Spread Mechanism and Control Strategies of Rumor Propagation Model Considering Rumor Refutation and Information Feedback in Emergency Management
<p>Rumor propagation model XYWZ1Z2-C in a closed system considering rumor refutation information feedback mechanism.</p> "> Figure 2
<p>Rumor propagation model XYWZ1Z2-O in an open system considering rumor refutation information feedback mechanism.</p> "> Figure 3
<p>Group density curves for rumor propagation in a closed system XYWZ1Z2-C.</p> "> Figure 4
<p>Group density curves with <span class="html-italic">φ</span> = 0.9, 0.7, 0.5, 0.3 for (<b>a</b>) X; (<b>b</b>) Y; (<b>c</b>) W; (<b>d</b>) Z1; (<b>e</b>) Z2. Note: The solid line was used for <span class="html-italic">φ</span> = 0.9, the dashed line for <span class="html-italic">φ</span> = 0.7, the dotted line for <span class="html-italic">φ</span> = 0.5, and the dash-dotted line for <span class="html-italic">φ</span> = 0.3.</p> "> Figure 5
<p>Group density curves with <span class="html-italic">λ</span> = 0.05, 0.1, 0.2, 0.4 for (<b>a</b>) X; (<b>b</b>) Y; (<b>c</b>) W; (<b>d</b>) Z1; (<b>e</b>) Z2. Note: the solid line was used for <span class="html-italic">λ</span> = 0.05, the dashed line for <span class="html-italic">λ</span> = 0.1 the dotted line for <span class="html-italic">λ</span> = 0.2, and the dash-dotted line for <span class="html-italic">λ</span> = 0.4.</p> "> Figure 6
<p>Group density curves with <span class="html-italic">η</span> = 0.01, 0.1, 0.99 for (<b>a</b>) X; (<b>b</b>) Y; (<b>c</b>) W; (<b>d</b>) Z1; (<b>e</b>) Z2. Note: solid line was used for <span class="html-italic">η</span> = 0.01; dashed line for <span class="html-italic">η</span> = 0.1; dotted line for <span class="html-italic">η</span> = 0.99.</p> "> Figure 7
<p>Group density curves with (1 − θ) = 0.1, 0.4, 0.7, 0.9 for (<b>a</b>) X; (<b>b</b>) Y; (<b>c</b>) W; (<b>d</b>) Z1; (<b>e</b>) Z2. Note: The solid line was used for (1 − θ) = 0.1; the dashed line for (1 − θ) = 0.4; dotted line for (1 − θ) = 0.7; the dash-dotted line for (1 − θ) = 0.9.</p> "> Figure 8
<p>Comparative analysis of rumor propagation general rules between open system XYWZ1Z2-O and closed system XYWZ1Z2-C for (<b>a</b>) X; (<b>b</b>) Y; (<b>c</b>) W; (<b>d</b>) Z1; (<b>e</b>) Z2. Note: The solid line was used for κ = μ = 0; dashed line for <span class="html-italic">κ</span> = <span class="html-italic">μ</span> = 0.005.</p> "> Figure 9
<p>Rumor propagation rules analysis at a critical point in an open system XYWZ1Z2-O for (<b>a</b>) X; (<b>b</b>) Y; (<b>c</b>) W; (<b>d</b>) Z1; (<b>e</b>) Z2. Note: solid line was used for <span class="html-italic">κ</span> = <span class="html-italic">μ</span> = 0.04, <span class="html-italic">φ</span> = 0.19 and R<sub>0</sub> < 1, dashed line for <span class="html-italic">κ</span> = <span class="html-italic">μ</span> = 0.04, <span class="html-italic">φ</span> = 0.2, R<sub>0</sub> = 1, and dotted line for κ = μ = 0.04, <span class="html-italic">φ</span> = 0.21, R<sub>0</sub> > 1.</p> "> Figure 10
<p>Impact analysis of immigration and emigration rate for rumor propagation in an open system XYWZ1Z2-O for (<b>a</b>) X; (<b>b</b>) Y; (<b>c</b>) W; (<b>d</b>) Z1; (<b>e</b>) Z2. Note: The solid line was used for <span class="html-italic">κ</span> = <span class="html-italic">μ</span> = 0.005; dashed line for <span class="html-italic">κ</span> = <span class="html-italic">μ</span> = 0.01.</p> ">
Abstract
:1. Introduction
- (1)
- The rumor refutation mechanism and information feedback mechanism are considered. The groups in the rumor propagation system are redivided and redefined, a new kind of people—the skeptic is introduced into the model, and the stiflers are divided into stiflers who believe the rumor and stiflers who do not believe the rumor.
- (2)
- The rumor propagation model is analyzed in both the closed system and open system, and the development process of rumor spreading is comprehensively described, and the general rules of rumor propagation under the influence of population migration are studied.
- (3)
- Multiple influencing factors besides effective feedback mechanisms are comprehensively considered in this paper.
