SIR epidemics and vaccination on random graphs with clustering

TL;DR

This paper analyzes SIR epidemic spread on clustered random graphs, extending previous models by relaxing infectivity assumptions, and investigates vaccination effects using branching process approximations.

Contribution

It introduces a generalized model for epidemics on clustered graphs with non-homogeneous infectivity and derives key epidemic metrics including R0 and outbreak probability.

Findings

R0 equals the vaccine-associated reproduction number in this model

Branching process approximations effectively estimate epidemic outcomes

Vaccination significantly reduces outbreak probability and size

Abstract

In this paper we consider SIR epidemics on random graphs with clustering. To incorporate group structure of the underlying social network, we use a generalized version of the configuration model in which each node is a member of a specified number of triangles. SIR epidemics on this type of graph have earlier been investigated under the assumption of homogeneous infectivity and also under the assumption of Poisson transmission and recovery rates. We extend known results from literature by relaxing the assumption of homogeneous infectivity. An important special case of the epidemic model analyzed in this paper is epidemics in continuous time with arbitrary infectious period distribution. We use branching process approximations of the spread of the disease to provide expressions for the basic reproduction number R0, the probability of a major outbreak and the expected final size. In addition, the impact of random vaccination with a perfect vaccine on the final outcome of the epidemic is investigated. We find that, for this particular model, R0 equals the perfect vaccine-associated reproduction number. Generalizations to groups larger than three are discussed briefly.