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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 |
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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.
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Received: 22 March 2021
Revised: 18 May 2021
Accepted manuscript online: 24 May 2021
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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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02.30.-f
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(Function theory, analysis)
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| Fund: 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). |
Corresponding Authors:
Ting-Ting Lin
E-mail: lintingting00@163.com
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Cite this article:
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 2021 Chin. Phys. B 30 080201
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