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Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model |
| Liang'an Huo(霍良安)† and Xiaomin Chen(陈晓敏) |
| Business School, University of Shanghai for Science and Technology, Shanghai 200093, China |
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Abstract The Internet era has brought great convenience to our life and communication. Meanwhile, it also makes a bunch of rumors propagate faster and causes even more harm to human life. Therefore, it is necessary to perform effective control mechanisms to minimize the negative social impact from rumors. Thereout, firstly, we formulate a rumor spreading model considering psychological factors and thinking time, then, we add white noise (i.e., stochastic interference) and two pulse control strategies which denote education mechanism and refutation mechanism into the model. Secondly, we obtain the global positive solutions and demonstrate the global exponential stability of the unique positive periodic rumor-free solution. Thirdly, we discuss the extinction and persistence of rumor. Moreover, we use Pontriagin's minimum principle to explore the optimal impulse control. Finally, several numerical simulations are carried out to verify the effectiveness and availability of the theoretical analysis. We conclude that the pulse control strategies have a great influence on controlling rumor spreading, and different control strategies should be adopted under different transmission scenarios.
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Received: 15 November 2021
Revised: 13 April 2022
Accepted manuscript online: 11 October 2022
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PACS:
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02.30.Jr
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(Partial differential equations)
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02.50.Ey
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(Stochastic processes)
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02.50.Fz
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(Stochastic analysis)
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| Fund: This work was partially supported by the Project for the National Natural Science Foundation of China (Grant Nos. 72174121 and 71774111), and 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 (Grant No. 21ZR1444100), and Project Soft Science Research of Shanghai (Grant No. 22692112600). |
Corresponding Authors:
Liang'an Huo
E-mail: huohuolin@yeah.net
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Cite this article:
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 2022 Chin. Phys. B 31 110204
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[1] Chiesa-Estomba C M, Lechien J R, Barillari M R and Saussez S 2020 Virol. Sin. 35 833
[2] Ngonghala C N, Iboi E, Eikenberry S, Scotch M, MacIntyre C R, Bonds M H and Gumel A B 2020 Math. Biosci. 325 108364
[3] Daley D J and Kendal D G 1964 Nature 204 1118
[4] Maki D P and Thompson M 1973 Mathematical models and applications: With emphasis on the social, life, and management sciences (Englewood Cliffs, New Jersey: Prentice-Hall)
[5] Zanette D H 2002 Phys. Rev. E 65 041908
[6] Moreno Y, Nekovee M and Pacheco A F 2004 Phys. Rev. E 69 066130
[7] Nekovee M, Moreno Y, Bianconi G and Marsili M 2007 Phys. A 374 457
[8] Ruan Z, Yu B, Shu X, Zhang Q and Xuan Q 2020 Chaos 30 083101
[9] Singh J 2019 Chaos 29 013137
[10] Zhu L H and Huang X Y 2020 Comm. Theoret. Phys. 72 13
[11] Cheng Y Y, Huo L A and Zhao L J 2021 Information Sci. 564 237
[12] Yu S Z, Yu Z Y, Jiang H J and Li J 2021 Chaos Solitons Frac. 145 110806
[13] Xie W H, Liang G Q, Wang W and She Y H 2019 Int. J. Biomath. 12 191
[14] Holling C S 1965 Memoirs of the Entomological Society of Canada 97 1
[15] Laarabi H, Abta A and Hattaf K 2015 Acta Biotheor. 63 87
[16] Zhu L H, Wang X W, Zhang H H, Shen S L, Li Y M and Zhou Y D 2020 Phys. Scr. 95 035213
[17] Zhu L H and Guan G 2019 Phys. A 533 121953
[18] Jia F and Cao C 2021 Mathematics 9 3277
[19] Cheng Y Y, Huo L A and Zhao L J 2020 Phys. A 559 125061
[20] Huo L A and Chen X M 2020 Adv. Difference Equ. 2020 1
[21] Zhu L H, Zhou M T and Zhang Z D 2020 J. Nonlinear Sci. 30 1
[22] Chen S S, Jiang H J, Li L and Li J R 2020 Chaos, Solitons Fract. 140 110206
[23] Huo L A, Wang L and Zhao X M 2019 Phys. A 517 551
[24] Abouelkheir I, El Kihal F, Rachik M and Elmouki I 2018 Math. Computat. Appl. 23 64
[25] Huo L A and Ma C Y 2018 Discrete Dyn. Nature Soc. 2018 1
[26] Jain A, Dhar J and Gupta V K 2019 Diff. Equ. Dynamical Sys. 2019 1
[27] Okosun K O, Ouifki R and Marcus N 2011 Biosystems 106 136
[28] Uzunca M, Kü?ükseyhan T, Yücel H and Karasözen B 2017 Comput. Math. Appl. 73 215
[29] Pei Y Z, Li S P, Gao S J and Zhong M 2017 Math. Comput. Simulat. 142 51
[30] Huo L A and Ma C Y 2017 Phys. A 471 653
[31] Pei Y Z, Liu S Y, Gao S J, Li S P and Li C G 2009 Comput. Math. Appl. 58 135
[32] Wang F Y, Wang X Y, Zhang S W and Ding C M 2014 Chaos, Solitons Fract. 66 127
[33] Li X D 2010 Neurocomputing 73 749
[34] Li X D, Bohner M and Wang C K 2015 Automatica 52 173
[35] Abouelkheir I, El Kihal F, Rachik M and Elmouki I 2019 Mathematics 7 420
[36] Ahmad M D, Usman M, Khan A and Imran M 2016 Infect. Diseases Poverty 5 72
[37] Chahim M, Hartl R F and Kort P M 2012 Euro. J. Operational Res. 219 18
[38] Yu S Z, Yu Z Y, Jiang H J and Li J R 2021 Chaos, Solitons Fract. 145 110806 |
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