The Rules of Contagion

by Adam Kucharski

  What effect did people like Landau have on the spread of Feynman diagrams? In 2005, physicist Luís Bettencourt, historian David Kaiser and their colleagues decided to find out.[6] Kaiser had previously collected academic journals published around the world in the years after Feynman announced his idea. He then went through each journal page-by-page, looking for references to Feynman diagrams, and tallying up how many authors adopted the idea over time. 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.

  The next step was to quantify how contagious the idea had been. Although the diagrams had originated in the US, they had spread quickly when they arrived in Japan. Things were more sluggish in the USSR, with a slower uptake than the other two countries. This was consistent with historical accounts. Japanese universities had expanded rapidly during the post-war period, with a strong particle physics community. In contrast, the emerging Cold War – combined with the scepticism of researchers like Landau – had stifled the diagrams in the USSR.

  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. Initially R was around 15 in the USA and potentially as high as 75 in Japan. It was one of the first times that researchers had tried to measure the reproduction number of an idea, putting a number on what had previously been a vague notion of contagiousness.

  This raised the question of why the idea had been so catchy. Perhaps it was because physicists were interacting with each other frequently during this period? Not necessarily: the high value of R instead seemed to be because people kept spreading the idea for a long time once they’d adopted it. ‘The spread of Feynman diagrams appears analogous to a very slowly spreading disease,’ the researchers noted. Adoption was ‘due primarily to the very long lifetime of the idea, rather than to abnormally high contact rates’.

  Tracing citation networks doesn’t just tell us how new ideas spread. We can also learn how they emerge. If high profile scientists dominate a field, it can hinder the growth of competing ideas. As a result, new theories may only gain traction once dominant scientists cede the limelight. As physicist Max Planck supposedly once said, ‘science advances one funeral at a time.’ 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.

  Scientific papers aren’t only relevant to scientists. Ed Catmull, co-founder of Pixar, has argued that publications are a useful way of building links with specialists outside their company.[8] ‘Publishing may give away ideas, but it keeps us connected with the academic community,’ he once wrote. ‘This connection is worth far more than any ideas we may have revealed’. Pixar is known for encouraging ‘small-world’ encounters between different parts of a network. This has even influenced the design of their building, which has a large central atrium containing potential hubs for random interactions, like mailboxes and the cafeteria. ‘Most buildings are designed for some functional purpose, but ours is structured to maximize inadvertent encounters,’ as Catmull put it. The idea of social architecture has caught on elsewhere too. 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]

  Unexpected encounters can help spark innovation, but if companies remove too many office boundaries, it can have the opposite effect. When researchers at Harvard University used digital trackers to monitor employees at two major companies, they found that the introduction of open-plan offices reduced face-to-face interactions by around 70 per cent. People instead chose to communicate online, with e-mail use increasing by over 50 per cent. Increasing the openness of the offices had decreased the number of meaningful interactions, reducing overall productivity.[10]

  For something to spread, susceptible and infectious people need to come into contact, either directly or indirectly. Whether we’re looking at innovations or infections, the number of opportunities for transmission will depend on how often contacts occur. If we want to understand contagion, we therefore need to work out how we interact with one another. However, it’s a task that turns out to be remarkably difficult.

  ‘Thatcher halts survey on sex,’ announced the headline in The Sunday Times. It was September 1989, and the government had just blocked a proposal to study sexual behaviour in the UK. Faced with a growing hiv epidemic, researchers had become increasingly aware of the importance of sexual encounters. The problem was that nobody really knew how common these encounters were. ’We had no idea of the parameter estimates that would drive an epidemic of hiv,’ Anne Johnson, one of the researchers who’d proposed the UK study, later said. ‘We didn’t know what proportion of the population had gay partners, we didn’t know the number of partners that people had.’[11]

  In the mid-1980s, a group of health researchers had come up with the idea of measuring sexual behaviour on a national scale. They’d run a successful pilot study, but had struggled to get the main survey off the ground. There were reports that Margaret Thatcher had vetoed government funding, believing that the study would intrude into people’s private lives, leading to ‘unseemly speculation’. Fortunately, there was another option. Shortly after The Sunday Times article came out, the team secured independent support from the Wellcome Trust.

