Clusters in an epidemic model with long-range dispersal

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.
Comment: 19 pages, 8 figures; v2: added an application to the Covid-19 outbreak in the US; v3: minor changes, published version