Public health crises of the past decade - such as the 2003 SARS
outbreak, which spread to 37 countries and caused about 1,000
deaths, and the 2009 H1N1 flu pandemic that killed about 300,000
people worldwide - have heightened awareness that new viruses or
bacteria could spread quickly across the globe, aided by air
travel.
While epidemiologists and scientists who study complex network
systems - such as contagion patterns and information spread in
social networks - are working to create mathematical models that
describe the worldwide spread of disease, to date these models have
focused on the final stages of epidemics, examining the locations
that ultimately develop the highest infection rates.
Containing the infection
But a
new study by researchers in MIT's Department of Civil and
Environmental Engineering (CEE) shifts the focus to the first few
days of an epidemic, determining how likely the 40 largest U.S.
airports are to influence the spread of a contagious disease
originating in their home cities. This new approach could help
determine appropriate measures for containing infection in specific
geographic areas and aid public health officials in making
decisions about the distribution of vaccinations or treatments in
the earliest days of contagion.
Unlike existing models, the new MIT model incorporates
variations in travel patterns among individuals, the geographic
locations of airports, the disparity in interactions among
airports, and waiting times at individual airports to create a tool
that could be used to predict where and how fast a disease might
spread.
"Our work is the first to look at the spatial spreading of
contagion processes at early times, and to propose a predictor for
which 'nodes' - in this case, airports - will lead to more
aggressive spatial spreading," says Ruben Juanes, the ARCO
Associate Professor in Energy Studies in CEE. "The findings could
form the basis for an initial evaluation of vaccine allocation
strategies in the event of an outbreak, and could inform national
security agencies of the most vulnerable pathways for biological
attacks in a densely connected world."
The flow of fluids though rock
Juanes' studies of the flow of fluids through fracture networks in
subsurface rock and the research of CEE's Marta González, who uses
cellphone data to model human mobility patterns and trace contagion
processes in social networks, laid the basis for determining
individual travel patterns among airports in the new study.
Existing models typically assume a random, homogenous diffusion of
travelers from one airport to the next.
However, people don't travel randomly; they tend to create patterns
that can be replicated. Using González's work on human mobility
patterns, Juanes and his research group - including graduate
student Christos Nicolaides and research associate Luis
Cueto-Felgueroso - applied Monte Carlo simulations to determine the
likelihood of any single traveler flying from one airport to
another.
"The results from our model are very different from those of a
conventional model that relies on the random diffusion of travelers
… [and] similar to the advective flow of fluids," says Nicolaides,
first author of a paper by the four MIT researchers that was
published in the journal PLoS ONE. "The advective transport
process relies on distinctive properties of the substance that's
moving, as opposed to diffusion, which assumes a random flow. If
you include diffusion only in the model, the biggest airport hubs
in terms of traffic would be the most influential spreaders of
disease. But that's not accurate."
Beware of Honolulu
For example, a simplified model using random diffusion might say
that half the travelers at the Honolulu airport will go to San
Francisco and half to Anchorage, Alaska, taking the disease and
spreading it to travelers at those airports, who would randomly
travel and continue the contagion.
In fact, while the Honolulu airport gets only 30 percent as much
air traffic as New York's Kennedy International Airport, the new
model predicts that it is nearly as influential in terms of
contagion, because of where it fits in the air transportation
network: Its location in the Pacific Ocean and its many connections
to distant, large and well-connected hubs gives it a ranking of
third in terms of contagion-spreading influence.
Kennedy Airport is ranked first by the model, followed by airports
in Los Angeles, Honolulu, San Francisco, Newark, Chicago (O'Hare)
and Washington (Dulles). Atlanta's Hartsfield-Jackson International
Airport, which is first in number of flights, ranks eighth in
contagion influence. Boston's Logan International Airport ranks
15th.
New but robust approach
"The study of spreading dynamics and human mobility, using tools
of complex networks, can be applied to many different fields of
study to improve predictive models," says González, the Gilbert W.
Winslow Career Development Assistant Professor of Civil and
Environmental Engineering. "It's a relatively new but very robust
approach. The incorporation of statistical physics methods to
develop predictive models will likely have far-reaching effects for
modeling in many applications."
"Nowadays, one of the most ambitious scientific goals is to predict
how different processes of great economic and societal impact
evolve as time goes on," says Professor Yamir Moreno of the
University of Zaragoza, who studies complex networks and spreading
patterns of epidemics. "We are currently capable of modeling with
some detail real disease outbreaks, but we are less effective when
it comes to identifying new countermeasures to minimize the impact
of an emerging disease. The work done by the MIT team paves the way
to find new containment strategies, as the newly developed measure
of influential spreading allows for a better comprehension of the
spatiotemporal patterns characterizing the initial stages of a
disease outbreak."