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

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.