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

by Adam Kucharski

The assumption that people remain affected indefinitely doesn’t usually apply to infectious diseases, because people may recover, receive treatment, or die from the infection. But it can capture other kinds of spread. The S-shaped curve would later become popular in sociology, after Everett Rogers featured it in his 1962 book Diffusion of Innovations.[51] He noted that the initial adoption of new ideas and products generally followed this shape.

According to Rogers, four different types of people are responsible for the growth of a product: initial uptake comes from ‘innovators’, followed by ‘early adopters’, then the majority of the population, and finally ‘laggards’. His research into innovations mostly followed this descriptive approach, starting with the S-curve and trying to find possible explanations.

In Ross’s simple model, the fastest growth occurs when just over 21 per cent of the potential audience have adopted the idea. Remarkably, this is the case regardless of how easily the innovation spreads.[54]

From innovations to infections, epidemics almost inevitably slow down as susceptibles become harder to find.

‘I can calculate the motion of heavenly bodies but not the madness of people.’ According to legend, Isaac Newton said this after losing a fortune investing in the South Sea Company.

Dietz outlined a quantity that would become known as the ‘reproduction number’, or R for short. R represented the number of new infections we’d expect a typical infectious person to generate on average.

If R is 10 in a fully susceptible population, we’d need to vaccinate at least 9 in every 10 people. If R is 20, as it can be for measles, we need to vaccinate 19 out of every 20, or over 95 per cent of the population, to stop outbreaks. This percentage is commonly known as the ‘herd immunity threshold’.

R therefore depends on four factors: the duration of time a person is infectious; the average number of opportunities they have to spread the infection each day they’re infectious; the probability an opportunity results in transmission; and the average susceptibility of the population. I like to call these the ‘DOTS’ for short. Joining them together gives us the value of the reproduction number: R = Duration × Opportunities × Transmission probability × Susceptibility

In 2006, researchers working with the Federal Reserve Bank of New York picked apart the structure of the US Fedwire payment network. When they looked at the $1.3 trillion of transfers that happened between thousands of US banks on a typical day, they found that 75 per cent of the payments involved just 66 institutions.

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.

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.

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.

They found that it was unlikely: many shootings occurred in a linked way that couldn’t be explained by homophily or environment, suggesting contagion was responsible. Having identified the shootings that were likely due to contagion, the team carefully reconstructed the chains of transmission between one shooting and the next. They estimated that for every 100 people who were shot, contagion would result in 63 follow-up attacks. In other words, gun violence in Chicago had a reproduction number of about 0.63.

In the world of public health advocacy, few have been as effective – or as pioneering – as Florence Nightingale. While John Snow was analysing cholera in Soho, Nightingale was surveying the illnesses faced by British troops fighting in the Crimean war. Nightingale had arrived in late 1854 to lead a team of nurses in the military hospitals. She found that soldiers were dying at an astonishing rate. It wasn’t just the fighting that was killing them; it was infections like cholera, typhoid, typhus and dysentery. In fact, infections were the main source of death. During 1854, eight times more soldiers died from diseases than from battle wounds.

In 1858, she published her analysis of health in the British Army as an 860-page book. Copies were shipped to leaders ranging from Queen Victoria and the Prime Minister to newspaper editors and European heads of state. Whether looking at hospitals or communities, Nightingale believed that nature followed predictable laws when it came to disease. She said those disastrous early months in Crimea happened because people ignored these laws. ‘Nature is the same everywhere, and never permits her laws to be disregarded with impunity.’ She was also adamant about what had caused the problems. ‘The three things which all but destroyed the army in Crimea were ignorance, incapacity, and useless rules.’

According to carl bell, a public health specialist at the University of Chicago, three things are required to stop an epidemic: an evidence base, a method for implementation, and political will.

