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

doi:10.1088/1674-1056/ac2f35

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.

Keywords: rumor propagation near-optimal control popular science education media coverage Lévy noise

Received: 04 April 2021
Revised: 21 September 2021
Accepted manuscript online: 13 October 2021

PACS:	02.30.Jr	(Partial differential equations)
	02.50.Ey	(Stochastic processes)
	02.50.Fz	(Stochastic analysis)
	02.30.-f	(Function theory, analysis)

Fund: 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).

Corresponding Authors: Liang'an Huo
E-mail: huohuolin@yeah.net

Cite this article:

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 2022 Chin. Phys. B 31 030202

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