Cluster size distribution of infection in a system of mobile agents

TL;DR

This paper models infection spread among mobile agents, revealing that at the critical infection rate, the cluster size distribution follows a universal power-law characterized by a single exponent, with no persistent giant cluster.

Contribution

It introduces a statistical physics-based model for infection clusters in mobile agents and characterizes their size distribution at criticality.

Findings

All moments of the cluster size distribution are governed by a single exponent.

No giant infection cluster persists regardless of infection rate.

The model links cluster size distribution to epidemic dynamics.

Abstract

Clusters of infected individuals are defined on data from health laboratories, but this quantity has not been defined and characterized by epidemy models on statistical physics. For a system of mobile agents we simulate a model of infection without immunization and show that all the moments of the cluster size distribution at the critical rate of infection are characterized by only one exponent, which is the same exponent that determines the behavior of the total number of infected agents. No giant cluster survives independent on the magnitude of the rate of infection.