Dynamics and near-optimal control in a stochastic rumor propagation model incorporating media coverage and Lévy noise

doi:10.1088/1674-1056/ac2f35

中国物理B ›› 2022, Vol. 31 ›› Issue (3): 30202-030202.doi: 10.1088/1674-1056/ac2f35

Dynamics and near-optimal control in a stochastic rumor propagation model incorporating media coverage and Lévy noise

Liang'an Huo(霍良安)^† and Yafang Dong(董雅芳)

Business School, University of Shanghai for Science and Technology, Shanghai 200093, China

收稿日期:2021-04-04 修回日期:2021-09-21 接受日期:2021-10-13 出版日期:2022-02-22 发布日期:2022-02-14
通讯作者: Liang'an Huo E-mail:huohuolin@yeah.net
基金资助:
Project supported by the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, and the Project for the Natural Science Foundation of Shanghai, China (Grant No. 21ZR1444100), and the Project for the National Natural Science Foundation of China (Grant Nos. 72174121, 71774111, 71871144, and 71804047).

Dynamics and near-optimal control in a stochastic rumor propagation model incorporating media coverage and Lévy noise

Liang'an Huo(霍良安)^† and Yafang Dong(董雅芳)

Business School, University of Shanghai for Science and Technology, Shanghai 200093, China

Received:2021-04-04 Revised:2021-09-21 Accepted:2021-10-13 Online:2022-02-22 Published:2022-02-14
Contact: Liang'an Huo E-mail:huohuolin@yeah.net
Supported by:
Project supported by the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, and the Project for the Natural Science Foundation of Shanghai, China (Grant No. 21ZR1444100), and the Project for the National Natural Science Foundation of China (Grant Nos. 72174121, 71774111, 71871144, and 71804047).

摘要/Abstract

摘要： The appearance of rumors intensifies people's panic and affects social stability. How to control the spread of rumors has become an important issue which is worth studying. In order to more accurately reflect the actual situation in the real world, a stochastic model incorporating media coverage and Lévy noise is proposed to describe the dynamic process of rumor propagation. By introducing two control strategies of popular science education and media coverage in an emergency event, an near-optimal control problem that minimizes the influence and control cost of rumor propagation is proposed. Sufficient conditions for near-optimal control of the model are established by using a Hamiltonian function. Then the necessary conditions for near-optimal control are obtained by using the Pontryagin maximum principle. Finally, the effect of popular science education, media coverage and Lévy noise on rumor propagation process control is verified by numerical simulation.

关键词: rumor propagation, near-optimal control, popular science education, media coverage, Lévy noise

Abstract: The appearance of rumors intensifies people's panic and affects social stability. How to control the spread of rumors has become an important issue which is worth studying. In order to more accurately reflect the actual situation in the real world, a stochastic model incorporating media coverage and Lévy noise is proposed to describe the dynamic process of rumor propagation. By introducing two control strategies of popular science education and media coverage in an emergency event, an near-optimal control problem that minimizes the influence and control cost of rumor propagation is proposed. Sufficient conditions for near-optimal control of the model are established by using a Hamiltonian function. Then the necessary conditions for near-optimal control are obtained by using the Pontryagin maximum principle. Finally, the effect of popular science education, media coverage and Lévy noise on rumor propagation process control is verified by numerical simulation.

Key words: rumor propagation, near-optimal control, popular science education, media coverage, Lévy noise

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) 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.

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]. Chin. Phys. B, 2022, 31(3): 30202-030202.

参考文献

[1] Chen X L and Wang N 2020 Sci. Rep. 10 5887
[2] Huo L A, Chen S J and Zhao L J 2021 Phys. A 571 125828
[3] Vardanjania H M, Heydaria S T, Dowranb B and Pasalarc M 2020 Integr. Med. Res. 9 100482
[4] Daley D J and Kendall D G 1965 IMA J. Appl. Math. 1 42
[5] 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
[6] Huo L A, Wang L and Zhao X M 2019 Phys. A 517 551
[7] Kawachi K, Seki M, Yoshida H, Otake Y, Warashina K and Ueda H 2008 J. Theor. Biol. 253 55
[8] Laarabi H, Abta A, Rachik M and Bouyaghroumni J 2016 Differ. Equ. Dyn. Syst. 24 407
[9] Zanette D H 2002 Phys. Rev. E 65 041908
[10] Albert R, Jeong H and Baraba'si A L 2000 Nature 406 378
[11] Doer B, Fouz M and Friedrich T 2012 Commun. ACM 55 70
[12] Liu Y, Diao S M, Zhu Y X and Liu Q 2016 Phys. A 461 543
[13] Dong S, Deng Y B and Huang Y C 2017 Commun. Theor. Phys. 68 545
[14] Zhao D L, Sun J B, Tan Y J and Wu J H 2018 Phys. A 512 1019
[15] Zhu L H and Huang X Y 2020 Commun. Theor. Phys. 72 015002
[16] Jia F J, Lv G Y and Zou G 2018 Math. Methods Appl. Sci. 41 1661
[17] Yu J Y and Liu M 2017 Phys. A 482 14
[18] Dauhoo M Z, Juggurnath D and Adam N R B 2016 Math. Soc. Sci. 82 85
[19] Jia F G and Lv G Y 2018 Phys. A 490 613
[20] Jia F G, Lv G Y, Wang S F and Zou G A 2018 J. Stat. Mech. Theory Exp. 2018 023502
[21] Jain A, Dhar J and Gupta V 2019 Phys. A 519 227
[22] El Bhih A, Ghazzali R, Ben Rhila S, Rachik M and Laaroussi A E 2020 Discrete Dyn. Nat. Soc. 2020 1
[23] Chen G H 2019 Phys. A 522 88
[24] Hui, H W, Zhou, C C, Lu X and Li J R 2020 Nonlinear Dyn. 101 1933
[25] Wang Q S and Song P J 2015 J. Organ. Comput. Electron. Commer. 25 98
[26] Huo L A and Cheng Y Y 2018 Discrete Dyn. Nat. Soc. 2018 4137129
[27] Nekovee M, Moreno Y, Bianconi G and Marsili M 2007 Phys. A 374 457
[28] Huo L A and Dong Y F 2020 Math. Methods Appl. Sci. 43 6903
[29] Applebaum D and Wang W 2004 Lévy Processes and Stochastic Calculus (New York:Cambridge University Press) 0521738652
[30] Mu X J and Zhang Q M 2019 Math. Methods Appl. Sci. 42 767
[31] Mu X J, Zhang Q M and Rong L B 2019 J. Franklin Inst. 356 11385
[32] Guo W J, Zhang Q M and Rong L B 2018 Inf. Sci. 467 670
[33] Ekeland I 1979 Bull. New. Ser. Am. Math. Soc. 1 443
[34] Menaldi J L 2001 SIAM Rev. 43 727
[35] Zhou Y L, Yuan S L and Zhao D L 2016 Appl. Math. Comput. 275 255
[36] Mao X R 2007 Stochastic Differential Equations and Applications 2nd ed. (Chichester:Horwood Publishing Ltd) 9781904275343
[37] Higham D J 2001 SIAM Rev. 43 525

Dynamics and near-optimal control in a stochastic rumor propagation model incorporating media coverage and Lévy noise

Dynamics and near-optimal control in a stochastic rumor propagation model incorporating media coverage and Lévy noise

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