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

Anton Chizhov1,2,3, Laurent Pujo-Menjouet4, Tilo Schwalger5,6

  • 1Institute for Theoretical Physics, University of Bremen, Bibliothekstr. 1, Bremen, 28359, Germany.

Infectious Disease Modelling
|April 11, 2025
PubMed

Insights

This study introduces a new multi-scale infectious disease model using the Refractory Density (RD) approach. The framework models individual infection and population-level epidemic spread, validated with coronavirus data.

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.
Keywords:
Age-structured modelFinite-size fluctuationsPartial differential equationsRefractory densityTime since last infection

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