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

by Adam Kucharski

Questions like these crop up in a whole range of fields. When we think of contagion, we tend to think about things like infectious diseases or viral online content. But outbreaks can come in many forms. They might involve things that bring harm – like malware, violence or financial crises – or benefits, like innovations and culture. Some will start with tangible infections such as biological pathogens and computer viruses, others with abstract ideas and beliefs. Outbreaks will sometimes rise quickly; on other occasions they will take a while to grow. Some will create unexpected patterns and, as we wait to see what happens next, these patterns will fuel excitement, curiosity, or even fear. So why do outbreaks take off – and decline – in the way they do?

for every influenza virus that jumps from animals to humans and spreads worldwide as a pandemic, there are millions that fail to infect any people at all. For every tweet that goes viral, there are many more that don’t.

a model is just a simplification of the world, designed to help us understand what might happen in a given situation.

Models give us the ability to examine outbreaks without interfering with reality. We

the pathogen remains equally infectious over time; it is the shifting numbers of susceptible and infectious people that lead to the rise and fall.

When there are enough immune people to prevent transmission, we say that the population has acquired ‘herd immunity’.

People need to bedcome infected in ordedr to become immune

herd immunity meant that the population as a whole could block transmission, even if some individuals were still susceptible.

Powerful tool for disease control

transmission was highly sensitive to small differences in the characteristics of the pathogen or human population.

According to the SIR model, outbreaks need three things to take off: a sufficiently infectious pathogen, plenty of interactions between different people, and enough of the population who are susceptible.

Ross noted that such epidemics would follow the shape of a ‘long-drawn-out letter S’. The number of people affected grows exponentially at first, with the number of new cases rising faster and faster over time. Eventually, this growth slows down and levels off.

Ross’s model also gives us an explanation for why the adoption of new ideas gradually slows down. As more people adopt, it becomes harder and harder to meet someone who has not yet heard about the idea. Although the overall number of adopters continues to grow, there are fewer and fewer people adopting it at each point in time. The number of new adoptions therefore begins to decline.

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

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.

R is particularly useful because it tells us whether to expect a large outbreak or not. If R is below one, each infectious person will on average generate less than one additional infection. We’d therefore expect the number of cases to decline over time. However, if R is above one, the level of infection will rise on average, creating the potential for a large epidemic.

As well as measuring transmission from a single infectious person, R can give clues about how quickly the epidemic will grow.

We can therefore use the reproduction number to work out how many people we need to vaccinate to control an infection.

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’. The idea follows from Kermack and McKendrick’s work: once this many people are immune, the infection won’t be able to spread effectively.

Reducing the susceptibility of a population is perhaps the most obvious way to bring down the reproduction number,

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

‘patient zero’, a term still used today to refer to the first case in an outbreak.

blame – and fear of blame – has pushed many outbreaks out of view. Suspicion around disease can result in many patients and their families being shunned by the local community.[74] This makes people reluctant to report the disease, which in turn amplifies transmission, by making the most important individuals harder to reach.

From innovations to infections, contagion is often a social process.

If we want to understand contagion, we therefore need to work out how we interact with one another.

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.

We often share characteristics with people we know, from health and lifestyle choices to politicial views and wealth. In general, there are three possible explanations for such similarities. One is social contagion: perhaps you behave in a certain way because your friends have influenced you over time. Alternatively, it may be the other way around: you may have chosen to become friends because you already shared certain characteristics. This is known as ‘homophily’, the idea that ‘birds of a feather flock together’. Of course, your behaviour might be nothing to do with social connections at all. You may just happen to share the same environment, which influences your behaviour.

‘Bayesian reasoning’. Named after eighteenth-century statistician Thomas Bayes, the idea is to treat knowledge as a belief that we have a certain level of confidence in.

Your belief after exposure to new information therefore depends on two things: the strength of your initial belief and the strength of the new evidence.[54] This concept is at the heart of Bayesian reasoning – and much of modern statistics.

From a Bayesian point of view, we are generally better at judging the effect of arguments that we disagree with.

people were far more persuasive when they tailored their argument to the moral values of their opponent.

It seems repetition matters: new beliefs survived longer if people were reminded of the truth several times, rather than just given one correction.[72]

Thinking about the moral position of others. Having face-to-face interactions. Finding ways to encourage long-term change. All of these things can help improve persuasion.

This isn’t to say that people with a history involving violence will always have a violent future; like many infections, exposure to violence won’t necessarily lead to symptoms later on. But like infectious diseases, there are a number of factors – in our backgrounds, in our lifestyles, in our social interactions – that can increase the risk of an outbreak.

He found that when British and American newspapers ran a front-page story about a suicide, the number of such deaths in the local area tended to increase immediately afterwards.

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.[40]

social media, three main factors influence what we read: whether one of our contacts shares an article; whether that content appears in our feed; and whether we click on it.

Psychologists refer to it as the ‘online disinhibition effect’: shielded from face-to-face responses and real-life identities, people’s personalities may adopt a very different form.

Analysis of antisocial behaviour online has found that a whole range of people can become trolls, given the right circumstances. In particular, we are more likely to act like trolls when we are in a bad mood, or when others in the conversation are already trolling.

most online content won’t reach many people unless there is some kind of mass broadcast event.

Researchers at MIT have found that false news tends to spread further and faster than true news.

An advertising campaign might generate a lot of likes and clicks, but this isn’t quite the behaviour they’re interested in. They don’t just want people to interact with their content; they eventually want people to buy their product or believe in their message. Just as people with more followers won’t necessarily generate larger cascades, content that’s more clickable or shareable won’t automatically generate more revenue or advocacy.

What are the main routes of transmission? And which of these routes should we target to control the infection? Marketers face a similar task when designing a campaign. First, they need to know the ways someone can be exposed to a message; then they need to decide which of these routes to target.

Whether we’re dealing with a disease outbreak or marketing campaign, we want to find the best way to allocate a limited budget. The problem is that historically it’s not always been clear which path leads to which outcome. ‘Half the money I spend on advertising is wasted; the trouble is I don’t know which half,’ as marketing pioneer John Wanamaker supposedly once said.

When we click on a website link, we often become the subject of a high-speed bidding war. Within about 0.03 seconds, the website server will gather all the information they have about us and send it to its ad provider. The provider then shows this information to a group of automated traders acting on behalf of advertisers. After another 0.07 seconds, the traders will have bid for the right to show us an advert. The ad provider selects the winning bid and sends the advert to our browser, which slots the advert into the webpage as it loads on the screen.

The average iPhone user unlocks their phone over eighty times a day.[88] According to Harris, this behaviour is similar to the psychological effects of gambling addiction: ‘When we pull our phone out of our pocket, we’re playing a slot machine to see what notifications we got,’ he suggested.

‘It’s a social-validation feedback loop,’ as Sean Parker put it. ‘It’s exactly the kind of thing that a hacker like myself would come up with, because you’re exploiting a vulnerability in human psychology.’

‘fake news’ can actually refer to several different types of content, including clickbait, conspiracy theories, misinformation, and disinformation.

According to Jamie Tehrani, an anthropologist at Durham University, we can think of culture as information that mutates as it gets transmitted from person-to-person and generation-to-generation.

the main reason governments are so worried about a future pandemic flu virus is that we won’t have an effective vaccine against the new strain. In the event of a pandemic, it would take six months to develop one,

as our knowledge of contagion has improved, infectious diseases have on the whole declined. The global death rate for such diseases has halved in the past two decades.[35]