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Chin. Phys. B, 2022, Vol. 31(11): 110204    DOI: 10.1088/1674-1056/ac98fb
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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
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.
Keywords:  rumor spreading      stochastic process      optimal impulse control      education mechanism      refutation mechanism  
Received:  15 November 2021      Revised:  13 April 2022      Accepted manuscript online:  11 October 2022
PACS:  02.30.Jr (Partial differential equations)  
  02.50.Ey (Stochastic processes)  
  02.50.Fz (Stochastic analysis)  
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:

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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