Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 409510, 7 pages
http://dx.doi.org/10.1155/2014/409510
Research Article

Effect of Heterogeneity of Vertex Activation on Epidemic Spreading in Temporal Networks

1School of Computer Science and Engineering, University of Electronic Science and Technology of China, No. 2006, Xiyuan Avenue, West Hi-Tech Zone, Chengdu, Sichuan 611731, China
2School of Computer Science and Engineering, Xinjiang University of Finance and Economics, No. 449, Central Beijing Road, Urumqi, Xinjiang 830012, China

Received 27 December 2013; Revised 10 March 2014; Accepted 17 March 2014; Published 8 April 2014

Academic Editor: Linying Xiang

Copyright © 2014 Yixin Zhu 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. M. J. Keeling and K. T. D. Eames, “Networks and epidemic models,” Journal of the Royal Society Interface, vol. 2, no. 4, pp. 295–307, 2005. View at Publisher · View at Google Scholar · View at Scopus
  2. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, “Complex networks: structure and dynamics,” Physics Reports, vol. 424, no. 4-5, pp. 175–308, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  3. S. Aral, L. Muchnik, and A. Sundararajan, “Distinguishing influence-based contagion from homophily-driven diffusion in dynamic networks,” Proceedings of the National Academy of Sciences of the United States of America, vol. 106, no. 51, pp. 21544–21549, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. A. Barrat, M. Barthélemy, and A. Vespignani, Dynamical Processes on Complex Networks, Cambridge University Press, Cambridge, 2008. View at MathSciNet
  5. E. Volz and L. A. Meyers, “Epidemic thresholds in dynamic contact networks,” Journal of the Royal Society Interface, vol. 6, no. 32, pp. 233–241, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. N. A. Christakis and J. H. Fowler, “The spread of obesity in a large social network over 32 years,” The New England Journal of Medicine, vol. 357, no. 4, pp. 370–379, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. R. M. Anderson, R. M. May, and B. Anderson, Infectious Diseases of Humans: Dynamics and Control, vol. 28, Wiley Online Library, 1992.
  8. M. E. J. Newman, Networks: An Introduction, Oxford University Press, Oxford, UK, 2010. View at MathSciNet
  9. C. Cioffi-Revilla, “Computational social science,” Wiley Interdisciplinary Reviews: Computational Statistics, vol. 2, no. 3, pp. 259–271, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. A. Vespignani, “Modelling dynamical processes in complex socio-technical systems,” Nature Physics, vol. 8, no. 1, pp. 32–39, 2012. View at Publisher · View at Google Scholar · View at Scopus
  11. C. T. Butts, “A relational event framework for social action,” Sociological Methodology, vol. 38, no. 1, pp. 155–200, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. P. Holme and J. Saramäki, “Temporal networks,” Physics Reports, vol. 519, no. 3, pp. 97–125, 2012. View at Publisher · View at Google Scholar
  13. N. Masuda and P. Holme, “Predicting and controlling infectious disease epidemics using temporal networks,” F1000prime Reports, vol. 5, article 6, 2013. View at Publisher · View at Google Scholar
  14. P. Holme and J. Saramäki, “Temporal networks as a modeling framework,” in Temporal Networks, pp. 1–14, Springer, 2013. View at Google Scholar
  15. T. Takaguchi, N. Masuda, and P. Holme, “Bursty communication patterns facilitate spreading in a threshold-based epidemic dynamics,” PLoS ONE, vol. 8, no. 7, Article ID e68629, 2013. View at Publisher · View at Google Scholar
  16. N. Masuda, K. Klemm, and V. M. Eguíluz, “Temporal networks: slowing down diffusion by long lasting interactions,” Physical Review Letters, vol. 111, Article ID 188701, 2013. View at Publisher · View at Google Scholar
  17. S. Lee, L. E. C. Rocha, F. Liljeros, and P. Holme, “Exploiting temporal network structures of human interaction to effectively immunize populations,” PLoS ONE, vol. 7, no. 5, Article ID e36439, 2012. View at Publisher · View at Google Scholar · View at Scopus
  18. F. Karimi and P. Holme, “A temporal network version of Watts’s cascade model,” in Temporal Networks, pp. 315–329, Springer, 2013. View at Google Scholar
  19. L. E. Rocha, A. Decuyper, and V. D. Blondel, “Epidemics on a stochastic model of temporal network,” in Dynamics on and of Complex Networks, Volume 2, Modeling and Simulation in Science, Engineering and Technology, pp. 301–314, Springer, 2013. View at Publisher · View at Google Scholar
  20. Z. Yang, A.-X. Cui, and T. Zhou, “Impact of heterogeneous human activities on epidemic spreading,” Physica A: Statistical Mechanics and Its Applications, vol. 390, no. 23-24, pp. 4543–4548, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  21. T. Zhou, X.-P. Han, X.-Y. Yan et al., “Statistical mechanics on temporal and spatial activities of human,” Journal of University of Electronic Science and Technology of China, vol. 42, no. 4, 2013. View at Google Scholar
  22. J.-P. Eckmann, E. Moses, and D. Sergi, “Entropy of dialogues creates coherent structures in e-mail traffic,” Proceedings of the National Academy of Sciences of the United States of America, vol. 101, no. 40, pp. 14333–14337, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. A. Vázquez, J. G. Oliveira, Z . Dezsö, K.I. Goh, I. Kondor, and A. L. Barabási, “Modeling bursts and heavy tails in human dynamics,” Physical Review E, vol. 73, no. 3, Article ID 036127, 2006. View at Publisher · View at Google Scholar
  24. A.-L. Barabási, “The origin of bursts and heavy tails in human dynamics,” Nature, vol. 435, no. 7039, pp. 207–211, 2005. View at Publisher · View at Google Scholar · View at Scopus
  25. A. Clauset, C. R. Shalizi, and M. E. J. Newman, “Power-law distributions in empirical data,” SIAM Review, vol. 51, no. 4, pp. 661–703, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. M. E. J. Newman, “Spread of epidemic disease on networks,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 66, no. 1, Article ID 016128, 11 pages, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  27. W. Feller, An Introduction to Probability Theory and Its Applications, vol. 2, 1974.
  28. A. Vazquez, “Polynomial growth in branching processes with diverging reproductive number,” Physical Review Letters, vol. 96, no. 3, Article ID 038702, 2006. View at Publisher · View at Google Scholar · View at Scopus
  29. M. E. J. Newman, S. H. Strogatz, and D. J. Watts, “Random graphs with arbitrary degree distributions and their applications,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 64, no. 2, Article ID 026118, 2001. View at Google Scholar · View at Scopus
  30. A.-L. Barabási and R. Albert, “Emergence of scaling in random networks,” American Association for the Advancement of Science, vol. 286, no. 5439, pp. 509–512, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. R. Pastor-Satorras and A. Vespignani, “Epidemic dynamics in finite size scale-free networks,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 65, no. 3, Article ID 035108, 2002. View at Publisher · View at Google Scholar · View at Scopus