A refractory density approach to a multi-scale SEIRS epidemic model.

Area of Science:

• Epidemiology
• Mathematical Modeling
• Statistical Physics

Background:

• Infectious disease modeling requires understanding individual and population dynamics.
• Existing models may not fully capture multi-scale epidemic behaviors.
• The Refractory Density (RD) approach offers novel tools for complex system analysis.

Purpose of the Study:

• To develop a novel multi-scale modeling framework for infectious disease spreading.
• To integrate microscopic, mesoscopic, and macroscopic scales of epidemic dynamics.
• To validate the framework's ability to reproduce complex dynamics and fluctuations.

Main Methods:

• Introduction of a microscopic model for individual infection probability and disease evolution.
• Development of corresponding population-level models at mesoscopic and macroscopic scales.
• Numerical illustrations using white Gaussian noise and escape noise.

Main Results:

• The framework successfully models disease spread across multiple scales.
• Demonstration of complex transient and asymptotic dynamics.
• Consistent reproduction of finite-size fluctuations across scales.
• Qualitative relevance corroborated by comparison with coronavirus epidemiology.

Conclusions:

• The proposed multi-scale modeling framework provides a robust approach to studying infectious diseases.
• The framework's ability to capture multi-scale dynamics and fluctuations enhances epidemic prediction.
• This approach offers valuable insights for understanding and managing disease outbreaks, including coronaviruses.