Epidemics on random graphs with tunable clustering

TL;DR

This paper develops a branching process model to analyze how clustering in random intersection graphs influences epidemic spread, providing insights into thresholds and outbreak probabilities.

Contribution

It introduces a new approximation for epidemics on clustered networks and explores how clustering affects epidemic thresholds and outbreak likelihoods.

Findings

Higher clustering lowers the epidemic threshold.

The probability of large outbreaks varies with clustering levels.

Derived explicit expressions for epidemic thresholds.

Abstract

In this paper, a branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large outbreak in the epidemic. It is investigated how these quantities varies with the clustering in the graph and it turns out for instance that, as the clustering increases, the epidemic threshold decreases. The network is modelled by a random intersection graph, in which individuals are independently members of a number of groups and two individuals are linked to each other if and only if they share at least one group.