Rumors spread among the crowd have an impact on media influence, while media influence also has an impact on rumor dissemination. This article constructs a two-layer rumor media interaction network model, in which the rumors spread in the crowd are described using the susceptibility-apathy-propagation-recovery model, and the media influence is described using the corresponding flow model. The rationality of the model is studied, and then a detailed analysis of the model is conducted. In the simulation section, we undertake a sensitivity analysis of the crucial parameters within our model, focusing particularly on their impact on the basic reproduction number. According to data simulation analysis, the following conclusion can be drawn: First, when the media unilaterally influences the crowd and does not accept feedback from the crowd, the influence of the media will decrease to zero over time, which has a negative effect on the spread of rumors among the crowd (the degree of rumor dissemination decreases). Second, when the media does not affect the audience and accepts feedback from the audience, this state is similar to the media collecting information stage, which is to accept rumors from the audience but temporarily not disclose their thoughts. At this time, both the media influence and the spread of rumors in the audience will decrease. Finally, the model is validated using an actual dataset of rumors. The simulation results show an R-squared value of 0.9606, indicating that the proposed model can accurately simulate rumor propagation in real social networks.

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