Inhomogeneous epidemics on weighted networks

TL;DR

This paper models inhomogeneous epidemics on weighted social networks, deriving the basic reproduction number and analyzing how heterogeneity influences outbreak size and probability.

Contribution

It extends the configuration model to weighted networks with heterogeneous individuals, providing new insights into epidemic thresholds and outbreak dynamics.

Findings

R_0 increases with community heterogeneity

Different heterogeneities can homogenize the community, reducing R_0

Outbreak probability and size are affected in complex ways

Abstract

A social (sexual) network is modeled by an extension of the configuration model to the situation where edges have weights, e.g. reflecting the number of sex-contacts between the individuals. An epidemic model is defined on the network such that individuals are heterogeneous in terms of how susceptible and infectious they are. The basic reproduction number R_0 is derived and studied for various examples, but also the size and probability of a major outbreak. The qualitative conclusion is that R_0 gets larger as the community becomes more heterogeneous but that different heterogeneities (degree distribution, weight, susceptibility and infectivity) can sometimes have the cumulative effect of homogenizing the community, thus making $R_0$ smaller. The effect on the probability and final size of an outbreak is more complicated.