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Taming obstinate spreaders: the dynamics of a rumor spreading model incorporating inhibiting mechanisms and attitude adjustment

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Abstract

This paper proposes and investigates a model for rumor spreading and control which accounts for different attitudes and for a distinct type of variable, related to the strength and effectiveness of rumor inhibiting mechanisms. The control mechanisms essentially amount to budgeting and to adjusting the attitude of spreaders. The existence and stability of the trivial (rumor-free) equilibrium and of the semi-trivial equilibrium are characterized in terms of two threshold parameters which quantify the influence of both categories of spreaders. The existence of a positive (rumor-prevailing) equilibrium is also established, its stability being discussed with the help of a bifurcation theorem. A nonstandard finite difference (NSFD) scheme is devised to construct approximate solutions while preserving their positivity, necessary conditions for the existence of the optimal discrete rumor spreading controls being then established.

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The choices of parameter values have been stated in the body of the paper. The graphs were produced using MATLAB version 2018a, available from https://www.mathworks.com/products/matlab.html.

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Funding

The work of H.Z. was supported by the “Blue Project” of Jiangsu Province and the Humanities and Social Science project of the Chinese Ministry of Education (20YJA630088). The work of T.L. was supported by the social science fund project of Jiangsu Province (No. 17XZB007).

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Authors and Affiliations

  1. School of Economics and Management, Changzhou Institute of Technology, Changzhou, 213032, Jiangsu, People’s Republic of China

    Chen Wenkai & Hong Zhang

  2. Department of Mathematics, Technical University of Iaşi, Bd. Copou 11A, 700506, Iaşi, Romania

    Paul Georgescu

  3. School of Innovation and Entrepreneurship, Changzhou Institute of Technology, Changzhou, 213032, Jiangsu, People’s Republic of China

    Tan Li

  4. School of Electrical and Information Engineering, Changzhou Institute of Technology, Changzhou, 213032, Jiangsu, People’s Republic of China

    Bing Zhang

Authors
  1. Chen Wenkai
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  2. Hong Zhang
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  3. Paul Georgescu
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  4. Tan Li
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  5. Bing Zhang
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Contributions

C.W. and H.Z conceived the study, participated in model formulation and model analysis, and helped drafting the intermediary versions of the manuscript. P.G. participated in model formulation and model analysis, helped drafting the intermediary versions of the manuscript, and drafted the final version of the manuscript. T.L. carried out the stability analysis of the model steady states and helped drafting the intermediary versions of the manuscript. B. Z. helped drafting the intermediary versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Paul Georgescu.

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The authors declare no competing interests.

Additional information

Communicated by Florence Hubert.

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The work of H.Z. was supported by the “Blue Project” of Jiangsu Province and the Humanities and Social Science project of the Chinese Ministry of Education (20YJA630088). The work of T.L. was supported by the social science fund project of Jiangsu Province (No. 17XZB007)

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Wenkai, C., Zhang, H., Georgescu, P. et al. Taming obstinate spreaders: the dynamics of a rumor spreading model incorporating inhibiting mechanisms and attitude adjustment. Comp. Appl. Math. 40, 125 (2021). https://doi.org/10.1007/s40314-021-01492-9

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  • DOI: https://doi.org/10.1007/s40314-021-01492-9

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