Abstract
On the basis of nonlinear dynamic model, we research the propagation of rumors after emergencies, describe the impact of media coverage and emergency strategies by government on the transmission dynamics of information, and then obtain the basic reproduction number of rumor spreading. In order to overcome the limit of traditional methods of the static decision problem, the dynamic optimal control model for the rumor spreading is proposed based on the theorem of the optimal control. An optimal objective based on the maximum social utility is established and the optimal solution is acquired by using the Pontryagin Maximum Principle. Finally, numerical simulations show that the dynamic optimal control method has obvious superiority in modeling compared with the method without control. By means of the dynamic optimal control of media coverage and emergency strategies for government, the final rumor scale and the peak of spreaders can be effectively reduced.
Highlights
When emergencies occur, people's thirst for information is different from normal
If there is a clear channel of information dissemination and effective information dissemination mode among the government, the media, and the public, this will be beneficial to reduce the social panic and prevent the expansion and dissemination of adverse effects in the event
Rapoport [5] first uses the epidemic model to study the spread of information
Summary
People's thirst for information is different from normal. If the propagation of information is not transparent, detailed, and controlled by the government and the media at this time, it may lead to people’s psychological and emotional tension, unnecessary public panic, and economic loss [1,2,3,4]. Based on the study of the classic D-K model, this paper adds two factors, media coverage and emergency strategies by government, to the spread of rumors, analyzes the spread mechanism of the rumor under the influence of these two factors, and lays a theoretical foundation for further discussion of the control strategy of the rumors. In order to incorporate the dimensions of massive news coverage, we introduce the information variable M(t) to describe the cumulative density of media coverage in other region at time t According to [34], if R0 < 1, there is no more rumor to spread in the networks; while if R0 > 1, the rumor will persist in the networks
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