The Hidden Geometry in Global Spreading Phenomena
We live in a globally connected world. More than 3 billion
passengers travel each year on the worldwide
air-transportation network and cover trillions of miles of
travel. There is no scale to modern mobility. Our global
connectivity has reshaped the way that spreading phenomena
evolve on the networks that connect us. The complexity of
modern mobility translates into a high degree of
spatio-temporal complexity of spreading phenomena such as
the spread of news, the dynamics of global diseases of
human mediated bio-invasion.
Understanding complex spreading phenomena, for example the
H1N1 pandemic in 2009 or the global spread of SARS in 2003,
at a fundamental level one is interested in answering three
1.) When is an the epidemic going to arrive at a given
2.) How fast is it moving?
3.) Where did it originate?
In simple contagion phenomena these questions are typically
easy to answer because many of them exhibit a dynamics that
yields concentric propagating wave. This is no longer the
case when contagion phenomena evolve on highly connected
networks. The clip below is a simulation of a hypothetical
epidemic, similar in characteristics to the 2009 swine flu
pandemic, on the worldwide air transportation network
(approx. 4000 nodes and 2500 links) with a hypothetical
outbreak in Atlanta. A qualitative characteristic is that
the pattern very quickly becomes irregular, no apparent
wavefront exists and it is very difficult to predict
arrival times at chosen nodes at the network. Also, given a
snapshot of the spread it’s nearly impossible to
reconstruct the origin of the spread.
One of they questions we tried addressing in this project
is whether all these dynamic phenomena that evolve on
networks are governed by some fundamental principle that is
masked by the apparent complexity of the network. The key
idea of the project is that geographic distance in a
globally connected world is no longer a good indicator of
how “far” locations are effectively separated from one
another. For example more people travel each day between
London and New York than e.g. London and some small town in
the UK. So would it not make sense to think of London and
New York as being close neighbors and London and a small
town in the UK be far apart.
It turns out that based on this principle we can define an
effective distance related to the traffic that connects
places for every pair of nodes in the network. This way we
extract all nodes from their geographic embedding and
represent them based on effective distance. Fig. 2
Illustrates how far every node in the network is separated
from Mexico City, for example. The radial distance in this
figure is proportional to the effective distance from Mex.
The tree structure in this representation is the most
probable path that a spreading phenomena will take if
initiated in Mexico.
When the world is mapped according to this node specific
perspective, patterns of spread that are complex in the
conventional view, become simple wave like propagations in
the new perspective. See For instance the video clip below.
The clips shows exactly the same dynamics as the previous
clip, only displayed in a different way. In this view then
it becomes possible to define epidemic speeds and predict
epidemic arrival times.
Figure 1: Snapshots of the spread of a disease
within the United States. Disease dynamics exhibit
geographically very complex patterns. However,
visualized using our method with radial distance
corresponding to “effective” network distance, that is
the shortest-path distance to the central node, the
same process appears more akin to a one-dimensional