Dynamic analysis of a rumor propagation model considering individual identification ability

Xintong Wang; Sida Kang; Yuhan Hu; Xintong Wang; Sida Kang; Yuhan Hu

doi:10.3934/math.2025107

AIMS Mathematics

2025, Volume 10, Issue 2: 2295-2320. doi: 10.3934/math.2025107

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Research article

Dynamic analysis of a rumor propagation model considering individual identification ability

1.
School of Science, University of Science and Technology Liaoning, Anshan, 114051, China
2.
School of Business Administration, University of Science and Technology Liaoning, Anshan 114051, China

Received: 04 December 2024 Revised: 20 January 2025 Accepted: 26 January 2025 Published: 10 February 2025
MSC : 34D20, 37D35, 49J15

In the 2016 US presidential election, the widespread propagation of false news on social media, especially rumors against Hillary Clinton, quickly affected the emotions and decisions of some voters, highlighting the potential impact of rumors on voters' perceptions and election results. An individual's ability to identify rumor information determines their tendency to judge and spread rumors, thus directly affecting the spread of rumors and society's trust in information. Considering the impact of individual identification ability on rumor propagation, this paper established a new rumor propagation model, calculated the basic reproductive number of the model, and proved the existence of equilibrium points in the model as well as their local and global asymptotic stability. Meanwhile, based on Pontryagin's maximum principle, we chose the probability of contact between ignorant individuals and rumor spreaders, the probability of conversion of spreaders into immunized individuals, and the contact rate between rumor spreaders and truth spreaders as the optimal control variables, and obtained an effective strategy for reducing rumor spreading. The numerical simulation verified the results of theoretical analysis. The findings of this study suggest that enhancing individual identification ability can effectively slow down the propagation of rumors.
- rumor propagation model,
- basic reproduction number,
- stability analysis,
- optimal control,
- individual identification ability
Citation: Xintong Wang, Sida Kang, Yuhan Hu. Dynamic analysis of a rumor propagation model considering individual identification ability[J]. AIMS Mathematics, 2025, 10(2): 2295-2320. doi: 10.3934/math.2025107

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Abstract

In the 2016 US presidential election, the widespread propagation of false news on social media, especially rumors against Hillary Clinton, quickly affected the emotions and decisions of some voters, highlighting the potential impact of rumors on voters' perceptions and election results. An individual's ability to identify rumor information determines their tendency to judge and spread rumors, thus directly affecting the spread of rumors and society's trust in information. Considering the impact of individual identification ability on rumor propagation, this paper established a new rumor propagation model, calculated the basic reproductive number of the model, and proved the existence of equilibrium points in the model as well as their local and global asymptotic stability. Meanwhile, based on Pontryagin's maximum principle, we chose the probability of contact between ignorant individuals and rumor spreaders, the probability of conversion of spreaders into immunized individuals, and the contact rate between rumor spreaders and truth spreaders as the optimal control variables, and obtained an effective strategy for reducing rumor spreading. The numerical simulation verified the results of theoretical analysis. The findings of this study suggest that enhancing individual identification ability can effectively slow down the propagation of rumors.

