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Spatial dynamics and optimization method for a rumor propagation model in both homogeneous and heterogeneous

Linhe Zhu1, Xuewei Wang1, Zhengdi Zhang1

  • 1School of Mathematical Sciences, Jiangsu University, Zhenjiang, 212013 People's Republic of China.

Nonlinear Dynamics
|August 23, 2021
PubMed
Summary

This study enhances the SIR rumor propagation model to analyze spread dynamics in varied environments. It explores stability, optimal control, and Hopf bifurcation, offering insights into rumor diffusion.

Keywords:
Hopf bifurcationOptimal controlReaction–diffusion systemSpatial heterogeneous environmentStability

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Area of Science:

  • Mathematical modeling
  • Epidemiology
  • Information diffusion

Background:

  • Traditional SIR models lack environmental capacity and forgetting factors.
  • Rumor spreading dynamics are complex in heterogeneous and homogeneous environments.

Purpose of the Study:

  • To develop and analyze improved rumor propagation models.
  • To investigate rumor dynamics considering environmental capacity and forgetting.
  • To explore optimal control strategies and bifurcation phenomena.

Main Methods:

  • Modified SIR (susceptible-infected-removed) models for homogeneous and heterogeneous environments.
  • Dynamic analysis, including uniform persistence and asymptotic behavior.
  • Optimal control theory and maximum principle application.
  • Hopf bifurcation analysis with time delay in reaction-diffusion models.
  • Numerical simulations to verify findings.

Main Results:

  • Analysis of rumor spread in spatial heterogeneous and homogeneous environments.
  • Identification of conditions for uniform persistence and stability.
  • Derivation of optimal control strategies for rumor mitigation.
  • Verification of Hopf bifurcation and the impact of diffusion coefficients.

Conclusions:

  • The improved models provide a more realistic framework for rumor propagation.
  • Dynamic analysis reveals key factors influencing rumor spread and stability.
  • Optimal control strategies can be developed based on model insights.
  • Hopf bifurcation analysis highlights the role of time delays and diffusion in complex dynamics.