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Dynamical Analysis and Control Strategies of Rumor Spreading Models in Both Homogeneous and Heterogeneous Networks

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Abstract

In recent years, rumor propagation in social networks attracts more researchers’ attention. In this paper, we have established I2S2R rumor spreading models in both homogeneous networks and heterogeneous networks considering the effect of time delay. In the homogeneous network model, we obtain the basic reproduction number by means of the next-generation matrix. Besides, the local stability and the global stability of the equilibrium points are discussed by linearization approach of nonlinear systems and Lyapunov function. In the heterogeneous network model, we calculate the basic reproduction number through algebraic method. In addition, Lyapunov functional method and Lasalle invariance principle are applied to study the stability of equilibrium points in the complex network model. Further, we put forward some useful strategies to control the spreading of rumor based on the complex network theory. Finally, we take advantage of numerical simulations to verify the theory above and come up with necessary conclusions.

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (Grant No. 11872189), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20190836), the China Postdoctoral Science Foundation (Grant No. 2019M661732), and the Natural Science Research of Jiangsu Higher Education Institutions of China (Grant No. 19KJB110001). Moreover, this research is also supported by the 18th Batch of Undergraduate Scientific Research Project of Jiangsu University (Grant No. 18A291) and College Students Innovation Training Program of Jiangsu University in 2020.

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  1. Faculty of Science, Jiangsu University, Zhenjiang, 212013, People’s Republic of China

    Linhe Zhu, Mengtian Zhou & Zhengdi Zhang

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  1. Linhe Zhu
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  2. Mengtian Zhou
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  3. Zhengdi Zhang
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Correspondence to Linhe Zhu.

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Communicated by Alain Goriely.

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Zhu, L., Zhou, M. & Zhang, Z. Dynamical Analysis and Control Strategies of Rumor Spreading Models in Both Homogeneous and Heterogeneous Networks. J Nonlinear Sci 30, 2545–2576 (2020). https://doi.org/10.1007/s00332-020-09629-6

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  • DOI: https://doi.org/10.1007/s00332-020-09629-6

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