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Fluctuation effects in metapopulation models: percolation and pandemic threshold

Marc Barthélemy1, Claude Godrèche, Jean-Marc Luck

  • 1Institut de Physique Théorique, CEA Saclay, and URA 2306, CNRS, 91191 Gif-sur-Yvette, France. marc.barthelemy@cea.fr

Journal of Theoretical Biology
|September 25, 2010
PubMed

Insights

This study introduces stochastic metapopulation models for disease spread, revealing a connection between global pandemic spread and network percolation. This provides a method to estimate pandemic thresholds for various network structures.

Area of Science:

  • Epidemiology
  • Network Science
  • Mathematical Biology

Background:

  • Metapopulation models are standard for simulating disease spread across connected populations.
  • Current models often neglect crucial fluctuations by using mean-field approximations.
  • Understanding pandemic spread requires accounting for stochasticity in disease dynamics.

Purpose of the Study:

  • To develop and analyze fully stochastic metapopulation models for disease spread.
  • To analytically investigate the existence and calculation of global pandemic thresholds.
  • To establish a connection between disease spread and network percolation theory.

Main Methods:

  • Development of fully stochastic metapopulation models for Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered (SIR) dynamics.
  • Analytical treatment of stochastic models to address disease spread thresholds.
  • Mapping the global spread of disease to bond percolation processes on networks.

Main Results:

  • Stochastic models allow for analytical solutions regarding disease spread thresholds.
  • The global spread of disease is shown to be equivalent to bond percolation on the network.
  • An estimate (lower bound) for the pandemic threshold in the SIR model is derived for all parameters and network types.

Conclusions:

  • Stochastic metapopulation models offer a more accurate framework for pandemic simulations.
  • Network percolation provides a powerful tool for understanding and quantifying pandemic thresholds.
  • The findings enable better prediction and management of global disease outbreaks.

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