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Nonconstant Steady States of a Rumor Propagation Model

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Abstract

This paper reports some qualitative results of a diffusive rumor propagation model with homogeneous no-flux boundary conditions. Firstly, the permanence is exhibited of the spatiotemporal rumor model. Then the boundedness of solutions, the nonexistence and existence of the non-constant steady states of the spatial rumor propagation model are explored. It is shown that the non-constant steady states may exist when the migration rate of the rumor-infected individuals is fixed and the migration rate of the rumor-susceptible individuals is large. By contrast, there are no non-constant steady states as the migration rates of the rumor-susceptible individuals and the rumor-infected individuals are fixed and large, respectively. These qualitative investigation results enhance the theoretical study of the spatial propagation rumor model.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 11971032, 12002297), and funded by China Postdoctoral Science Foundation (No. 2021M701118).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

    Mengxin Chen

  2. School of Mathematics and Center for Pure Mathematics, Anhui University, Hefei, 230601, China

    Ranchao Wu

  3. School of Science, Xuchang University, Xuchang, 461000, China

    Qianqian Zheng

Authors
  1. Mengxin Chen
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  2. Ranchao Wu
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  3. Qianqian Zheng
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Contributions

Mengxin Chen: Formal analysis, Writing-original draft, Review & editing; Ranchao Wu: Supervision, Methodology, Revision; Qianqian Zheng: Software, Review & editing.

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Correspondence to Ranchao Wu.

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Chen, M., Wu, R. & Zheng, Q. Nonconstant Steady States of a Rumor Propagation Model. Differ Equ Dyn Syst (2023). https://doi.org/10.1007/s12591-023-00641-2

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