Abstract
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.
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References
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). https://doi.org/10.1177/0165551515574974
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)
Freeman, M., McVittie, J., Sivak, I., Wu, J.: Viral information propagation in the Digg online social network. Physica A 415, 87–94 (2014). https://doi.org/10.1016/j.physa.2014.06.011
Gerald, C.F.: Applied Numerical Analysis. Higher Education Press, Beijing (2006)
Goffman, W., Newill, V.: Generalization of epidemic theory. Nature 204(4955), 225–228 (1964)
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)
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)
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)
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). https://doi.org/10.1177/0266666914551072
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)
Mozafari, N., Hamzeh, A.: An enriched social behavioural information diffusion model in social networks. J. Inf. Sci. 41(3), 273–283 (2015). https://doi.org/10.1177/0165551514565318
Nekovee, M., Moreno, Y., Bianconi, G., Marsili, M.: Theory of rumour spreading in complex social networks. Physica A 374(1), 457–470 (2007)
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)
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)
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)
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)
Walters, C.E., Kendal, J.R.: An SIS model for cultural trait transmission with conformity bias. Theor. Popul. Biol. 90(12), 56–63 (2013)
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)
Zanette, D.H.: Critical behavior of propagation on small-world networks. Phys. Rev. E 64(5), 050901 (2001)
Zanette, D.H.: Dynamics of rumor propagation on small-world networks. Phys. Rev. E 65(4), 041908 (2002)
Zhang, F., Si, G., Luo, P.: A survey for rumor propagation models. Complex Syst. Complex. Sci. 6(4), 1–11 (2009)
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)
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)
Zhou, J., Liu, Z., Li, B.: Influence of network structure on rumor propagation. Phys. Lett. A 368(6), 458–463 (2007)
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). https://doi.org/10.1142/s0129183115500187
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Jiang, P., Yan, X. A quantitative model for the spread of online information. Qual Quant 53, 1981–2001 (2019). https://doi.org/10.1007/s11135-019-00851-3
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DOI: https://doi.org/10.1007/s11135-019-00851-3