Guo Haoming, Yan Xuefeng, Niu Yanbiao, Zhang Juping
School of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106 China.
Complex Systems Research Center Shanxi University, Taiyuan, 030006 China.
J Appl Math Comput. 2023;69(3):2473-2502. doi: 10.1007/s12190-022-01829-5. Epub 2023 Feb 20.
When a rumor appears on social networks, the media of relevant departments need reaction time to make an authoritative announcement. Considering the effects of the media report and time delay on a rumor spreading, and the different attitudes of individuals towards media reports. We proposed a susceptible-expose-infective-media-remover (SEIMR) rumor propagation model with media reports and time delay. Firstly, the basic reproduction number of the model is obtained. Secondly, the positivity, boundedness and existence of the solutions of the model are analyzed. Then, the local asymptotic stability of the rumor free equilibrium and the boundary equilibriums is proved, and the global asymptotic stability of the equilibriums is proved by constructing Lyapunov function when the time delay is zero. Besides, the prevention and control effects of the media report on rumor spreading and the effect of time delay are analyzed. The shorter time delay in media report and the greater the impact of the media report, the more effective the suppression of rumors will be. Finally, the accuracy of the theoretical results as well as the effects of different parameters of the model have been verified through numerical simulations, and the effectiveness of the SEIMR model has been verified via comparative experiments.
当谣言出现在社交网络上时，相关部门的媒体需要时间做出权威声明。考虑到媒体报道和时间延迟对谣言传播的影响，以及个体对媒体报道的不同态度，我们提出了一个带有媒体报道和时间延迟的易感-暴露-感染-媒体-清除者（SEIMR）谣言传播模型。首先，得到了该模型的基本再生数。其次，分析了模型解的正性、有界性和存在性。然后，证明了无谣言平衡点和边界平衡点的局部渐近稳定性，并在时间延迟为零时通过构造Lyapunov函数证明了平衡点的全局渐近稳定性。此外，分析了媒体报道对谣言传播的防控效果以及时间延迟的影响。媒体报道的时间延迟越短，媒体报道的影响越大，对谣言的抑制效果就越有效。最后，通过数值模拟验证了理论结果的准确性以及模型不同参数的影响，并通过对比实验验证了SEIMR模型的有效性。
