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Area of Science:

  • Complex Systems
  • Epidemiology
  • Network Science

Background:

  • Individuals in realistic networks can display collective behaviors during epidemics.
  • Understanding the link between collective behaviors and epidemic spread is crucial.

Purpose of the Study:

  • To mathematically model and analyze epidemic synchronization in networks.
  • To investigate the influence of delays (coupling and epidemic) on synchronization dynamics.
  • To compare the predictive accuracy of different mean-field theories for epidemic synchronization.

Main Methods:

  • Construction of mathematical models for epidemic synchronization, incorporating adaptive feedback and various delay types (no delay, coupling delay, double delays).
  • Application of Lyapunov function methods to determine conditions for local and global stability of the models.
  • Utilizing quenched mean-field theory and heterogeneous mean-field theory for comparative analysis.
  • Performing numerical simulations to validate theoretical findings and explore emergent phenomena.

Main Results:

  • Established conditions for the local and global stability of epidemic synchronization models.
  • Demonstrated that quenched mean-field theory offers higher accuracy than heterogeneous mean-field theory in predicting epidemic synchronization.
  • Numerical simulations confirmed that coupling and epidemic delays affect the speed of epidemic synchronization, revealing unexpected dynamics.

Conclusions:

  • Mathematical models and stability analysis provide insights into epidemic synchronization.
  • Delay parameters play a critical role in modulating the speed and patterns of epidemic spread and synchronization.
  • This research contributes to understanding the interplay between epidemic dynamics and synchronization phenomena in complex networks.