Redrawn maps of the world's air-transport network could change the way we track disease from city to city.
Five hundred years ago, the spread of disease was largely constrained by the main mode of transportation of the time: people traveling on foot. An outbreak in one town would slowly ripple outward with a pattern similar to what occurs when a rock drops onto a surface of still water. The Black Death moved across 14th century Europe in much this way, like concentric waves unfurling across the continent.
Today, disease migrates across populations and geography with a curiously different pattern. In 2003, SARS first appeared in China, then spread to Hong Kong, then turned up from there in Europe, Canada and the United States. Plot the spread of the disease on a map of the world, and its movement looks downright random.
What has changed dramatically in the intervening centuries is not necessarily the diseases themselves, but human mobility networks. Dirk Brockmann, a theoretical physicist and professor of complex systems at Northwestern University, has long been interested in how evolving modes of long-distance transportation have changed many things: disease dynamics, the spread of information, the transport of species from one ecosystem to others where they don’t belong.
For about a decade, Brockmann and other researchers have been incorporating real datasets on the world air-transport network into models of disease dynamics. They can simulate an outbreak in one location and estimate its arrival in another. But early on, Brockmann noticed that models created by him and other colleagues often produced strikingly similar results, even with simulations built on different assumptions about infection rates, disease dynamics, seasonality, or the age structure of infected populations.
"That made me think about, 'what is it that makes these different simulations be so much in agreement?'"Brockmann says. All of those other factors seemed to play little role. "My hypothesis was that much of it is driven by the structure of these mobility networks."
Brockmann’s research ultimately led him to a surprisingly simple conclusion. Diseases spread across the globe today in precisely the same way they did during the time of foot-only travel and the Black Death. We’ve just been looking at the map of the world all wrong.
Consider first these two "toy models" of Brockmann's, which simulate the spatial patterns of how an epidemic spreads. This first one shows a disease spread by only local traffic (as would have been the case centuries ago):
And this is what an epidemic looks like hitching a ride with long-range traffic in the age of air travel:
So how do you make out a coherent pattern in that second picture, especially one that would allow you to predict the spread of future epidemics? Brockmann and colleagues came up with what he calls a “very simple idea”: "We figured, what if we redefined the notion of geographic distance?"
We’ve been primed for centuries to think about distance in miles or kilometers. But in the age of airplane travel, London and New York are not as far apart as they once seemed. The air travel network means that the world is connected today in fundamentally different ways than it was years ago. Here is a map of the 4,000 or so airports in the world, with 40,000 connections between them:
With a little bit of math, Brockmann says, researchers can remap that picture according not to literal geography, but instead to temporal distance between two places defined by the flow of air travel between them.
"What you can do then is place yourself on any arbitrary location in this network," Brockmann says. 'And you can ask yourself from this perspective, 'what does the world look like?'"
Pretend you’re standing on the Cyprus city of Paphos, from which you can connect by plane to London, and then Barcelona or Washington, D.C. or Salt Lake City. This is what the world looks like now, on a "shortest path tree" that shows your most probable route to all of the other airports in the network:
The same map could be drawn from any starting place in the world’s air-travel network. The structure of the map, by definition, has to be a tree, Brockmann says. But that doesn’t mean these connections and routes are the only ones possible; rather, they’re those with the highest probability.
This is a simulation from Brockmann of a hypothetical disease resembling pandemic influenza, across the course of 53 days:
The pattern on a traditional map appears random. This is what it looks like through the lens of Brockmann’s shifted perspective:
"If you look at the outbreak and how it spreads globally in this new kind of representation, everything becomes very simple," he says. Once again, the pattern resembles the concentric ripples of that rock on water that characterized epidemics centuries ago. "Nowadays, it doesn’t look much different," Brockmann adds. "You just have to look at the whole process from the right angle."
Here is another pair of simulations showing the spread of a similar hypothetical disease originating in Atlanta:
The real power of this insight comes from its diagnostic potential. Imagine a scenario where a new pandemic – its origins unknown – has already appeared in parts of China, Buenos Aires, Quebec, and Vancouver. This new representation of distance can help pinpoint the origin of the outbreak.
"It’s the only location from which the pattern looks concentric," Brockmann says. Any child, he adds, can tell you where the rock landed in the rippling water. "It’s at the center."
The idea that disease travels through airport networks is not a novel one to epidemiologists. But the discovery that pandemic patterns have not changed so much after all in the last 500 years is.
"That’s been overlooked for some reason, which in retrospect is a little weird," Brockmann says. "But it’s sometimes like that in science. You do this, and then you think, ‘Why didn’t we think of all this earlier?'"