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Area of Science:

  • Epidemiology and statistical physics

Background:

  • Epidemics can spread across spatially disconnected regions, forming clusters, especially with long-range dispersal.
  • Understanding the statistical properties of these epidemic clusters is crucial for predicting disease spread.

Purpose of the Study:

  • To characterize the statistical properties of epidemic clusters in a solvable model.
  • To identify key parameters and exponents governing cluster formation and distribution.
  • To explore potential applications in other complex systems.

Main Methods:

  • Analysis of a solvable model exhibiting epidemic spread with long-range dispersal.
  • Characterization of statistical properties in both supercritical (outbreak) and critical regimes.
  • Identification of diverging length scales and critical exponents.

Main Results:

  • Two distinct diverging length scales were identified: one for the cluster bulk and one for the outskirt.
  • A nontrivial critical exponent was revealed, governing cluster number, size distribution, and inter-cluster distances.
  • The findings provide exact statistical properties of epidemic clusters.

Conclusions:

  • The study provides a precise mathematical framework for understanding epidemic cluster dynamics.
  • The identified critical exponent offers new insights into spatial epidemic spread.
  • Applications to depinning avalanches with long-range elasticity are discussed.