Epidemics do not require long-distance travel by virus carriers to spread
Epidemic spread
Hallatschek typically studies in a Petri dish how new mutations spread in colonies of microbes, activity that he models mathematically to understand how evolution fixes new traits in a population. When looking at simple theories of such “epidemic” spread, however, he was surprised to discover that no one knew the answer to a simple question: How does the long-distance dispersal of individuals during an outbreak affect the spread?
Simulations show that if the chance of individuals traveling away from the center of an outbreak drops off exponentially with distance – for example, if the chance of distant travel drops by half every ten miles — the disease spreads as a relatively slow wave.
Simulations also suggested that a slower “power-law” drop off — for example, if the chance of distant travel drops by half every time the distance is doubled – would let the disease get quickly out of control.”
“We were shocked to see that this had not been demonstrated, and saw a chance to prove something really fundamental,” Hallatschek said.
The simple model he used was stripped of real-world complexity, but contained the crucial ingredients needed to predict evolutionary spread and, more importantly, could be captured by a mathematical formula. Hallatschek discovered three types of epidemic situations involving power-law distributions.
In cases where long-range jumps are very rare, epidemics spread in a slow wave, typified by the Black Death. The invasive cane toad also spread in a slow wave after being introduced to Australia in the 1930s. When long-range jumps are common, the disease spreads very rapidly, as in 2002-2003 with SARS (severe acute respiratory syndrome), which was spread around the world by air travelers. An intermediate situation produces satellite outbreaks, but spreads far more slowly than SARS-like cases.
Hallatschek said that previous studies failed to take into account the randomness of jumps, which led people to think that any long-range jump would lead to new outbreaks and rapid spread. But if long-range jumps are extremely rare, distant outbreaks tend to be overtaken by the slow, wavelike spread of the initial outbreak before they can contribute much to the overall epidemic.
He noted that two recent studies of human dispersal — the “Where’s George?” dollar bill tracking study and a 2008 cellphone-user mobility study — suggest that in the real world, humans disperse according to a power-law distribution over distances of up to hundreds of kilometers and exponentially over even longer distances.
The release notes that in the future, he plans to make his model more and more realistic, first by incorporating networks to mimic the real world where people do not jump randomly, but must travel through airport hubs or train stations. Hallatschek also hopes to test his model by using data on the evolving genome sequences of pathogens as they spread, which provide one measure of where and when satellite outbreaks occur.
The work was supported by the Simons Foundation and QB3, as well as grants from Germany’s Deutsche Forschungsgemeinschaft and the U.S. National Science Foundation.
— Read more in Oskar Hallatscheka and Daniel S. Fisherb, “Acceleration of evolutionary spread by long-range dispersal,” Proceedings of the National Academy of Sciences (2 September 2014) (doi: 10.1073/pnas.1404663111)
