Black Death Predated “Small World” Effect, Say Network Theorists

The slow advance of bubonic plague in the 14th century suggests that medieval society lacked the long distance links.So when did the small world effect emerge?

The Black Death was a particularly virulent form of bubonic plague that originated in China, spread along the Silk Route and eventually infected much of Europe during the 14th Century.

Historians have pieced together a remarkably detailed picture of the way the disease spread. It first reached Mediterranean in 1347 and spread north across Europe, reaching France and Austria in 1348, Germany and Britain in 1349 and Scandinavia and Russia in 1350.

So the disease advanced like a slow-moving wave, taking three years to infect the entire continent, with the wave front moving at a rate of around 2 kilometres a day.

That’s in stark contrast to modern pandemics which can appear almost simultaneously in many places around the world.

Epidemiologists know that this pattern of infection is the result of the small world effect, the idea that although the global population is huge, it is possible to connect any two people by a short number of steps.

So an individual who becomes infected in Hong Kong can infect friends in New York the following day. In other words, diseases piggyback on this small world network.

So why did the Black Death spread so slowly?

Today, Seth Marvel at the University of Michigan in Ann Arbor and a few pals say the answer is that early societies were not “small worlds”. Instead, they argue that the network of links between individuals must have been crucially different from those that exist today.

The small world effect is ubiquitous in modern society. Network scientists find it at work in the spread of disease, information, gossip, fashions, conflicts and so on.

It’s easy to assume that this small word effect must also have existed in the ancient world, albeit on a different scale. A constant flow across the continent of messengers, diplomats, merchants, armies, pilgrims and so on would have provided exactly the kind of conditions in which a highly infectious disease like the Black Death could spread rapidly. And yet, that did not happen.

To find out why, Marvel and co created a computer model of the population in ancient Europe and simulated the spread of disease across it in two different ways.

In the first, they assumed that the network of connections between individuals formed a small world, with most people having links to individuals nearby but a few having long distance links. In this case, the disease spreads in the same way as modern epidemics, with a central area of infection surrounded by satellite outbreaks caused by the long distance transmission.

In the second, they assumed that people only have links to others nearby and that almost nobody has long distance links. In this case, the disease spreads in a slow-moving wave that propagates away from the origin of infection, just like the Black Death in the 14th century.

Marvel and co say that this second “large world” network must better represent the links that existed in medieval Europe. In other words, long distance links in medieval society must have been so rare that they had no effect on the spread of disease. “The small-world effect is, we contend, a modern phenomenon,” they conclude.

That’s a fascinating result but could there be other explanations for the slow-moving spread of Black death? One possibility is that it was not the network that limited the spread of disease but the nature of the plague itself.

Marvel and co’s model assumes that people become infected and stay infected. In reality, however, they would have died quickly, limiting the range of people they could have come into contact with.

But Marvel and co say this is unlikely to influence the dynamics of the disease. “Travelling on horseback, for example (the fastest form of land transport in the 14th century), an individual carrying the Black Death could travel a maximum of 160 kilometres in the four days for which the victims of the disease remain infectious,” they say.

That’s more than enough to spread the disease more rapidly than the observed 2 km per day. Indeed, a person on foot could travel faster than this. “This suggests that travel velocity was not the limiting factor in the spread of the disease,” they say.

Another possibility is that news of the disease spread faster than the plague itself and that people chose not to travel as a result. So the lack of a small word effect may only have been temporary.

Be that as it may, Marvel and co conclude that the spread of the disease must have been limited by the lack of long distance links. In other words, there must have been a vanishingly small number of long distance travellers in those days, whatever the reason.

The absence of the small world effect in the ancient world will puzzle some researchers. In recent years, network theorists have studied the network of links between characters in ancient links such as Homer’s Iliad and Odyssey and the Icelandic Sagas. These networks are essentially indistinguishable from the social networks that exist today.

Various theorists say this is evidence that these stories must be based on the real world networks that existed in those days.

However, this assumes that ancient networks must have been small worlds, just as today’s one’s are. Marvel and co’s work suggests that this may not be the case after all.

Beyond this, the conclusion that small world networks are an exclusively modern phenomena raises an interesting question. If today’s global network is a small world but the global network in the 14th century was not, when did things change?

Marvel and co say that the finger of blame points to the emergence of relatively inexpensive long distance travel which allowed pandemics to spread rapidly in the 19th century.

In other words, the invention of the railways and steam ships transformed the nature of society and also the nature of disease.

Ref: arxiv.org/abs/1310.2636: The Small-World Effect is a Modern Phenomenon