Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise

doi:10.1088/1674-1056/ac0423

中国物理B ›› 2021, Vol. 30 ›› Issue (8): 80201-080201.doi: 10.1088/1674-1056/ac0423

• • 下一篇

Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise

Liang-An Huo(霍良安)¹, Ya-Fang Dong(董雅芳)¹, and Ting-Ting Lin(林婷婷)^2,†

1 Business School, University of Shanghai for Science and Technology, Shanghai 200093, China;
2 School of Electrical and Information Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

收稿日期:2021-03-22 修回日期:2021-05-18 接受日期:2021-05-24 出版日期:2021-07-16 发布日期:2021-08-09
通讯作者: Ting-Ting Lin E-mail:lintingting00@163.com
基金资助:
Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, and the Project for the Natural Science Foundation of Shanghai (Grant No. 21ZR1444100), and the Project for the National Natural Science Foundation of China (Grant Nos. 71774111, 61702331, 71871144).

Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise

Liang-An Huo(霍良安)¹, Ya-Fang Dong(董雅芳)¹, and Ting-Ting Lin(林婷婷)^2,†

1 Business School, University of Shanghai for Science and Technology, Shanghai 200093, China;
2 School of Electrical and Information Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Received:2021-03-22 Revised:2021-05-18 Accepted:2021-05-24 Online:2021-07-16 Published:2021-08-09
Contact: Ting-Ting Lin E-mail:lintingting00@163.com
Supported by:
Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, and the Project for the Natural Science Foundation of Shanghai (Grant No. 21ZR1444100), and the Project for the National Natural Science Foundation of China (Grant Nos. 71774111, 61702331, 71871144).

摘要/Abstract

摘要： With the development of information technology, rumors propagate faster and more widely than in the past. In this paper, a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise is proposed. The global positivity of the solution process is proved, and further the basic reproductive number R₀ is obtained. When R₀ < 1, the dynamical process of system with Lévy jump tends to the rumor-free equilibrium point of the deterministic system, and the rumor tends to extinction; when R₀ > 1, the rumor will keep spreading and the system will oscillate randomly near the rumor equilibrium point of the deterministic system. The results show that the oscillation amplitude is related to the disturbance of the system. In addition, increasing media coverage can effectively reduce the final spread of rumors. Finally, the above results are verified by numerical simulation.

关键词: rumor propagation, stochastic process, Lévy jump, media coverage

Abstract: With the development of information technology, rumors propagate faster and more widely than in the past. In this paper, a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise is proposed. The global positivity of the solution process is proved, and further the basic reproductive number R₀ is obtained. When R₀ < 1, the dynamical process of system with Lévy jump tends to the rumor-free equilibrium point of the deterministic system, and the rumor tends to extinction; when R₀ > 1, the rumor will keep spreading and the system will oscillate randomly near the rumor equilibrium point of the deterministic system. The results show that the oscillation amplitude is related to the disturbance of the system. In addition, increasing media coverage can effectively reduce the final spread of rumors. Finally, the above results are verified by numerical simulation.

Key words: rumor propagation, stochastic process, Lévy jump, media coverage

中图分类号: (Partial differential equations)

02.30.Jr

02.50.Ey (Stochastic processes) 02.50.Fz (Stochastic analysis) 02.30.-f (Function theory, analysis)

Liang-An Huo(霍良安), Ya-Fang Dong(董雅芳), and Ting-Ting Lin(林婷婷). Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise[J]. 中国物理B, 2021, 30(8): 80201-080201.

Liang-An Huo(霍良安), Ya-Fang Dong(董雅芳), and Ting-Ting Lin(林婷婷). Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise[J]. Chin. Phys. B, 2021, 30(8): 80201-080201.

