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.

Infectious diseases exert a large and in many contexts growing burden on human health, but violate most of the assumptions of classical epidemiological statistics and hence require a mathematically sophisticated approach. Viral shedding data are collected during human studies—either where volunteers are infected with a disease or where existing cases are recruited—in which the levels of live virus produced over time are measured. These have traditionally been difficult to analyse due to strong, complex correlations between parameters. Here, we show how a Bayesian approach to the inverse problem together with modern Markov chain Monte Carlo algorithms based on information geometry can overcome these difficulties and yield insights into the disease dynamics of two of the most prevalent human pathogens—influenza and norovirus—as well as Ebola virus disease.

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