2. Rumor Propagation Models Considering Rumor Refutation and Information Feedback
2.1. Rumour Propagation Model XYWZ1Z2-C in a Closed System
2.2. Rumor Propagation Model XYWZ1Z2-O in an Open System
3. Analysis of Rumor Propagation Rules in a Closed System
3.1. Analysis of the General Rules of Rumor Propagation in a Closed System
3.2. Impact of Ignorant with Critical Ability on Rumor Propagation
3.3. Impact of Rumor Refutation Mechanism on Rumor Propagation
3.4. Impact of the Importance of Identifying Rumor on Rumor Propagation
3.5. Impact of Skeptics’ Ability to Identify Rumors on Rumor Propagation
4. Analysis of Rumor Propagation Rules in an Open System
4.1. Analysis of the General Rules of Rumor Propagation in an Open System
4.2. Analysis on the Rumor Spreading Rules at the Critical Point
4.3. Impact of Immigration and Emigration Rate on Rumor Propagation
5. Discussion and Conclusions
5.1. Discussion about the Application
5.2. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Daley, D.J.; Kendall, D.G. Stochastic rumours. J. Inst. Math. Its Appl. 1965, 1, 42–55. [Google Scholar] [CrossRef]
- Maki, D.P.; Thompson, M. Mathematical Models and Applications: With Emphasis on the Social, Life, and Management Sciences; Prentice-Hall: Princeton, NJ, USA, 1973. [Google Scholar]
- Huo, L.-A.; Chen, S.; Zhao, L.-J. Dynamic analysis of the rumor propagation model with consideration of the wise man and social reinforcement. Phys. A Stat. Mech. Its Appl. 2021, 571, 125828. [Google Scholar] [CrossRef]
- Yang, S.; Jiang, H.-J.; Hu, C.; Yu, J.; Li, J.-R. Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment. Adv. Differ. Equations 2020, 2020, 628. [Google Scholar] [CrossRef]
- Zhu, L.-H.; Huang, X.-Y.; Liu, Y.; Zhang, Z.-D. Spatiotemporal dynamics analysis and optimal control method for an SI reaction-diffusion propagation model. J. Math. Anal. Appl. 2021, 493, 124539. [Google Scholar] [CrossRef]
- Abta, A.; Laarabi, H.; Rachik, M.; Alaoui, H.T.; Boutayeb, S. Optimal control of a delayed rumor propagation model with saturated control functions and L^(1-) type objectives. Soc. Netw. Anal. Min. 2020, 10, 1–15. [Google Scholar] [CrossRef]
- Laarabi, H.; Abta, A.; Rachik, M.; Bouyaghroumni, J. Stability analysis of a delayed rumor propagation model. Differ. Equ. Dyn. Syst. 2016, 24, 407–415. [Google Scholar] [CrossRef]
- Huo, L.-A.; Huang, P.-Q.; Guo, C.-X. Analyzing the dynamics of a rumor transmission model with incubation. Discret. Dyn. Nat. Soc. 2012, 328151. [Google Scholar] [CrossRef]
- Jain, A.; Dhar, J.; Gupta, V. Rumor model on homogeneous social network incorporating delay in expert intervention and government action. Commun. Nonlinear Sci. 2020, 84, 105189. [Google Scholar] [CrossRef]
- Wang, H.; Deng, L.; Huang, Y.-S.; Zhao, S. A variant epidemic propagation model suitable for rumor spreading in online social network. In Proceedings of the International Conference on Machine Learning & Cybernetics, Xi′an, China, 15–17 July 2012; pp. 1258–1262. [Google Scholar] [CrossRef]
- Zan, Y.-L.; Wu, J.-J.; Li, P.; Yu, Q.-L. SICR rumor spreading model in complex networks: Counterattack and self-resistance. Phys. A Stat. Mech. Its Appl. 2014, 405, 159–170. [Google Scholar] [CrossRef]
- Xia, L.-L.; Jiang, G.-P.; Song, B.; Song, Y.R. Rumor spreading model considering hesitating mechanism in complex social networks. Phys. A Stat. Mech. Its Appl. 2015, 437, 295–303. [Google Scholar] [CrossRef]
- Fu, M.-L.; Feng, J.; Lande, D.; Dmytrenko, O.; Manko, D.; Prakapovich, R. Dynamic model with super spreaders and lurker users for preferential information propagation analysis. Phys. A Stat. Mech. Its Appl. 2021, 561, 125266. [Google Scholar] [CrossRef]
- Huo, L.A.; Lin, T.; Huang, P. Dynamical behavior of a rumor transmission model with psychological effect in emergency event. Abstr. Appl. Anal. 2013, 4339–4344. [Google Scholar] [CrossRef] [Green Version]
- Nekovee, M.; Moreno, Y.; Bianconi, G.; Marsili, M. Theory of rumour spreading in complex social networks. Phys. A Stat. Mech. Its Appl. 2008, 374, 457–470. [Google Scholar] [CrossRef] [Green Version]
