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Rumor spreading model with a focus on educational impact and optimal control

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Abstract

Rumor spreading brings great misconception and harm to society. To control the spread of rumors, it is essential to model rumor propagation and provide appropriate interference in inhibiting the propagation. In this paper, we establish an extended rumor-spreading model with a focus on the influence of knowledge education and intervention strategies in reducing rumor propagation. The mathematical rationality of the proposed model is examined, which demonstrates the existence of equilibrium and local asymptotic stability. To simulate the dynamics of rumor spreading in the proposed model and calibrate its unknown variables to a real case, we employ a novel rumor-informed neural network (RINN), which is constructed based on the physics-informed neural network (PINN) and real rumor spreading. The numerical simulation experiments indicate that the reinforcement of education on rumor identification and timely refutation of false information is effective in controlling the propagation of rumors. Moreover, the optimal control strategies are further proposed to determine the efficient means of mitigating the risk associated with the rapid spread of rumors. Our findings present that proactive dissemination of publicity and educational content can effectively enhance individuals’ awareness of rumor information. Specifically, prompt dispelling of false information can result in a higher success rate of dispelling rumors, a shorter duration of rumor dissemination, and a lower peak in the number of rumor disseminators, thereby facilitating effective control of the spread of rumors.

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Data availibility

The datasets analyzed in the current research are obtained from the database of the paper titled Reciprocal spreading and debunking processes of online misinformation: A new rumor spreading-debunking model with a case study in the journal Physica A.

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Funding

This work was supported by the Nature Science Foundation of Guangdong Province under Project No. 2021A1515011594 and the University Innovative Team Project of Guangdong Province under Grant No. 2022KCXTD039.

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Authors and Affiliations

  1. School of Science, Harbin Institute of Technology, Shenzhen, 518055, China

    Deliang Li, Yi Zhao & Yang Deng

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  1. Deliang Li
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  2. Yi Zhao
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Contributions

All authors contributed to the study’s conception and design. DL, YZ, and YD were involved in material preparation, data collection, and analysis. The first draft of the manuscript was written by DL, YZ, and YD. All authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Yi Zhao.

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Li, D., Zhao, Y. & Deng, Y. Rumor spreading model with a focus on educational impact and optimal control. Nonlinear Dyn 112, 1575–1597 (2024). https://doi.org/10.1007/s11071-023-09102-5

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