Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 608315, 12 pages
http://dx.doi.org/10.1155/2014/608315
Research Article

SIRS Model of Passengers’ Panic Propagation under Self-Organization Circumstance in the Subway Emergency

School of Economic and Management, Tongji University, Shanghai 200092, China

Received 31 January 2014; Revised 13 April 2014; Accepted 14 April 2014; Published 8 May 2014

Academic Editor: X. Zhang

Copyright © 2014 Haifeng Zhao 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. S. L. Zhang, M. L. Liu, and E. M. Sun, “Comprehensive assessment on emergency evacuation capability of the subway station based on fuzzy network analysis,” Applied Mechanics and Materials, vol. 357, pp. 2935–2939, 2013. View at Google Scholar
  2. T. Okumura, K. Suzuki, A. Fukuda et al., “The Tokyo subway sarin attack: disaster management, part 1: community emergency response,” Academic Emergency Medicine, vol. 5, no. 6, pp. 613–617, 1998. View at Publisher · View at Google Scholar · View at Scopus
  3. L. Yan, W. Tong, Z. Wei, and W. Zongzhi, “Computer simulation of human emergency evacuation in subway station,” in Proceedings of the 2nd International Conference on Risk Analysis and Crisis Response, pp. 513–519, 2009.
  4. Z. Zou and H. Guo, “Research on a fuzzy neural network based medical institutions selection in subway station emergency,” Advanced Materials Research, vol. 361–363, pp. 1204–1210, 2012. View at Publisher · View at Google Scholar · View at Scopus
  5. P. Li, R. Lu, and F. Wang, “Study on supervision, alarm and emergency system for subway in big city,” in Proceedings of the 2nd IEEE International Conference on Emergency Management and Management Sciences (ICEMMS '11), pp. 286–289, August 2011. View at Publisher · View at Google Scholar · View at Scopus
  6. L. Hu, L. Wu, K. Lu et al., “Optimization of emergency ventilation mode for a train on fire stopping beside platform of a metro station,” Building Simulation, vol. 7, no. 2, pp. 137–146, 2014. View at Publisher · View at Google Scholar
  7. C. S. Jiang, Y. Ling, C. Hu, Z. Yang, H. Ding, and W. K. Chow, “Numerical simulation of emergency evacuation of a subway station: a case study in Beijing,” Architectural Science Review, vol. 52, no. 3, pp. 183–193, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. P. Yang, C. Li, and D. Chen, “Fire emergency evacuation simulation based on integrated fire-evacuation model with discrete design method,” Advances in Engineering Software, vol. 65, pp. 101–111, 2013. View at Publisher · View at Google Scholar
  9. J. Wan, J. Sui, and H. Yu, “Research on evacuation in the subway station in China based on the Combined Social Force Model,” Physica A: Statistical Mechanics and Its Applications, vol. 394, pp. 33–46, 2014. View at Publisher · View at Google Scholar
  10. W. Lei, A. Li, R. Gao et al., “Simulation of pedestrian crowds' evacuation in a huge transit terminal subway station,” Physica A: Statistical Mechanics and Its Applications, vol. 391, no. 22, pp. 5355–5365, 2012. View at Publisher · View at Google Scholar
  11. E. Quarantelli, “The behavior of panic participants,” Sociology and Social Research, vol. 41, no. 3, pp. 187–194, 1957. View at Google Scholar
  12. G. Le Bon, The Crowd: A Study of the Popular Mind, Macmillan, 1897.
  13. A. R. Mawson, “Is the concept of panic useful for study purposes,” in Proceedings of the 2nd International Seminar on Behavior in Fire Emergencies, p. 29, National Bureau of Standards, Special Publication, 1978.
  14. B. E. Aguirre, “Emergency evacuations, panic, and social psychology,” Psychiatry, vol. 68, no. 2, pp. 121–129, 2005. View at Publisher · View at Google Scholar · View at Scopus
  15. H. H. Kelley, J. C. Condry Jr., A. E. Dahlke, and A. H. Hill, “Collective behavior in a simulated panic situation,” Journal of Experimental Social Psychology, vol. 1, no. 1, pp. 20–54, 1965. View at Publisher · View at Google Scholar · View at Scopus
  16. M. Ebihara, A. Ohtsuki, and H. Iwaki, “A model for simulating human behavior during emergency evacuation based on classificatory reasoning and certainty value handling,” Computer-Aided Civil and Infrastructure Engineering, vol. 7, no. 1, pp. 63–71, 1992. View at Publisher · View at Google Scholar