- Kawachi, K.; Seki, M.; Yoshida, H.; Otake, Y.; Warashina, K.; Ueda, H. A rumor transmission model with various contact interactions. J. Theor. Biol. 2008, 253, 55–60. [Google Scholar] [CrossRef] [PubMed]
- Zhao, L.-J.; Wang, Q.; Cheng, J.-J.; Chen, Y.C.; Wang, J.-J.; Huang, W. Rumor spreading model with consideration of forgetting mechanism: A case of online blogging LiveJournal. Phys. A Stat. Mech. Its Appl. 2011, 390, 2619–2625. [Google Scholar] [CrossRef]
- Wang, Y.-Q.; Yang, X.-Y.; Han, Y.-L.; Wang, X.-A. Rumor spreading model with trust mechanism in complex social networks. Commun. Theor. Phys. 2013, 59, 510–516. [Google Scholar] [CrossRef]
- Qiu, L.-Q.; Liu, S.-Q. C-SIW rumor propagation model with variable propagation rate and perception mechanism in social networks. Discret. Dyn. Nat. Soc. 2020, 5712968. [Google Scholar] [CrossRef]
- Afassinou, K. Analysis of the impact of education rate on the rumor spreading mechanism. Phys. A Stat. Mech. Its Appl. 2014, 414, 43–52. [Google Scholar] [CrossRef]
- Hui, H.-W.; Zhou, C.-C.; Lu, X.; Li, J.-R. Spread mechanism and control strategy of social network rumors under the influence of COVID-19. Nonlinear Dyn. 2020, 101, 1933–1949. [Google Scholar] [CrossRef]
- Hosni, A.I.E.; Li, K.; Ahmad, S. Analysis of the impact of online social networks addiction on the propagation of rumors. Phys. A Stat. Mech. Its Appl. 2020, 542, 123456. [Google Scholar] [CrossRef]
- Chen, X.-L.; Wang, N. Rumor spreading model considering rumor credibility, correlation and crowd classification based on personality. Sci. Rep. 2020, 10, 5887. [Google Scholar] [CrossRef] [Green Version]
- Srinivasan, S.; Babu, D.L.D. A social immunity based approach to suppress rumors in online social networks. Int. J. Mach. Learn. Cybern. 2021, 12, 1281–1296. [Google Scholar] [CrossRef]
- Zhang, Z.-L.; Zhang, Z.-Q. An interplay model for rumour spreading and emergency development. Phys. A Stat. Mech. Its Appl. 2009, 388, 4159–4166. [Google Scholar] [CrossRef]
- Huo, L.-A.; Huang, P.-Q.; Fang, X. An interplay model for authorities′ actions and rumor spreading in emergency event. Phys. A Stat. Mech. Its Appl. 2011, 390, 3267–3274. [Google Scholar] [CrossRef]
- Zhao, L.-J.; Wang, Q.; Cheng, J.-J.; Zhang, D.; Ma, T.; Chen, Y.-C.; Wang, J.-J. The impact of authorities′ media and rumor dissemination on the evolution of emergency. Phys. A Stat. Mech. Its Appl. 2012, 391, 3978–3987. [Google Scholar] [CrossRef]
- Zhao, L.-J.; Wang, X.-L.; Qiu, X.-Y.; Wang, J.-J. A model for the spread of rumors in Barrat–Barthelemy–Vespignani (BBV) networks. Phys. A Stat. Mech. Its Appl. 2013, 392, 5542–5551. [Google Scholar] [CrossRef]
- Zhao, L.-J.; Wang, J.-J.; Chen, Y.-C.; Wang, Q.; Cheng, J.-J.; Cui, H.-X. SIHR rumor spreading model in social networks. Phys. A Stat. Mech. Its Appl. 2012, 391, 2444–2453. [Google Scholar] [CrossRef]
φ | α | δ | η | θ | λ |
---|---|---|---|---|---|
0.5 | 0.2 | 0.2 | 0.1 | 0.5 | 0.2 |
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Chen, J.; Chen, C.; Song, Q.; Zhao, Y.; Deng, L.; Xie, R.; Yang, S. Spread Mechanism and Control Strategies of Rumor Propagation Model Considering Rumor Refutation and Information Feedback in Emergency Management. Symmetry 2021, 13, 1694. https://doi.org/10.3390/sym13091694
Chen J, Chen C, Song Q, Zhao Y, Deng L, Xie R, Yang S. Spread Mechanism and Control Strategies of Rumor Propagation Model Considering Rumor Refutation and Information Feedback in Emergency Management. Symmetry. 2021; 13(9):1694. https://doi.org/10.3390/sym13091694
Chicago/Turabian StyleChen, Jianhong, Chaoqun Chen, Qinghua Song, Yifei Zhao, Longxin Deng, Raoqing Xie, and Shan Yang. 2021. "Spread Mechanism and Control Strategies of Rumor Propagation Model Considering Rumor Refutation and Information Feedback in Emergency Management" Symmetry 13, no. 9: 1694. https://doi.org/10.3390/sym13091694
APA StyleChen, J., Chen, C., Song, Q., Zhao, Y., Deng, L., Xie, R., & Yang, S. (2021). Spread Mechanism and Control Strategies of Rumor Propagation Model Considering Rumor Refutation and Information Feedback in Emergency Management. Symmetry, 13(9), 1694. https://doi.org/10.3390/sym13091694