Epidemics in networks: A master equation approach

TL;DR

This paper models epidemic spreading in networks using a master equation approach, analyzing how the dynamics of infection depend on network topology and the timescale of contagion processes.

Contribution

It introduces a master equation framework to study epidemic dynamics on different network types, emphasizing the impact of contagion timescales on spreading efficiency.

Findings

Relaxation timescales significantly influence infected subgraph topology.

Scale-free networks facilitate faster disease spread than exponential networks.

Contagion dynamics are sensitive to the annealed and quenched limits.

Abstract

A problem closely related to epidemiology, where a subgraph of 'infected' links is defined inside a larger network, is investigated. This subgraph is generated from the underlying network by a random variable, which decides whether a link is able to propagate a disease/information. The relaxation timescale of this random variable is examined in both annealed and quenched limits, and the effectiveness of propagation of disease/information is analyzed. The dynamics of the model is governed by a master equation and two types of underlying network are considered: one is scale-free and the other has exponential degree distribution. We have shown that the relaxation timescale of the contagion variable has a major influence on the topology of the subgraph of infected links, which determines the efficiency of spreading of disease/information over the network.