Abstract
With an increasing number of people sharing feelings and opinions online, the online platforms have become one of the most important channels for public opinion dissemination. Moreover, recurring online public opinion has become a primary form of online public opinion and has begun to have major effects on prompting social change. Therefore, this paper establishes a novel dynamic dissemination model to systematically study the recurrence of online public opinion. Through an in-depth analysis, three major influencing factors are determined, a recurrence probability function is identified, and then a SIR-I-based dynamic dissemination model is successfully developed, for which the uniformly asymptotically stability is fully proved. A case study from “Child abuse in Ctrip kindergarten” is conducted to demonstrate the validity of the proposed model. The parameter analysis proved that controlling of the public opinion heat, control effectiveness, event topic relevance, and recurrence time point is an effective way to manage the recurrence dissemination, and that opinion leaders play an important role in dissemination. Meanwhile, comparative analysis shows that our model efficiently characterized the dissemination process of recurring online public opinion. As our paper expanded the research cycle of public opinion to its recurrence, it not only enriches online public opinion dissemination model development, but also provides a reference for quantitative analysis of recurring online public opinions dissemination.
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Abbreviations
- t :
-
Time
- m :
-
Recurrence time point
- \(y_1\) :
-
Public opinion heat
- \(y_2\) :
-
Control effectiveness
- \(y_3\) :
-
Event topic relevance
- \(E_i\) :
-
Event i
- ce :
-
Control effectiveness score
- \(ce_1\) :
-
Rapid reaction level
- \(ce_2\) :
-
Disposal guidance level
- \(ce_3\) :
-
Legalization level
- \(ce_{11}\) :
-
Information publicity degree
- \(ce_{12}\) :
-
Response speed
- \(ce_{21}\) :
-
Channelization
- \(ce_{22}\) :
-
Authority of spokesperson
- \(ce_{211}\) :
-
Network interaction level
- \(ce_{212}\) :
-
Understanding the demands level
- \(ce_{31}\) :
-
Law enforcement level
- \(ce_{32}\) :
-
Standardization level
- v :
-
The weight of influencing factor
- P :
-
Equilibrium point
- \({\mathfrak {R}_0}\) :
-
Dissemination threshold
- y :
-
Overall level of factors influencing online public opinion recurrence
- \(WV({E_i})\) :
-
Online public opinion-related feature word vectors for event i
- \({t_g}\) :
-
The gth feature word in the VSM
- \(w_{{E_i}}^g\) :
-
The weight of \({t_g}\) in event i
- r(t):
-
Recurring online public opinion function
- k :
-
Adjustment coefficient
- N :
-
Number of netizens
- S :
-
The ignorant
- I :
-
The spreaders
- R :
-
The stiflers
- S(t):
-
Proportion of the ignorant in the population at time t
- I(t):
-
Proportion of spreaders in the population at time t
- R(t):
-
Proportion of stiflers in the population at time t
- \(S_0\) :
-
Proportion of the ignorant in the population at time 0
- \(I_0\) :
-
Proportion of spreaders in the population at time 0
- \(R_0\) :
-
Proportion of stiflers in the population at time 0
- a :
-
Spreading rate
- b :
-
Stifling rate
- V :
-
Lyapunov function
- \(\hat{I}_{t}\) :
-
Simulation values vector of I
- \({I_t}\) :
-
Actual values vector of I
References
Statista: Number of social networks users worldwide from 2010 to 2021 (in billions). https://www.statista.com/statistics/278414/number-of-worldwide-social-network-users/
Lee, M.J., Chun, W.: Reading others’ comments and public opinion poll results on social media: social judgment and spiral of empowerment. Comput. Hum. Behav. 65, 479–487 (2016)
