Reaction-diffusion on random spatial networks with scale-free jumping rates via effective medium theory

TL;DR

This paper develops an effective medium theory to analyze epidemic spread on complex spatial networks with long-range connections, demonstrating exponential growth of infected regions and extending EMA applicability to intricate network dynamics.

Contribution

It introduces a novel EMA variant for long-range, scale-free networks and applies it to epidemic modeling, revealing exponential growth behavior.

Findings

Exponential growth of infected domain size over time.

Effective medium approximation applicable to complex, long-range networks.

Demonstrates EMA's utility beyond simple diffusion models.

Abstract

We study epidemic processes using a metapopulation approach on the line featuring random transport rates between arbitrarily distant sites. An average transport network is found using a recently developed variant of the effective medium approximation (EMA) that is capable of dealing with these long-range connections. Using a Feynman-Kac argument in the effective medium, we derive an estimate on the size of the infected domain, and reproduce the known result of its exponential growth in time. We hereby demonstrate the applicability of long-range EMA to dynamical processes on networks more intricate than simple diffusion.