Epidemics and Dimensionality in Hierarchical Networks

TL;DR

This paper investigates how the number of social dimensions in hierarchical networks influences epidemic spread, showing that multiple dimensions facilitate global outbreaks, while a single dimension can limit spread depending on homophily.

Contribution

It introduces a hierarchical network model with multiple dimensions and analyzes how these dimensions affect epidemic spreading dynamics.

Findings

Multiple dimensions lead to widespread epidemic outbreaks regardless of homophily.

Single dimension networks exhibit a transition from global to local spread with increased homophily.

Hierarchical structure significantly impacts epidemic susceptibility in social and computer networks.

Abstract

Epidemiological processes are studied within a recently proposed hierarchical network model using the susceptible-infected-refractory dynamics of an epidemic. Within the network model, a population may be characterized by $H$ independent hierarchies or dimensions, each of which consists of groupings of individuals into layers of subgroups. Detailed numerical simulations reveal that for $H>1$, global spreading results regardless of the degree of homophily of the individuals forming a social circle. For H=1, a transition from global to local spread occurs as the population becomes decomposed into increasingly homophilous groups. Multiple dimensions in classifying individuals (nodes) thus make a society (computer network) highly susceptible to large scale outbreaks of infectious diseases (viruses).