Networks and the epidemiology of infectious disease

Abstract

The science of networks has revolutionised research into the dynamics of interacting elements. It could be argued that epidemiology in particular has embraced the potential of network theory more than any other discipline. Here we review the growing body of research concerning the spread of infectious diseases on networks, focusing on the interplay between network theory and epidemiology. The review is split into four main sections, which examine: the types of network relevant to epidemiology; the multitude of ways these networks can be characterised; the statistical methods that can be applied to infer the epidemiological parameters on a realised network; and finally simulation and analytical methods to determine epidemic dynamics on a given network. Given the breadth of areas covered and the ever-expanding number of publications, a comprehensive review of all work is impossible. Instead, we provide a personalised overview into the areas of network epidemiology that have seen the greatest progress in recent years or have the greatest potential to provide novel insights. As such, considerable importance is placed on analytical approaches and statistical methods which are both rapidly expanding fields. Throughout this review we restrict our attention to epidemiological issues.

Figure 1

Examples of networks used in epidemiology. (a) Contacts between 22 intravenous drug users, as recorded in [3]; squares refer to primary contacts. Given that the identity of contacts is known, they can be interlinked. (b) Caricature of a snowball sampling algorithm, squares are primary contacts, diamonds are secondary, and circles are tertiary contacts. Given that the identity of contacts is known they can be linked. (c) Example of a configuration model network. Each individual has a prescribed degree distribution, which gives rise to “half-links” that are connected at random. (d) A household configuration network, consisting of completely interconnected households (cliques) with each individual also having one random link to another household. (e) Map showing Great Britain, together with the movements of cattle from six farms (each represented in a separate colour). Notice the heterogeneity between farms and the generally localised nature of movements. (f) Example of a small-world model based on a 2D lattice with nearest neighbor connections. The small-world property is given by the presence of rare random links that can connect distant parts of the network.

Figure 2

Comparison of random and scale-free networks. (a) Degree distributions for two classes of networks: scale free and random networks. (b) Example random network with 100 nodes and 300 links. All nodes have similar numbers of links. (c) Example scale-free network with 100 nodes and 300 links. Most nodes have few links, with a few nodes having many links.

Figure 3

Comparison of simulation and deterministic models for six networks. (a) Two-group configuration model network. (b) Two-group assortative network. (c) Static regular network. (d) Dynamical regular network. (e) Regular clustered network. (f) One-dimensional lattice.