Krueger, A.B., Malečková, J.: Attitudes and action: public opinion and the occurrence of international terrorism. Science 325(5947), 1534–1536 (2009)
Yang, L.X., Li, P., Yang, X., Wu, Y., Yuan, Y.T.: On the competition of two conflicting messages. Nonlinear Dyn. 91, 1853–1869 (2018)
Howell, L.: Digital wildfires in a hyperconnected world. Tech. rep, WEF Report (2013)
Yi, W., Cao, J., Li, X., Alsaedi, A.: Edge-based epidemic dynamics with multiple routes of transmission on random networks. Nonlinear Dyn. 91, 1–18 (2018)
Sudbury, A.: The proportion of the population never hearing a rumour. J. Appl. Probab. 22(2), 443–446 (1985)
Wang, Y., Cai, W.: Epidemic spreading model based on social active degree in social networks. China Commun. 12(12), 101–108 (2015)
Zhao, H., Jie, J., Xu, R., Ye, Y.: Sirs model of passengers’ panic propagation under self-organization circumstance in the subway emergency. Math. Probl. Eng. 2014, 1–12 (2014)
Zhu, H., Kong, Y., Wei, J., Ma, J.: Effect of users’ opinion evolution on information diffusion in online social networks. Phys. A Stat. Mech. Appl. 492, 2034–2045 (2018)
Xiong, F., Liu, Y., Zhang, Z.J., Zhu, J., Zhang, Y.: An information diffusion model based on retweeting mechanism for online social media. Phys. Lett. A 376(30–31), 2103–2108 (2012)
Hosseini, S., Azgomi, M.A.: A model for malware propagation in scale-free networks based on rumor spreading process. Comput. Netw. 108((C)), 97–107 (2016)
Zhuang, Y.B., Chen, J.J., Li, Z.H.: Modelling the cooperative and competitive contagions in online social networks. Phys. A Stat. Mech. Appl. 484, 141 (2017)
Xu, J., Zhang, Y.: Event ambiguity fuels the effective spread of rumors. Int. J. Mod. Phys. C 26(03), 571–586 (2015)
Xiao, Y., Chen, D., Wei, S., Li, Q., Wang, H.: Rumor propagation dynamic model based on evolutionary game and anti-rumor. Nonlinear Dyn. 95, 523–539 (2019)
Li, W., Fan, P., Li, P., Wang, H., Pan, Y.: An opinion spreading model in signed networks. Mod. Phys. Lett. B 27(12), 137–146 (2013)
Xia, L., Jiang, G., Song, Y., Song, B.: Modeling and analyzing the interaction between network rumors and authoritative information. Entropy 17, 471–482 (2015)
Zhang, L., Su, C., Jin, Y., Goh, M., Wu, Z.: Cross-network dissemination model of public opinion in coupled networks. Inf. Sci. 451–452, 240–252 (2018)
Woo, J., Chen, H.: An event-driven sir model for topic diffusion in web forums. In: IEEE International Conference on Intelligence & Security Informatics (2012)
Zhang, Y., Xu, J.: A rumor spreading model considering the cumulative effects of memory. Discrete Dyn. Nat. Soc. 2015, 1–11 (2015)
Tudor, D.: A deterministic model for herpes infections in human and animal populations. SIAM Rev. 32(1), 136–139 (1990)
Moreira, H.N., Wang, Y.: Classroom note: global stability in an \(S \rightarrow I \rightarrow R \rightarrow I\) model. Soc. Ind. Appl. Math. 39(3), 496–502 (1997)
Van, D.P., Wang, L., Zou, X.: Modeling diseases with latency and relapse. Math. Biosci. Eng. 4(2), 205–219 (2017)
eddine Berrhazi, B., Fatini, M.E., Caraballo, T., Pettersson, R.: A stochastic siri epidemic model with lévy noise. Discrete Contin. Dyn. Syst. B 23(6), 2415–2431 (2018)
Cao, X., Zhang, X., Liu, L., Fang, K., Duan, F., Li, S.: Research on internet public opinion heat based on the response level of emergencies. Chin. J. Manag. Sci. 22(3), 82–89 (2014). (in chinese)
wrd webset. http://www.wrd.cn/login.shtml
Stebler, N., Schuepbach-Regula, G., Braam, P., Falzon, L.C.: Use of a modified delphi panel to identify and weight criteria for prioritization of zoonotic diseases in switzerland. Prev. Vet. Med. 121(1–2), 165–169 (2015)
Husserl, E., Fleischer, M.: Analysen zur Passiven Synthesis. Martinus Nijhoff, Leiden (1966)
