The Rules of Contagion: Why Things Spread - and Why They Stop

by Adam Kucharski

‘You couldn’t tell a story about why Lehman had brought the financial system down without telling a contagion story.’

If you were to make a list of network features that could amplify contagion, you’d find that the pre-2008 b...

In 1989, epidemiologist Sunetra Gupta led a study showing that the dynamics of infections could depend on whether a network is what mathematicians call ‘assortative’ or ‘disassortative’.

In an assortative network, highly connected individuals are linked mostly to other highly connected people.

In contrast, a disassortative network is when high-risk people are mostly linked to low risk ones.

The banking network, of course, turned out to be disassortative.

Although each individual bank had diversified their investments, there was little diversity in the way they had collectively done it.

During the Great Depression that followed the 1929 Wall Street crash, economist John Maynard Keynes observed that there is a strong incentive to follow the crowd. ‘A sound banker, alas, is not one who foresees danger and avoids it,’ he once wrote, ‘but one who, when he is ruined, is ruined in a conventional way along with his fellows, so that no one can really blame him.’[88]

The more the largest banks diversify their investments, the more opportunities for shared contagion. Several studies have found that during a financial crisis, diversification can destabilise the wider network.[90]

Likewise, when banks lose confidence in the financial system – as happened in 2007/8 – they often hoard money rather than lending it out.

They found that if bankers started hoarding money when they lost confidence in the system, it could exacerbate a crisis: banks that would otherwise have had enough capital to ride it out would instead fail.

One major change has been to get banks to hold more capital if they are important to the network, reducing their susceptibility to infection.

In 2011, a commission chaired by John Vickers recommended that larger British banks put a ‘ring-fence’ around their riskier trading activities.[94]

‘A channel of financial system interconnectedness – and hence of contagion – would be made safer.’

They now have to go through independently run central hubs which have the effect of simplifying the network structure.

The danger, of course, is that if a hub fails, it could become a giant superspreader.

‘It should act as a risk buffer, but in extreme cases it could act as a risk amplifier.’ To guard against this problem, hubs have access to emergency capital from the members who use them.

But by removing the tangle of hidden loops from the network, the hubs should mean fewer opportunities for contagion, and less uncertainty about who is at risk.

One of the big obstacles is access to trading information. Banks are naturally protective of their business activities, making it difficult for researchers to form a picture of exactly how institutions are connected, particularly at the global level.

We need to consider how beliefs and behaviours arise, and how they can spread. This means thinking about people as well as pathogens. From innovations to infections, contagion is often a social process.

During the early 1960s, US mathematician William Goffman suggested that the transfer of information between scientists worked much like an epidemic.[3]

When the team plotted the data, the number of authors using the diagrams followed the familiar S-shaped adoption curve, rising exponentially before eventually plateauing.

With the data they had available, Bettencourt and colleagues could also estimate the reproduction number, R, of a Feynman diagram: for each physicist who adopted the idea, how many others did they eventually pass it on to? Their results suggested a lot: as an idea, it was highly contagious.

This raised the question of why the idea had been so catchy.

Researchers at MIT have since tested this famous comment by analysing what happens after the premature deaths of elite scientists.[7]

They found that competing groups would subsequently publish more papers – and pick up more citations – while collaborators of the ‘star’ researcher tended to fade in prominence.

In 2016, the Francis Crick Institute opened in London. Europe’s largest biomedical lab, it would become home to over 1,200 scientists in a £650 million building. According to its director Paul Nurse, the layout was designed to get people interacting by creating ‘a bit of gentle anarchy’.[9]

Increasing the openness of the offices had decreased the number of meaningful interactions, reducing overall productivity.[10]

Whether we’re looking at innovations or infections, the number of opportunities for transmission will depend on how often contacts occur.

The National Survey of Sexual Attitudes and Lifestyles – or Natsal – would eventually run in 1990, then again in 2000 and 2010.

The most recent Natsal study found that a typical twenty-something in the UK has sex about five times a month on average, with less than one new sexual partner per year.[12]

During the past decade or so, researchers have increasingly tried to measure social contacts that are relevant for respiratory infections like flu. The best known is the polymod study, which asked over 7,000 participants in eight European countries who they interacted with.

Even so, the overall number of interactions can vary a lot between locations. Hong Kong residents typically have physical contact with around five other people each day; the UK is similar, but in Italy, the average is ten.[15]

We also need to think about their contacts’ contacts, and their contacts’ contacts.

It turns out that the spread of flu in 2009 is much easier to explain if we instead define distances according to airline passenger flows. And not just flu: sars followed

Although long-distance flight connections are important for introducing viruses to new countries, travel within the US is dominated by local movements.

The idea is that we are drawn to places depending on how close and populous they are, much like larger, denser planets have a stronger gravitational pull.

As well as suggesting that obesity could spread between friends, they proposed that there could be a knock-on effect further into the network, potentially influencing friends-of-friends and friends-of-friends-of-friends.

‘On the periphery, people have fewer friends, which makes them lonely, but it also drives them to cut the few ties that they have left. But before they do, they tend to transmit the same feeling of loneliness to their remaining friends, starting the cycle anew.’

The nature of social relationships seems to be particularly important for transmission: the better we know someone, the more likely it is that we’ll catch their yawn.[27]

Yawn in front of a stranger and there’s a less than 10 per cent chance it will spread; yawn near a family member and they’ll catch it in about half the time.

Experiments suggest yawning doesn’t become contagious until children reach about four years old.[29]

The birds grouped together into several different sub-populations; in five of these populations, the researchers taught a couple of birds how to solve the puzzle.

A few eventually worked out how to get into the box, but it took much longer for the idea to emerge and spread.

In the trained populations, the idea was also highly resilient. Many of the birds died from one season to the next, but the knowledge didn’t.

‘The behaviour re-emerged very quickly each winter,’ Aplin said, ‘even if there were only a small number of individuals that were alive from the previous...

‘Some general principles are similar to how disease spreads through populations, for instance more social individuals being more likely to encounter and adopt new behaviours, and socially central individuals can act as “keyst...

There were actually a couple of ways to get into the puzzle box, but it was the solution the researchers had introduced that became the accepted method. Such conformity is even more common when we look at humans. ‘We’re social learning specialists,’ Aplin said.

‘The social learning and culture we observe in human societies is of a magnitude greater than anything we observe in the rest of the animal kingdom.’

In general, there are three possible explanations for such similarities.