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Rumor spreading in complex networks under stochastic node activity.

Yingying Cheng1, Liang'an Huo1, Laijun Zhao1

  • 1Business School, University of Shanghai for Science and Technology, Shanghai 200093, China.

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|August 25, 2020
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Summary

This study introduces a stochastic rumor spreading model, incorporating random individual activity. It identifies critical thresholds for rumor propagation and analyzes noise effects on model stability.

Keywords:
Rumor spreadingSocial network dynamicsStochastic differential equationWiener process

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Area of Science:

  • Mathematical modeling
  • Epidemiology
  • Complex systems

Background:

  • Rumor spreading significantly impacts society.
  • Individual activity is crucial in rumor dynamics.
  • Environmental randomness influences individual behavior.

Purpose of the Study:

  • To explore a stochastic rumor spreading model with random individual activity.
  • To analyze the impact of Stratonovich stochastic noise on rumor dynamics.
  • To determine critical values and threshold conditions for rumor propagation.

Main Methods:

  • Development of a stochastic version of a rumor model.
  • Mathematical analysis of non-linear rumor spreading dynamics.
  • Investigation of Stratonovich stochastic noise effects.
  • Numerical simulations for verification.

Main Results:

  • Identification of critical values for rumor spread in deterministic and stochastic models.
  • Determination of threshold conditions for widespread rumor propagation.
  • Analysis of noise effects on rumor-free and endemic equilibrium points.
  • Conditions for global asymptotic stability of the rumor-free equilibrium.

Conclusions:

  • Stochastic noise influences rumor spreading dynamics.
  • The study provides insights into rumor propagation thresholds and stability.
  • Theoretical findings are validated through numerical simulations.