Public health crises of the past decade – such as the 2003 SARSoutbreak, which spread to 37 countries and caused about 1,000deaths, and the 2009 H1N1 flu pandemic that killed about 300,000people worldwide – have heightened awareness that new viruses orbacteria could spread quickly across the globe, aided by airtravel.
While epidemiologists and scientists who study complex networksystems – such as contagion patterns and information spread insocial networks – are working to create mathematical models thatdescribe the worldwide spread of disease, to date these models havefocused on the final stages of epidemics, examining the locationsthat ultimately develop the highest infection rates.
Containing the infection
Unlike existing models, the new MIT model incorporatesvariations in travel patterns among individuals, the geographiclocations of airports, the disparity in interactions amongairports, and waiting times at individual airports to create a toolthat could be used to predict where and how fast a disease mightspread.
“Our work is the first to look at the spatial spreading ofcontagion processes at early times, and to propose a predictor forwhich ‘nodes’ – in this case, airports – will lead to moreaggressive spatial spreading,” says Ruben Juanes, the ARCOAssociate Professor in Energy Studies in CEE. “The findings couldform the basis for an initial evaluation of vaccine allocationstrategies in the event of an outbreak, and could inform nationalsecurity agencies of the most vulnerable pathways for biologicalattacks in a densely connected world.”
The flow of fluids though rock
Juanes’ studies of the flow of fluids through fracture networks insubsurface rock and the research of CEE’s Marta González, who usescellphone data to model human mobility patterns and trace contagionprocesses in social networks, laid the basis for determiningindividual travel patterns among airports in the new study.Existing models typically assume a random, homogenous diffusion oftravelers from one airport to the next.
However, people don’t travel randomly; they tend to create patternsthat can be replicated. Using González’s work on human mobilitypatterns, Juanes and his research group – including graduatestudent Christos Nicolaides and research associate LuisCueto-Felgueroso – applied Monte Carlo simulations to determine thelikelihood of any single traveler flying from one airport toanother.
“The results from our model are very different from those of aconventional 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 waspublished in the journal PLoS ONE. “The advective transportprocess relies on distinctive properties of the substance that’smoving, as opposed to diffusion, which assumes a random flow. Ifyou include diffusion only in the model, the biggest airport hubsin terms of traffic would be the most influential spreaders ofdisease. But that’s not accurate.”
Beware of Honolulu
For example, a simplified model using random diffusion might saythat half the travelers at the Honolulu airport will go to SanFrancisco and half to Anchorage, Alaska, taking the disease andspreading it to travelers at those airports, who would randomlytravel and continue the contagion.
In fact, while the Honolulu airport gets only 30 percent as muchair traffic as New York’s Kennedy International Airport, the newmodel predicts that it is nearly as influential in terms ofcontagion, because of where it fits in the air transportationnetwork: Its location in the Pacific Ocean and its many connectionsto distant, large and well-connected hubs gives it a ranking ofthird in terms of contagion-spreading influence.
Kennedy Airport is ranked first by the model, followed by airportsin Los Angeles, Honolulu, San Francisco, Newark, Chicago (O’Hare)and Washington (Dulles). Atlanta’s Hartsfield-Jackson InternationalAirport, which is first in number of flights, ranks eighth incontagion influence. Boston’s Logan International Airport ranks15th.
New but robust approach
“The study of spreading dynamics and human mobility, using toolsof complex networks, can be applied to many different fields ofstudy to improve predictive models,” says González, the Gilbert W.Winslow Career Development Assistant Professor of Civil andEnvironmental Engineering. “It’s a relatively new but very robustapproach. The incorporation of statistical physics methods todevelop predictive models will likely have far-reaching effects formodeling in many applications.”
“Nowadays, one of the most ambitious scientific goals is to predicthow different processes of great economic and societal impactevolve as time goes on,” says Professor Yamir Moreno of theUniversity of Zaragoza, who studies complex networks and spreadingpatterns of epidemics. “We are currently capable of modeling withsome detail real disease outbreaks, but we are less effective whenit comes to identifying new countermeasures to minimize the impactof an emerging disease. The work done by the MIT team paves the wayto find new containment strategies, as the newly developed measureof influential spreading allows for a better comprehension of thespatiotemporal patterns characterizing the initial stages of adisease outbreak.”
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