  17. C. Saloma, G. J. Perez, G. Tapang, M. Lim, and C. Palmes-Saloma, “Self-organized queuing and scale-free behavior in real escape panic,” Proceedings of the National Academy of Sciences of the United States of America, vol. 100, no. 21, pp. 11947–11952, 2003. View at Publisher · View at Google Scholar · View at Scopus
  18. D. J. Low, “Following the crowd,” Nature, vol. 407, no. 6803, pp. 465–466, 2000. View at Publisher · View at Google Scholar · View at Scopus
  19. D. Helbing, I. Farkas, and T. Vicsek, “Simulating dynamical features of escape panic,” Nature, vol. 407, no. 6803, pp. 487–490, 2000. View at Publisher · View at Google Scholar · View at Scopus
  20. M. Kermack and A. Mckendrick, “Contributions to the mathematical theory of epidemics: part II,” Proceedings of the Royal Society A, vol. 138, pp. 55–83, 1932. View at Publisher · View at Google Scholar
  21. M. Kermack and A. Mckendrick, “Contributions to the mathematical theory of epidemics: part I,” Proceedings of the Royal Society A, vol. 115, pp. 700–721, 1927. View at Publisher · View at Google Scholar
  22. C. H. Li, C. C. Tsai, and S. Y. Yang, “Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 4, pp. 1042–1054, 2014. View at Publisher · View at Google Scholar
  23. B. Dybiec, “SIR model of epidemic spread with accumulated exposure,” European Physical Journal B, vol. 67, no. 3, pp. 377–383, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. L. Zhao, Q. Wang, J. Cheng, Y. Chen, J. Wang, and W. Huang, “Rumor spreading model with consideration of forgetting mechanism: a case of online blogging Live Journal,” Physica A: Statistical Mechanics and Its Applications, vol. 390, no. 13, pp. 2619–2625, 2011. View at Publisher · View at Google Scholar · View at Scopus
  25. L. Zhao, J. Wang, Y. Chen, Q. Wang, J. Cheng, and H. Cui, “SIHR rumor spreading model in social networks,” Physica A: Statistical Mechanics and Its Applications, vol. 391, no. 7, pp. 2444–2453, 2012. View at Publisher · View at Google Scholar · View at Scopus
  26. L. J. Zhao, H. X. Cui, X. Y. Qiu, and X. L. Wang, “SIR rumor spreading model in the new media age,” Physica A: Statistical Mechanics and Its Applications, vol. 392, no. 4, pp. 995–1003, 2013. View at Publisher · View at Google Scholar
  27. F. R. Durand, M. L. F. Abbade, E. Moschim et al., “SIR optimization in wavelength-hopping time spreading optical code routed networks,” Optik, vol. 124, no. 18, pp. 3208–3214, 2013. View at Publisher · View at Google Scholar
  28. Y. Maki and H. Hirose, “Infectious disease spread analysis using stochastic differential equations for SIR model,” in Proceedings of the 4th IEEE International Conference on Intelligent Systems Modelling & Simulation (ISMS '13), pp. 152–156, 2013.
  29. D. F. Bernardes, M. Latapy, and F. Tarissan, “Relevance of SIR model for real-world spreading phenomena: experiments on a large-scale p2p system,” in Proceedings of the International Conference on Advances in Social Networks Analysis and Mining (ASONAM '12), pp. 327–334, IEEE Computer Society, 2012.
  30. S. Bargmann and P. M. Jordan, “A second-sound based, hyperbolic SIR model for high-diffusivity spread,” Physics Letters A: General, Atomic and Solid State Physics, vol. 375, no. 5, pp. 898–907, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  31. S.-K. Zhang, S.-R. Gong, and Z.-M. Cui, “Study on spreading of virus infection with SIRS characteristic in wireless sensor networks,” in Proceedings of the WRI International Conference on Communications and Mobile Computing (CMC '09), vol. 3, pp. 512–517, January 2009. View at Publisher · View at Google Scholar · View at Scopus
  32. H. Fukś, A. T. Lawniczak, and R. Duchesne, “Effects of population mixing on the spread of SIR epidemics,” European Physical Journal B, vol. 50, no. 1-2, pp. 209–214, 2006. View at Publisher · View at Google Scholar · View at Scopus
  33. H. W. Hethcote, “Mathematics of infectious diseases,” SIAM Review, vol. 42, no. 4, pp. 599–653, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  34. R. Pastor-Satorras and A. Vespignani, “Epidemic spreading in scale-free networks,” Physical Review Letters, vol. 86, no. 14, pp. 3200–3203, 2001. View at Publisher · View at Google Scholar · View at Scopus