References

[1]	M. Nekovee, Y. Moreno, G. Bianconi, M. Marsili, Theory of rumour spreading in complex social networks, Physica A, 374 (2007), 457–470. http://doi.org/10.1016/j.physa.2006.07.017 doi: 10.1016/j.physa.2006.07.017
[2]	F. Chierichetti, S. Lattanzi, A. Panconesi, Rumor spreading in social networks, Theor. Comput. Sci., 412 (2011), 2602–2610. https://doi.org/10.1016/j.tcs.2010.11.001 doi: 10.1016/j.tcs.2010.11.001
[3]	J. Wu, M. Zheng, Z. K. Zhang, W. Wang, C. Gu, Z. Liu, A model of spreading of sudden events on social networks, Chaos, 28 (2018), 033105. https://doi.org/10.1063/1.5009315 doi: 10.1063/1.5009315
[4]	D. J. Daley, D. G. Kendall, Stochastic rumours, IMA J. Appl. Math., 1 (1965), 42–55. https://doi.org/10.1093/imamat/1.1.42 doi: 10.1093/imamat/1.1.42
[5]	D. J. Daley, D. G. Kendall, Epidemics and rumours, Nature, 204 (1964), 1118. http://doi.org/10.1038/2041118a0 doi: 10.1038/2041118a0
[6]	C. Lefevre, P. Picard Distribution of the final extent of a rumour process, J. Appl. Probab., 31 (1994), 244–249. https://doi.org/10.2307/3215250 doi: 10.2307/3215250
[7]	B. Pittel, On a Daley-Kendall model of random rumours, J. Appl. Probab., 27 (1990), 14–27. https://doi.org/10.2307/3214592 doi: 10.2307/3214592
[8]	D. P. Maki, Mathematical models and applications, with emphasis on the social, life, and management sciences, Prentice-Hall, 1973.
[9]	J. Liu, J. Qi, Online public rumor engagement model and intervention strategy in major public health emergencies: From the perspective of social psychological stress, Int. J. Environ. Res. Public Health, 19 (2022), 1988. https://doi.org/10.3390/ijerph19041988 doi: 10.3390/ijerph19041988
[10]	K. Fan, Y. Zhang, S. Gao, X. Wei, A class of stochastic delayed SIR epidemic models with generalized nonlinear incidence rate and temporary immunity, Physica A, 481 (2017), 198–208. https://doi.org/10.1016/j.physa.2017.04.055 doi: 10.1016/j.physa.2017.04.055
[11]	K. Hattaf, A. Lashari, Y. Louartassi, N. Yousfi, A delayed SIR epidemic model with a general incidence rate, Electron. J. Qual. Theory Differ. Equ., 2013, 1–9. http://doi.org/10.14232/ejqtde.2013.1.3 doi: 10.14232/ejqtde.2013.1.3
[12]	S. Kwon, M. Cha, K. Jung, W. Chen, Y. Wang, Prominent features of rumor propagation in online social media, In: 2013 IEEE 13th International Conference on Data Mining, 2013, 1103–1108. https://doi.org/10.1109/ICDM.2013.61
[13]	P. Ozturk, H. Li, Y. Sakamoto, Combating rumor spread on social media: The effectiveness of refutation and warning, In: 2015 48th Hawaii International Conference on System Sciences, 2015, 2406–2414. https://doi.org/10.1109/HICSS.2015.288
[14]	W. Pan, W. Yan, Y. Hu, R. He, L. Wu, Dynamic analysis and optimal control of rumor propagation model with reporting effect, Adv. Math. Phys., 2022, 5503137. https://doi.org/10.1155/2022/5503137 doi: 10.1155/2022/5503137
[15]	W. Pan, W. Yan, Y. Hu, R. He, L. Wu, Dynamic analysis of a SIDRW rumor propagation model considering the effect of media reports and rumor refuters, Nonlinear Dyn., 111 (2023), 3925–3936. https://doi.org/10.1007/s11071-022-07947-w doi: 10.1007/s11071-022-07947-w
[16]	L. Huo, Y. Dong, Analyzing the dynamics of a stochastic rumor propagation model incorporating media coverage, Math. Method. Appl. Sci., 43 (2020), 6903–6920. https://doi.org/10.1002/mma.6436 doi: 10.1002/mma.6436
[17]	H. Guo, X. Yan, Y. Niu, J. Zhang, Dynamic analysis of rumor propagation model with media report and time delay on social networks, J. Appl. Math. Comput., 69 (2023), 2473–2502. https://doi.org/10.1007/s12190-022-01829-5 doi: 10.1007/s12190-022-01829-5
