  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.
