Levy-flight spreading of epidemic processes leading to percolating clusters

TL;DR

This paper investigates how long-range infection probabilities, decaying as 1/R^{d+\sigma}, influence epidemic spreading and critical behavior, revealing a continuous transition to short-range behavior at a critical decay exponent.

Contribution

It introduces a renormalization-group analysis of epidemic processes with long-range infections, extending understanding of critical phenomena in disease spreading models.

Findings

Critical exponents depend on the decay exponent 

Long-range behavior transitions to short-range at =2

Critical behavior varies continuously with 

Abstract

We consider two stochastic processes, the Gribov process and the general epidemic process, that describe the spreading of an infectious disease. In contrast to the usually assumed case of short-range infections that lead, at the critical point, to directed and isotropic percolation respectively, we consider long-range infections with a probability distribution decaying in d dimensions with the distance as 1/R^{d+\sigma}. By means of Wilson's momentum shell renormalization-group recursion relations, the critical exponents characterizing the growing fractal clusters are calculated to first order in an \epsilon-expansion. It is shown that the long-range critical behavior changes continuously to its short-range counterpart for a decay exponent of the infection \sigma =\sigma_c>2.