Quality & Quantity

, Volume 53, Issue 4, pp 1981–2001 | Cite as

A quantitative model for the spread of online information

  • Ping JiangEmail author
  • Xiangbin Yan


This paper quantifies the spreading speed, scale and influence of online information. Based on the epidemic Susceptible-Infected-Removed (SIR) model, we propose a piecewise SIR model to study the problem of information spreading in online social networks. In the model, we propose that the recovery rate of spreaders should be a piecewise function rather than a constant. Only in this way can the model reveal the different roles of online spreaders in different spreading periods. Based on this piecewise recovery rate, we give a formula to calculate the sustained influence of a message. Calculation results of Weibo data show that there is no a proportional relationship between the sustained influence of a message and the number of spreaders. This finding not only is of great significance for the control of negative information, but also is of great reference value for the promotion of positive information. Moreover, our model can be used to predict the number of spreaders and compute a reasonable intervention time in emergency management. The quantitative model we proposed provides a theoretical basis for the formulation of emergency measures.


Online information spreading Piecewise SIR model Emergency management Sustained influence 



  1. Ahn, H., Park, J.-H.: The structural effects of sharing function on Twitter networks: focusing on the retweet function. J. Inf. Sci. 41(3), 354–365 (2015). CrossRefGoogle Scholar
  2. Cui, P., Tang, M., Wu, Z.-X.: Message spreading in networks with stickiness and persistence: large clustering does not always facilitate large-scale diffusion. Sci. Rep. 4, 6303 (2014)CrossRefGoogle Scholar
  3. Freeman, M., McVittie, J., Sivak, I., Wu, J.: Viral information propagation in the Digg online social network. Physica A 415, 87–94 (2014). CrossRefGoogle Scholar
  4. Gerald, C.F.: Applied Numerical Analysis. Higher Education Press, Beijing (2006)Google Scholar
  5. Goffman, W., Newill, V.: Generalization of epidemic theory. Nature 204(4955), 225–228 (1964)CrossRefGoogle Scholar
  6. Huo, L., Huang, P., Guo, C.: Analyzing the dynamics of a rumor transmission model with incubation. Discrete Dyn. Nat. Soc. 65(2012), 267–278 (2012)Google Scholar
  7. Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 772, pp. 700–721. The Royal Society (1927)Google Scholar
  8. Li, D., Zhang, Y., Chen, X., Cao, L.: Propagation regularity of hot topics in Sina Weibo based on SIR model: a simulation research. In: Computing, Communications and IT Applications Conference, pp. 310–315. IEEE (2014)Google Scholar
  9. Luarn, P., Chiu, Y.-P.: Influence of network density on information diffusion on social network sites: the mediating effects of transmitter activity. Inf. Dev. 32(3), 389–397 (2016). CrossRefGoogle Scholar
  10. Luarn, P., Yang, J.-C., Chiu, Y.-P.: The network effect on information dissemination on social network sites. Comput. Hum. Behav. 37, 1–8 (2014)CrossRefGoogle Scholar
  11. Mozafari, N., Hamzeh, A.: An enriched social behavioural information diffusion model in social networks. J. Inf. Sci. 41(3), 273–283 (2015). CrossRefGoogle Scholar
  12. Nekovee, M., Moreno, Y., Bianconi, G., Marsili, M.: Theory of rumour spreading in complex social networks. Physica A 374(1), 457–470 (2007)CrossRefGoogle Scholar
  13. Oh, O., Agrawal, M., Rao, H.R.: Community intelligence and social media services : a rumor theoretic analysis of tweets during social crises. MIS Q. 37(2), 407–426 (2013)CrossRefGoogle Scholar
  14. Ren, D., Zhang, X., Wang, Z., Li, J., Yuan, X.: Weiboevents: a crowd sourcing weibo visual analytic system. In: 2014 IEEE Pacific Visualization Symposium (PacificVis), pp. 330–334. IEEE (2014)Google Scholar
  15. Tripathy, R.M., Bagchi, A., Mehta, S.: A study of rumor control strategies on social networks. In: Proceedings of the 19th ACM International Conference on Information and Knowledge Management, pp. 1817–1820. ACM (2010)Google Scholar
  16. Van den Driessche, P., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180(1), 29–48 (2002)CrossRefGoogle Scholar
  17. Walters, C.E., Kendal, J.R.: An SIS model for cultural trait transmission with conformity bias. Theor. Popul. Biol. 90(12), 56–63 (2013)CrossRefGoogle Scholar
  18. Wei, Z., Yanqing, Y., Hanlin, T., Qiwei, D., Taowei, L.: Information diffusion model based on social network. In: Proceedings of the 2012 International Conference of Modern Computer Science and Applications, pp. 145–150. Springer (2013)Google Scholar
  19. Zanette, D.H.: Critical behavior of propagation on small-world networks. Phys. Rev. E 64(5), 050901 (2001)CrossRefGoogle Scholar
  20. Zanette, D.H.: Dynamics of rumor propagation on small-world networks. Phys. Rev. E 65(4), 041908 (2002)CrossRefGoogle Scholar
  21. Zhang, F., Si, G., Luo, P.: A survey for rumor propagation models. Complex Syst. Complex. Sci. 6(4), 1–11 (2009)Google Scholar
  22. Zhao, J., Wu, J., Feng, X., Xiong, H., Xu, K.: Information propagation in online social networks: a tie-strength perspective. Knowl. Inf. Syst. 32(3), 589–608 (2012)CrossRefGoogle Scholar
  23. Zhao, L., Wang, X., Qiu, X., Wang, J.: A model for the spread of rumors in Barrat–Barthelemy–Vespignani (BBV) networks. Physica A 392(21), 5542–5551 (2013)CrossRefGoogle Scholar
  24. Zhou, J., Liu, Z., Li, B.: Influence of network structure on rumor propagation. Phys. Lett. A 368(6), 458–463 (2007)CrossRefGoogle Scholar
  25. Zhou, X., Hu, Y., Wu, Y., Xiong, X.: Influence analysis of information erupted on social networks based on SIR model. Int. J. Mod. Phys. C 26(02), 1550018 (2015). CrossRefGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of ManagementShanghai University of International Business and EconomicsShanghaiChina
  2. 2.Donlinks School of Economics and ManagementUniversity of Science and Technology BeijingBeijingChina

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