  35. A. Ramani, A. S. Carstea, R. Willox, and B. Grammaticos, “Oscillating epidemics: a discrete-time model,” Physica A: Statistical Mechanics and Its Applications, vol. 333, no. 1–4, pp. 278–292, 2004. View at Publisher · View at Google Scholar · View at Scopus
  36. C. Piccardi and R. Casagrandi, “Inefficient epidemic spreading in scale-free networks,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 77, no. 2, Article ID 026113, 2008. View at Publisher · View at Google Scholar · View at Scopus
  37. R. Pastor-Satorras and A. Vespignani, “Epidemic dynamics and endemic states in complex networks,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 63, no. 6, Article ID 066117, 2001. View at Google Scholar · View at Scopus
  38. Y. Moreno, J. B. Gómez, and A. F. Pacheco, “Epidemic incidence in correlated complex networks,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 68, no. 3, Article ID 035103, 2003. View at Google Scholar · View at Scopus
  39. Y. Moreno, M. Nekovee, and A. F. Pacheco, “Dynamics of rumor spreading in complex networks,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 69, no. 6, Article ID 066130, 2004. View at Publisher · View at Google Scholar · View at Scopus
  40. C.-H. Li, C.-C. Tsai, and S.-Y. Yang, “Analysis of the permanence of an SIR epidemic model with logistic process and distributed time delay,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 9, pp. 3696–3707, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  41. M. Yuanyuan, Z. Xintian, and L. Linguan, “Susceptible-Infected-Removed (SIR) model of crisis spreading in the correlated network of listed companies and their main stock-holders.,” Journal of Management Sciences in China, vol. 16, no. 7, pp. 80–94, 2013. View at Google Scholar
  42. M. Sekiguchi and E. Ishiwata, “Global dynamics of a discretized SIRS epidemic model with time delay,” Journal of Mathematical Analysis and Applications, vol. 371, no. 1, pp. 195–202, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  43. J. M. Tchuenche, A. Nwagwo, and R. Levins, “Global behaviour of an SIR epidemic model with time delay,” Mathematical Methods in the Applied Sciences, vol. 30, no. 6, pp. 733–749, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  44. J. M. Tchuenche and C. Chiyaka, “Global dynamics of a time delayed SIR model with varying population size,” Dynamical Systems, vol. 27, no. 2, pp. 145–160, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  45. A. D'Onofrio, “On pulse vaccination strategy in the SIR epidemic model with vertical transmission,” Applied Mathematics Letters, vol. 18, no. 7, pp. 729–732, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  46. S. Gao, D. Xie, and L. Chen, “Pulse vaccination strategy in a delayed SIR epidemic model with vertical transmission,” Discrete and Continuous Dynamical Systems B, vol. 7, no. 1, pp. 77–86, 2007. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  47. Z. Lu, X. Chi, and L. Chen, “The effect of constant and pulse vaccination on SIR epidemic model with horizontal and vertical transmission,” Mathematical and Computer Modelling, vol. 36, no. 9-10, pp. 1039–1057, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  48. J. Li and N. Cui, “Dynamic behavior for an SIRS model with nonlinear incidence rate and treatment,” The Scientific World Journal, vol. 2013, Article ID 209256, 5 pages, 2013. View at Publisher · View at Google Scholar
  49. Y. Lin and D. Jiang, “Dynamics of a multigroup SIR epidemic model with nonlinear incidence and stochastic perturbation,” Abstract and Applied Analysis, vol. 2013, Article ID 917389, 12 pages, 2013. View at Publisher · View at Google Scholar
  50. Z. Hu, W. Ma, and S. Ruan, “Analysis of SIR epidemic models with nonlinear incidence rate and treatment,” Mathematical Biosciences, vol. 238, no. 1, pp. 12–20, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  51. J. Li, N. Cui, and H. Sun, “Dynamic behavior for an SIRS model with nonlinear incidence rate,” Advanced Materials Research, vol. 479–481, pp. 1495–1498, 2012. View at Publisher · View at Google Scholar · View at Scopus