  The National Survey of Sexual Attitudes and Lifestyles – or Natsal – would eventually run in 1990, then again in 2000 and 2010. According to Kaye Wellings, who helped develop the study, it was clear the data would have applications beyond STIs. ‘Even as we were writing the proposal, I think we realised that it was going to answer a whole host of questions of relevance to public health policy, which there hadn’t been data available to answer before.’ In recent years, Natsal has provided insights into a whole range of social issues, from birth control to marriage breakdowns.

  Still, it wasn’t easy to get people talking about their sex lives. Interviewers had to persuade people to take part – often by emphasising the benefits for wider society – and build enough trust for participants to answer honestly. Then there was the issue of sexual terminology. ‘There was that mismatch between the public health language and the language of everyday, which was so full of euphemisms,’ Wellings noted. She recalled that several participants didn’t recognise terms like ‘heterosexual’ or ‘vaginal’. ‘All the Latin-sounding names, or any word with more than three syllables, was thought of as something completely weird and unorthodox.’

  Yet the Natsal team did have some advantages, such as the relatively low frequency of sexual encounters. 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] Even the most active individuals are unlikely to sleep with more than a few dozen people in a given year. It means that most interviewees will know how many partners they’ve had and what those partnerships involved. Contrast that with the sort of interactions that might spread flu, such as conversations or handshakes. Each day, we may have dozens of face-to-face encounters like these.

  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. This included physical contacts, like handshakes, as well as conversations. Researchers have since run similar studies in countries ranging from Kenya to Hong Kong. The studies are
also getting more ambitious: I recently worked with collaborators at the University of Cambridge to run a public science project collecting social behaviour data from over 50,000 volunteers in the UK.[13]

  Thanks to these studies, we now know that certain aspects of behaviour are fairly consistent around the world. People tend to mix with people of a similar age, with children having by far the most contacts.[14] Interactions in schools and at home typically involve physical contact, and encounters that occur on a daily basis often last longer than an hour. 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]

  It’s one thing to measure such behaviour, but can this new information help predict the shape of epidemics? At the start of this book, we saw that during the 2009 influenza pandemic, there were two outbreak peaks in the United Kingdom: one in the spring and one in the autumn. To understand what caused this pattern, we simply need to look at schools. These bring children together in an intensely social environment, creating a potential mixing pot of infection; during the school holidays, children have around 40 per cent fewer daily social contacts on average. As you can see from the graph above, the gap between the two pandemic peaks in 2009 coincided with the school holiday. This lengthy drop in social contacts was large enough to explain the summer lull in the pandemic. However, school holidays can’t fully explain the second wave of infection. Although the first peak was probably due to changes in social behaviour, the second peak was mostly down to herd immunity.[16] The rise and fall of infections during school terms and holidays can influence other health conditions too. In many countries, asthma cases peak at the start of a school term. These outbreaks can also have a knock-on effect in the wider community, exacerbating asthma in adults.[17]

  Dynamics of the 2009 influenza pandemic in the UK

  If we want to predict a person’s risk of infection, it’s not enough to measure how many contacts they have. We also need to think about their contacts’ contacts, and their contacts’ contacts. A person with seemingly few interactions might be just a couple of steps away from a high transmission environment like a school. A few years ago, my colleagues and I looked at social contacts and infections during the 2009 flu pandemic in Hong Kong.[18] We found that it was the high number of social contacts among children that drove the pandemic, with a drop in contacts and infection after childhood. But there was a subsequent increase in risk when people reached parenthood age. As any teacher or parent will know, interactions with children means an increased risk of infection. In the US, people without children in their house typically spend a few weeks of the year infected with viruses; people with one child have an infection for about a third of the year; and those with two children will on average carry viruses more often than not.[19]

  As well as driving transmission in communities, social interactions can also transport infections to other locations. In the early stages of the 2009 flu pandemic, the virus didn’t spread according to the as-the-crow-flies distance between countries. When the outbreak started in Mexico in March, it quickly reached faraway places like China, but took longer to appear in nearby countries such as Barbados. The reason? If we define ‘near’ and ‘far’ in terms of locations on a map, we’re using the wrong notion of distance. Infections are spread by people, and there are more major flight routes linking Mexico and China – such as those via London – than those connecting Mexico with places like Barbados. China might be far away for a crow, but it’s relatively close for a human. 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 similar airline routes when it emerged in China in 2003, arriving in countries like the Republic of Ireland and Canada before Thailand and South Korea.[20]