[18]	S. Yang, S. Liu, K. Su, J. Chen, A rumor propagation model considering media effect and suspicion mechanism under public emergencies, Mathematics, 12 (2024), 1906. https://doi.org/10.3390/math12121906 doi: 10.3390/math12121906
[19]	Y. Tian, X. Ding, Rumor spreading model with considering debunking behavior in emergencies, Appl. Math. Comput., 363 (2019), 124599. https://doi.org/10.1016/j.amc.2019.124599 doi: 10.1016/j.amc.2019.124599
[20]	N. Zhang, J. Song, K. Chen, S. Jia, Emotional contagion in the propagation of online rumors, Issues Inform. Syst., 23 (2022), 1–19. https://doi.org/10.48009/2_iis_2022_101 doi: 10.48009/2_iis_2022_101
[21]	L. Qiu, S. Liu, SVIR rumor spreading model considering individual vigilance awareness and emotion in social networks, Int. J. Mod. Phys. C, 32 (2021), 2150120. https://doi.org/10.1142/s0129183121501205 doi: 10.1142/s0129183121501205
[22]	R. Zeng, D. Zhu, A model and simulation of the emotional contagion of netizens in the process of rumor refutation, Sci. Rep., 9 (2019), 14164. https://doi.org/10.1038/s41598-019-50770-4 doi: 10.1038/s41598-019-50770-4
[23]	L. L. Xia, G. P. Jiang, B. Song, Y. R. Song, Rumor spreading model considering hesitating mechanism in complex social networks, Physica A, 437 (2015), 295–303. https://doi.org/10.1016/j.physa.2015.05.113 doi: 10.1016/j.physa.2015.05.113
[24]	X. Liu, T. Li, M. Tian, Rumor spreading of a $SEIR$ model in complex social networks with hesitating mechanism, Adv. Differ. Equ., 2018 (2018), 391. https://doi.org/10.1186/s13662-018-1852-z doi: 10.1186/s13662-018-1852-z
[25]	J. Chen, H. Ma, S. Yang, SEIOR rumor propagation model considering hesitating mechanism and different rumor-refuting ways in complex networks, Mathematics, 11 (2023), 283. https://doi.org/10.3390/math11020283 doi: 10.3390/math11020283
[26]	L. Zhao, Q. Wang, J. Cheng, Y. Chen, J. Wang, W. Huang, Rumor spreading model with consideration of forgetting mechanism: A case of online blogging LiveJournal, Physica A, 390 (2011), 2619–2625. https://doi.org/10.1016/j.physa.2011.03.010 doi: 10.1016/j.physa.2011.03.010
[27]	L. Zhao, X. Qiu, X. Wang, J. Wang, Rumor spreading model considering forgetting and remembering mechanisms in inhomogeneous networks, Physica A, 392 (2013), 987–994. https://doi.org/10.1016/j.physa.2012.10.031 doi: 10.1016/j.physa.2012.10.031
[28]	L. Zhao, J. Wang, Y. Chen, Q. Wang, J. Cheng, H. Cui, SIHR rumor spreading model in social networks, Physica A, 391 (2012), 2444–2453. https://doi.org/10.1016/j.physa.2011.12.008 doi: 10.1016/j.physa.2011.12.008
[29]	H. Ding, L. Xie, Simulating rumor spreading and rebuttal strategy with rebuttal forgetting: An agent-based modeling approach, Physica A, 612 (2023), 128488. https://doi.org/10.1016/j.physa.2023.128488 doi: 10.1016/j.physa.2023.128488
[30]	H. Sha, L. Zhu, Dynamic analysis of pattern and optimal control research of rumor propagation model on different networks, Inform. Process. Manag., 62 (2025), 104016. https://doi.org/10.1016/j.ipm.2024.104016 doi: 10.1016/j.ipm.2024.104016
[31]	B. Li, L. Zhu, Turing instability analysis of a reaction–diffusion system for rumor propagation in continuous space and complex networks, Inform. Process. Manag., 61 (2024), 103621. https://doi.org/10.1016/j.ipm.2023.103621 doi: 10.1016/j.ipm.2023.103621
[32]	T. Yuan, G. Guan, S. Shen, L. Zhu, Stability analysis and optimal control of epidemic-like transmission model with nonlinear inhibition mechanism and time delay in both homogeneous and heterogeneous networks, J. Math. Anal. Appl., 526 (2023), 127273. https://doi.org/10.1016/j.jmaa.2023.127273 doi: 10.1016/j.jmaa.2023.127273

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