The Hidden Geometry of Complex, Network-Driven Contagion Phenomena

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Science        
13 December 2013 vol 342, issue 6164, pages 1281-1404
http://www.sciencemag.org/current.dtl

Perspective – Epidemiology
Coming to an Airport Near You
Angela R. McLean
Zoology Department, Oxford University, Oxford OX1 3PS, UK.
Faced with the complexity of the global spread of new infections, a common approach has been to create enormous computer simulations (1, 2). Most of these studies have yielded only tenuous insights, and scientific understanding has been slow to accrue. On page 1337 of this issue, Brockmann and Helbing (3) identify a useful metric—the effective distance—that helps to understand the spread of contagion across a travel network. Once this measure is specified, the global spread of infection can be understood as a simple reaction-diffusion process across the defined transportation network.

Research Article
The Hidden Geometry of Complex, Network-Driven Contagion Phenomena
Dirk Brockmann1,2,3,*, Dirk Helbing4,5
1Robert-Koch-Institute, Seestraße 10, 13353 Berlin, Germany.
2Institute for Theoretical Biology, Humboldt-University Berlin, Invalidenstraße 42, 10115 Berlin, Germany.
3Department of Engineering Sciences and Applied Mathematics and Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL 60208, USA.
4ETH Zurich, Swiss Federal Institute of Technology, CLU E1, Clausiusstraße 50, 8092 Zurich, Switzerland.
5Risk Center, ETH Zurich, Scheuchzerstraße 7, 8092 Zurich, Switzerland.
http://www.sciencemag.org/content/342/6164/1337.abstract

Abstract
The global spread of epidemics, rumors, opinions, and innovations are complex, network-driven dynamic processes. The combined multiscale nature and intrinsic heterogeneity of the underlying networks make it difficult to develop an intuitive understanding of these processes, to distinguish relevant from peripheral factors, to predict their time course, and to locate their origin. However, we show that complex spatiotemporal patterns can be reduced to surprisingly simple, homogeneous wave propagation patterns, if conventional geographic distance is replaced by a probabilistically motivated effective distance. In the context of global, air-traffic–mediated epidemics, we show that effective distance reliably predicts disease arrival times. Even if epidemiological parameters are unknown, the method can still deliver relative arrival times. The approach can also identify the spatial origin of spreading processes and successfully be applied to data of the worldwide 2009 H1N1 influenza pandemic and 2003 SARS epidemic.