Prasetyo, V.R., Winarko, E.: Rating of indonesian sinetron based on public opinion in twitter using cosine similarity. In: International Conference on Science and Technology-Computer, pp. 200–205 (2017)
Zhang, W., He, M.S.: Influence of opinion leaders on dynamics and diffusion of network public opinion. In: International Conference on Management Science and Engineering, pp. 139–144 (2013)
Pastor-Satorras, R., Castellano, C., Van Mieghem, P., Vespignani, A.: Epidemic processes in complex networks. Rev. Mod. Phys. 87, 925–979 (2015)
Attri, R., Grover, S.: Analysis of quality enabled factors in the product design stage of a production system life cycle: a relationship modelling approach. Int. J. Manag. Sci. Eng. Manag. 13, 65–73 (2018)
Amer, T.S., Abady, I.M.: On the application of kbm method for the 3-d motion of asymmetric rigid body. Nonlinear Dyn. 89(3), 1591–1609 (2017)
Ma, Z.E., Zhou, Y.C.: The Qualitative and Stability Theory of Ordinary Differential Equations. Science Press, Beijing (2001). (in Chinese)
Duarte, J., Januário, C., Martins, N., et al.: Chaos analysis and explicit series solutions to the seasonally forced sir epidemic model. J. Math. Biol. 78(7), 2235–2258 (2019)
Meucci, R., Euzzor, S., Zambrano, S., Pugliese, E., Francini, F., Arecchi, F.T.: Energy constraints in pulsed phase control of chaos. Phys. Lett. A 381, 82–86 (2017)
Shi, W., Wang, H., He, S.: Sentiment analysis of chinese microblogging based on sentiment ontology: a case study of 7.23 wenzhou train collision. Connect. Sci. 25(4), 161–178 (2013)
Banda, W.: An integrated framework comprising of ahp, expert questionnaire survey and sensitivity analysis for risk assessment in mining projects. Int. J. Manag. Sci. Eng. Manag. 14(3), 1–13 (2018)
Koyuncu, I., Ozcerit, A.T., Pehlivan, I.: Implementation of fpga-based real time novel chaotic oscillator. Nonlinear Dyn. 77(1–2), 49–59 (2014)
Albert, R., Barabási, A.: Statistical Mechanics of Complex Networks. Springer, Berlin (2003)
Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)
Watts, D.J., Strogatz, S.H.: Collective dynamics of small-word network. Nature 393, 393–440 (1998)
Barabasi, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)
Xia, C., Li, W., Sun, S., Wang, J.: An sir model with infection delay and propagation vector in complex networks. Nonlinear Dyn. 69(3), 927–934 (2012)
Bamakan, S.M.H., Nurgaliev, I., Qu, Q.: Opinion leader detection: a methodological review. Expert Syst. Appl. 15(5439), 200–222 (2019)
Ameur, L., Berdjoudj, L., Abbas, K.: Sensitivity analysis of the m/m/1 retrial queue with working vacations and vacation interruption. Int. J. Manag. Sci. Eng. Manag. 14(4), 1–11 (2019)
Dong, S., Fan, F.-H., Huang, Y.-C.: Studies on the population dynamics of a rumor-spreading model in online social networks. Phys. A Stat. Mech. Appl. 492, 10–20 (2018)
Acknowledgements
This work was supported by the Research on Social Public Opinion Management of Urban Disaster Events under the Background of Big Data, PR China, the National Social Science Fund Major Bidding Project (No. 17ZDA286) and the Basic Research Business Expenses Project for the Central Universities of Sichuan University (No. skzd2018-pt06). The authors would like to thank the anonymous referees for their insightful comments and suggestions to improve this paper, as well as the Uncertainty Decision-Making Laboratory of Sichuan University for helpful comments and discussion.
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Xu, J., Tang, W., Zhang, Y. et al. A dynamic dissemination model for recurring online public opinion. Nonlinear Dyn 99, 1269–1293 (2020). https://doi.org/10.1007/s11071-019-05353-3
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DOI: https://doi.org/10.1007/s11071-019-05353-3