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Related Experiment Video

Updated: Oct 28, 2025

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Self-driven criticality in a stochastic epidemic model.

Gil Ariel1, Yoram Louzoun1

  • 1Department of Mathematics, Bar-Ilan University, Ramat Gan 52900, Israel.

Physical Review. E
|July 17, 2021
PubMed
Summary

This study introduces a generic epidemic model where stochastic parameters lead to self-organization into a critical state. This state suppresses exponential growth, resulting in prolonged epidemic durations and a reproduction rate near one.

Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Statistical Physics

Background:

  • Epidemic dynamics often exhibit complex behaviors, including periods of suppressed growth.
  • Understanding the factors that lead to prolonged epidemic durations is crucial for public health preparedness.

Purpose of the Study:

  • To present a generic epidemic model with stochastic parameters.
  • To investigate the self-organization of epidemic dynamics into a critical state.
  • To analyze the characteristics of this critical regime, including suppressed exponential growth and prolonged durations.

Main Methods:

  • Development of a generic epidemic model incorporating stochastic parameters.
  • Analysis of the model's dynamics, focusing on self-organization to a critical state.

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  • Numerical and analytical stability analysis of the critical regime.

    • Main Results:

    • The model demonstrates self-organization into a quasi-steady critical state.
    • In this state, the effective reproduction rate fluctuates near the critical value of 1 for extended periods.
    • The critical regime is characterized by significantly suppressed exponential growth and an extremely long epidemic duration.

    Conclusions:

    • Stochastic parameters in epidemic models can drive self-organization towards a critical state.
    • This critical state explains observed epidemic dynamics with suppressed growth and long durations.
    • The findings offer insights into the stability and longevity of epidemics.