  Once the 2009 flu pandemic arrived in a country, however, long travel distance seemed to be less important for transmission. In the US, the virus spread like a ripple, gradually travelling from the southeast outwards. It took about three months to move 2,000 kilometres across the eastern US, which works out at a speed of just under 1 km/h. On average, you could have outwalked it.[21]

  Although long-distance flight connections are important for introducing viruses to new countries, travel within the US is dominated by local movements. The same is true of many other countries.[22] To simulate these local movements, researchers often use what’s known as a ‘gravity model’. 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. If you live in a village, you might visit a nearby town more often than a city further away; if you live in a city, you’ll probably spend little time in the surrounding towns.

  This might seem like an obvious way to think about interactions and movements, but historically people have thought otherwise. In the mid-1840s, at the peak of Britain’s railway bubble, engineers assumed that most traffic would come from long-distance travel between big cities. Unfortunately, few bothered to question this assumption. There were some studies on the continent, though. To work out how people might actually travel, Belgian engineer Henri-Guillaume Desart designed the first ever gravity model in 1846. His analysis showed that there would be a lot of demand for local trips, an idea that was ignored by rail operators on the other side of the channel. The British railway network would probably have been far more efficient had it not been for this oversight.[23]

  It can be easy to underestimate the importance of social ties. When Ronald Ross and Hilda Hudson wrote those papers on the ‘theory of happenings’ in the early twentieth century, they suggested it could apply to things like accidents, divorce and chronic diseases. In their minds, these things were independent happenings: if something happened to one person, it didn’t affect the chances of it happening to someone else. There was no element of contagion from one person to another. At the start of the twenty-first century, researchers started to question whether this was really the case. In 2007, physician Nicholas Christakis and social scientist James Fowler published a paper titled ‘The Spread of Obesity in a Large Social Network over 32 Years’. They had studied health data from participants in the long-running Framingham Heart Study, based in the city of Framingham, Massachusetts. 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.

  The pair subsequently looked at several other forms of social contagion in the same network, including smoking, happiness, divorce, and loneliness.[24] It might seem odd that loneliness could spread through social contacts, but the researchers pointed to what might be happening at the edge of a friendship network. ‘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.’

  These papers have been hugely influential. In the decade after it was published, the obesity study alone was cited over 4,000 times, with many seeing the research as evidence that such traits can spread. But it’s also come under fire. Soon after the obesity and smoking studies were published, a paper in the British Medical Journal suggested that Christakis and Fowler’s analysis might have flagged up effects that weren’t really there.[25] Then mathematician Russell Lyons wrote a paper arguing that the researchers had made ‘fundamental errors’ and that ‘their major claims are unfounded’.[26] So where does that leave us? Do things like obesity actually spread? How do we even work out if behaviour is contagious?

  One of the most familiar examples of social contagion is yawning, and it’s also one of the easiest forms of contagion to study. Because it’s common, easy to spot, and the delay from one person’s yawn to another is relatively short, resear
chers can look at transmission in detail.

  By setting up lab experiments, several studies have analysed what makes yawns spread. 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] The transmission process is also faster, with a smaller delay between yawns among family members than among acquaintances. 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. It’s not just humans who are more likely to pick up yawns from individuals they care about. Similar social yawning can occur among animals, from monkeys to wolves.[28] However, it can take a while for us to become susceptible to a yawn. Although infants and toddlers sometimes yawn, they don’t seem to catch them from their parents. Experiments suggest yawning doesn’t become contagious until children reach about four years old.[29]

  As well as yawning, researchers have looked at the spread of other short-term behaviours, like itching, laughter, and emotional reactions. These social responses can manifest on very fast timescales: in experiments looking at teamwork, leaders were able to spread a positive or negative mood to their team in a matter of minutes.[30]

  If researchers want to study yawning or mood, they can use laboratory set-ups to control what people see, and avoid distractions that could skew results. This is feasible for things that spread quickly, but what about behaviours and ideas that take much longer to propagate through a population? It’s much harder to study social contagion outside a laboratory. This isn’t just a challenge for human populations. Among birds, great tits have a long-standing reputation for innovation. In the 1940s, British ecologists noted that they had worked out how to peck through the foil of milk bottles to get at the cream. The tactic would persist for decades, but it wasn’t clear how such innovations spread through bird populations.[31]