Clusters in an Epidemic Model with Long-Range Dispersal

In the 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 and the distribution of their sizes and of the distances between them. We also discuss applications to depinning avalanches with long-range elasticity.

Automated summary

This study characterizes the statistical properties of clusters in the presence of long-range dispersal in a solvable model. Two diverging length scales and a nontrivial critical exponent are identified, governing the cluster number, size distribution, and distances between them. Applications to depinning avalanches are also discussed.