Assessing node risk and vulnerability in epidemics on networks

TL;DR

This paper uses the cavity method to analyze node vulnerability and risk in epidemic spreading on networks, revealing complex properties and dependencies on infection strength and duration.

Contribution

It introduces a novel application of the cavity method to approximate node vulnerability and risk, uncovering nuanced behaviors in epidemic dynamics on networks.

Findings

Some nodes are more vulnerable to weak infections but less to strong ones

A node is more likely to be caught in an outbreak than to initiate one

Node risk ranking depends on infectious period distribution

Abstract

Which nodes are most vulnerable to an epidemic spreading through a network, and which carry the highest risk of causing a major outbreak if they are the source of the infection? Here we show how these questions can be answered to good approximation using the cavity method. Several curious properties of node vulnerability and risk are explored: some nodes are more vulnerable than others to weaker infections, yet less vulnerable to stronger ones; a node is always more likely to be caught in an outbreak than it is to start one, except when the disease has a deterministic lifetime; the rank order of node risk depends on the details of the distribution of infectious periods.