Clusters in an epidemic model with long-range dispersal

TL;DR

This paper provides an exact characterization of epidemic clusters in models with long-range dispersal, revealing critical exponents and length scales that describe their statistical properties in different regimes.

Contribution

It introduces a solvable model that analytically describes the statistical properties of epidemic clusters with long-range dispersal, including critical behavior and length scales.

Findings

Identification of two diverging length scales

Derivation of a nontrivial critical exponent

Analysis of cluster size and distance distributions

Abstract

In presence of long range dispersal, epidemics spread in spatially disconnected regions known as clusters. Here, we characterize exactly their statistical properties in a solvable model, in both the supercritical (outbreak) and critical regimes. We identify two diverging length scales, corresponding to the bulk and the outskirt of the epidemic. We reveal a nontrivial critical exponent that governs the cluster number, the distribution of their sizes and of the distances between them. We also discuss applications to depinning avalanches with long range elasticity.