay malaria epidemic model,” Mathematics and Computers in Simulation, vol. 82, no. 4, pp. 558–569, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. C. Y. Ji, D. Q. Jiang, Q. S. Yang, and N. Z. Shi, “Dynamics of a multigroup SIR epidemic model with stochastic perturbation,” Automatica, vol. 48, no. 1, pp. 121–131, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. V. Mendez, D. Campos, and W. Horsthemke, “Stochastic fluctuationsof the transmission rate in the susceptible-infected-susceptible epidemicmodel,” Physical Review E, vol. 86, no. 1, Article ID 011919, 8 pages, 2012. View at Publisher · View at Google Scholar