参考文献

[1] Chen G H 2019 Phys. A 522 88
[2] Zhou X Z and Feng H H 2019 J. Comput. Commun. 7 1
[3] Choi D J, Chun S L, Oh H C, Han J Y and Kwon T 2020 Sci. Rep. 1
[4] Alkhodair S A, Ding S H H, Fung B C M and Liu J Q 2020 Inf. Process. Manag. 57 102018
[5] Li Q Z, Zhang Q, Si L and Liu Y C 2019 Rumor Detection on Social Media:Datasets, Methods and Opportunities p. 66
[6] Daley D J and Kendal D G 1965 J. Inst. Maths Applics 1 42
[7] Maki D P and Thompson M 1973 Mathematical models and applications:With emphasis on the social, life, and management sciences (New Jersey:Prentice-Hall) 9780135616703
[8] Zanette D H 2001 Phys. Rev. E 64 050901
[9] Zanette D H 2002 Phys. Rev. E 65 041908
[10] Moreno Y, Nekovee M and Pacheco A F 2004 Phys. Rev. E 69 066130
[11] Li Y F and Cui J G 2009 Commun. Nonlinear Sci. Numer. Simul 14 2353
[12] Sun C J, Yang W Arino J and Khan K 2011 Math. Biosci. 230 87
[13] Tchuenche J Dube N Bhunu C Smith R and Bauch C 2011 BMC Public Health 11 1
[14] Li J R, Jiang H J, Yu Z Y and Hu C 2019 Appl. Math. Comput. 359 374
[15] Huo L A, Wang L and Zhao X M 2019 Phys. A 517 551
[16] Yan J, Santosh V, Itai H and Glen N 2018 Am. J. Infect. Control 46 850
[17] Misra A K, Sharma A and Shukla J B 2011 Math. Comput. Model. Dyn. Syst. 53 1221
[18] Zhou X Z and Feng H H 2019 J. Comput. Commun. 7 1
[19] Lung X Y and Wan Y H 2017 Nanjing Youdian Daxue Xuebao 37 120
[20] Dauhoo M Z, Juggurnath D and Badurally A N 2016 Math. Soc. Sci. 82 85
[21] Jia F G and Lv G Y 2018 Phys. A 490 613
[22] Li D X and Li Y 2017 Chin. Phys. B 26 090203
[23] Ankur J, Joydip D and Vijay G 2019 Phys. A 519 227
[24] Lévy P 1934 Ann. R. Scuola Norm. Super. Pisa 3 337
[25] Khintchine 1937 Bull. Moscow State Univ. 1 1
[26] Brockmann D, Hufnagel L and Geisel T 2006 Nature 439 462
[27] Nekovee M, Moreno Y Bianconi G and Marsili M 2007 Phys. A 374 457
[28] Applebaum D 2009 Lévy process and stochastic calculus (New York:Cambridge Press)
[29] Øksendal B and Sulen A 2005 Applied stochastic control of jump diffusions (Berlin:Springer)
[30] Situ R 2005 Theory of stochastic differential equations with jumps and applications (Berlin:Springer)
[31] Mao X 2008 Stochastic differential equations and applications 2nd Ed. (Chichester:Horwood)
[32] Zheng J, Lin Z Y, Tong C Q and Ye R D 2017 Phys. A 473 461

Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise

Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Yuhuai Zhang(张宇槐) and Jianjun Zhu(朱建军). Ergodic stationary distribution of a stochastic rumor propagation model with general incidence function[J]. 中国物理B, 2022, 31(6): 60202-060202.
[2]	Xian-Li Sun(孙先莉), You-Guo Wang(王友国), and Lin-Qing Cang(仓林青). Correlation and trust mechanism-based rumor propagation model in complex social networks[J]. 中国物理B, 2022, 31(5): 50202-050202.
[3]	Wei-Jing Zhu(朱薇静) and Bao-Quan Ai(艾保全). Ratchet transport of self-propelled chimeras in an asymmetric periodic structure[J]. 中国物理B, 2022, 31(4): 40503-040503.
[4]	Liang'an Huo(霍良安) and Yafang Dong(董雅芳). Dynamics and near-optimal control in a stochastic rumor propagation model incorporating media coverage and Lévy noise[J]. 中国物理B, 2022, 31(3): 30202-030202.
[5]	Liang'an Huo(霍良安) and Xiaomin Chen(陈晓敏). Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model[J]. 中国物理B, 2022, 31(11): 110204-110204.
[6]	Liang'an Huo(霍良安) and Xiaomin Chen(陈晓敏). Near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters[J]. 中国物理B, 2021, 30(12): 120205-120205.
[7]	朱薇静, 黄小群, 艾保全. Transport of velocity alignment particles in random obstacles[J]. 中国物理B, 2018, 27(8): 80504-080504.
[8]	胡高歌, 高社生, 种永民, 高兵兵. Stochastic stability of the derivative unscented Kalman filter[J]. 中国物理B, 2015, 24(7): 70202-070202.
[9]	王蕊, 孙辉, 马振洋. Stability and performance analysis of a jump linear control system subject to digital upsets[J]. , 2015, 24(4): 40201-040201.
[10]	Ferhat Nutku, Ekrem Aydıner. Current and efficiency of Brownian particles under oscillating forces in entropic barriers[J]. 中国物理B, 2015, 24(4): 40501-040501.
[11]	袁若石, 马易安, 苑波, 敖平. Lyapunov function as potential function：A dynamical equivalence[J]. Chin. Phys. B, 2014, 23(1): 10505-010505.
[12]	邢琦彬, 张元标, 梁志宁, 张帆. Dynamics of organizational rumor communication on connecting multi-small-world networks[J]. 中国物理B, 2011, 20(12): 120204-120204.
[13]	覃英华, 罗晓曙, 韦笃取. Random-phase-induced chaos in power systems[J]. 中国物理B, 2010, 19(5): 50511-050511.
[14]	王成玉, 高云, 宋玉敏, 周鹏, 杨海. Stochastic systems with cross-correlated Gaussian white noises[J]. 中国物理B, 2010, 19(11): 116401-116801.
[15]	商朋见, 申金升. Multi-fractal analysis of highway traffic data[J]. 中国物理B, 2007, 16(2): 365-373.