Rough infection fronts in a random medium

TL;DR

This paper investigates how infection fronts propagate through a randomly disordered medium using a spatially extended SIR model, revealing critical behavior in the front's velocity, shape, and roughness as disorder varies.

Contribution

It introduces a numerical study of infection front dynamics in a spatially random environment, highlighting critical phenomena near a disorder threshold.

Findings

Identification of non-trivial critical behavior in front velocity and shape

Observation of rough geometry in the infection front

Discovery of a disorder threshold for spatial spreading

Abstract

We study extended infection fronts advancing over a spatially uniform susceptible population by solving numerically a diffusive Kermack McKendrick SIR model with a dichotomous spatially random transmission rate, in two dimensions. We find a non-trivial dynamic critical behavior in the mean velocity, in the shape, and in the rough geometry of the displacement field of the infective front as the disorder approaches a threshold value for spatial spreading of the infection.