Pattern mechanism in stochastic SIR networks with ER connectivity

Area of Science:

• Epidemiology
• Mathematical Biology
• Network Science

Background:

• Previous SIR models lack mechanisms for periodic behavior and endemic diseases.
• Diffusion and network effects are crucial but often unintegrated factors in disease spread.

Purpose of the Study:

• To incorporate diffusion and network effects into the SIR model.
• To elucidate the dynamical mechanisms behind periodic outbreaks and endemic diseases.
• To introduce and analyze network structured entropy (NSE).

Main Methods:

• Incorporation of diffusion and network effects into the SIR model.
• Analysis using wavenumber and saddle-node bifurcation.
• Application of the mean-field method.
• Introduction of standard network structured entropy (NSE).

Main Results:

• Diffusion effects can induce saddle-node bifurcation and Turing instability.
• The network-organized SIR model provides conditions for Turing instability via wavenumber.
• The mean-field method reveals mechanisms for periodic outbreaks and endemic diseases.
• Theoretical results were validated using COVID-19 data.

Conclusions:

• The enhanced SIR model accurately describes periodic and endemic infectious disease dynamics.
• Diffusion and network structure are key drivers of complex disease patterns.
• The study provides a robust framework for understanding and predicting disease spread.