Despite constraints on funding, some evidence about gun violence is available. In the early 1990s, before the Dickey Amendment, CDC-funded studies found that having a gun in the home increased the risk of homicide and suicide. The latter finding was particularly notable, given that around two-thirds of gun deaths in the US are from suicide. Opponents of this research have argued that such suicides might have occurred anyway, even if guns hadn’t been present.[48] But easy access to deadly methods can make a difference for what are often impulse decisions. In 1998, the UK switched from selling paracetamol in bottles to blister packs containing up to thirty-two tablets. The extra effort involved with blister packs seemed to deter people; in the decade after the packs were introduced, there was about a 40 per cent reduction in deaths from paracetamol overdoses.[49]

Successful crime reduction can come in a variety of forms. In 1980, for example, West Germany made it mandatory for motorcyclists to wear helmets. Over the next six years, motorcycle thefts fell by two thirds. The reason was simple: inconvenience. Thieves could no longer decide to steal a motorcycle on the spur of the moment. Instead, they’d have to plan ahead and carry a helmet around.

In 1759, mathematician Daniel Bernoulli decided to try and settle the debate. To work out whether the risk of smallpox infection outweighed the risk from variolation, he developed the first-ever outbreak model. Based on patterns of smallpox transmission, he estimated that variolation would increase life expectancy so long as the risk of death from the procedure was below 10 per cent, which it was.

Because measles is so contagious, at least 95 per cent of a population needs to be vaccinated to have a hope of preventing outbreaks.

Remarkably, there were no examples of Facebook content that reached lots of friends and had a consistently high probability of spreading to each person that saw it. This serves as a reminder of just how weak online outbreaks are compared to biological infections: even the most popular content on Facebook is ten times less contagious than measles can be.

‘When a measure becomes a target, it ceases to be a good measure’ as economist Charles Goodhart reportedly once said.[74]

Roberts would later divide online censorship strategies into what she calls the ‘three Fs’: flooding, fear, and friction. By flooding online platforms with the opposing views, censors can drown out other messages. The threat of repercussions for rule breaking leads to fear. And removing or blocking content creates friction by slowing down access to information.[93]

Then there’s the final aspect of the reproduction number: the inherent transmissibility of an idea. Recall how there are media guidelines for reporting events like suicides, to limit the potential for contagion effects. Researchers like Whitney Phillips have suggested we treat manipulative information in the same way, avoiding coverage that spreads the problem further. ‘As soon as you’re reporting on a particular hoax or some other media manipulation effort, you’re legitimising it,’ she said, ‘and you’re essentially providing a blueprint for what somebody down the road knows is going to work.’[122]

Recent events have shown that some media outlets still have a long way to go. In the aftermath of the 2019 mosque shootings in Christchurch, New Zealand, several outlets ignored well-established guidelines for reporting on terrorist attacks. Many published the shooter’s name, detailed his ideology, or even displayed his video and linked to his manifesto. Worryingly, this information caught on: the stories that were widely shared on Facebook were far more likely to have broken reporting guidelines.[123]

This shows we need to rethink about how we interact with malicious ideas, and who is really benefitting when we give them our attention. A common argument for featuring extreme views is that they would spread anyway, even without media amplification. But studies of online contagion have found the opposite: content rarely goes far without broadcast events to amplify it. If an idea becomes popular, it’s generally bec...

Like disease outbreaks, information rarely respects boundaries. Just as the 1918 ‘Spanish flu’ was blamed on Spain because it was the only country reporting cases, our picture of online contagion can be skewed by where we see outbreaks. In recent years, researchers have published almost five times more studies looking at contagion on Twitter than on Facebook, despite the latter having seven times more users.[125]

contagion is so hard to investigate is that it’s been difficult for most of us to see what other people are actually exposed to. A couple of decades ago, if we wanted to see what campaigns were out there, we could pick up a newspaper or turn on our televisions.

Biologist Peter Medawar once called the flu virus ‘a piece of nucleic acid surrounded by bad news’.

‘Why is it that when the mind of man has stretched so far as to discover the structure of the atom we have been unable to devise the political means to keep the atom from destroying us?’ ‘That is simple, my friend,’ replied Einstein. ‘It is because politics is more difficult than physics.’