The Hidden Geometry of Complex, Network-Driven Contagion Phenomena

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.

Flow distances on open flow networks

“…It is reasonable to develop a novel method based on flow distances discussed in this paper to partition and coarse-grain. Third, the flow distances metrics and network embedding can help us to understand some underlying dynamical processes on the network in a geometric way [37]. The current flow distances metrics also have shortcomings.…”

“…Distance on graph is a very useful concept [37]. Both the shortest path distance [38], resistance distance [39] and the mean first-passage distance of a random walker [40][41][42][43] can reflect the intrinsic properties of the graph.…”

Forecasting the size and peak of cholera epidemic in Yemen, 2017

“…The success of global forecasting has been partly supported by recent advances in computational statistics, especially those employing the Markov Chain Monte Carlo technique. Additionally, the epidemiological dynamics of global spread has been shown to be mainly (and mostly) characterized by the global mobility pattern of humans [3]. The time from emergence of a novel infectious disease in a country to arrival at an importing country is linearly predicted by using a simple metric of the airline transportation network (which is referred to as the 'effective distance').…”

The Ecology of Financial Markets

“…For instance, equilibrium analysis has implicitly a long-term horizon, but given that the time is entirely unspecified, it will be considered as a timeless analysis. Network approaches offer a useful framework for understanding the dynamics of contagion processes in biological, social, and financial systems (Brockmann & Helbing, 2013;Chmiel, Klimek, & Thurner, 2014;Elliott, Golub, & Jackson, 2014;Gai et al, 2011). By constructing and examining the topology of interdependencies between agents in a system, this approach can be used to model a number of important factors influencing the dynamics of contagion, such as structural properties of the system, properties of agents in the system, triggers of the distress, and contagion mechanisms.…”

“…Instead, network approaches are suggested as a tool that provides realism to modeling the structure of market interactions. Examples of the application across different domains are network models of social (Barabási et al, 2002;Brockmann & Helbing, 2013), biological (Albert, 2005), ecological (McCann, Hastings, & Huxel, 1998), engineering (Guimerà, Mossa, Turtschi, & Amaral, 2005), and financial (Arinaminpathy et al, 2012;Gai, Haldane, & Kapadia, 2011) systems.…”