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

by Adam Kucharski

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. Near the critical herd immunity threshold, a small change in one of these factors can be the difference between a handful of cases and a major epidemic.

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. In the mid twentieth century, the diffusion of products, like radios and refrigerators, all traced out an S-curve; later on, televisions, microwave ovens and mobile phones would do so as well. 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. Ross had worked in the opposite

‘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. He’d bought shares in late 1719 and initially seen his investment rise, which persuaded him to cash in. However, the share price continued to climb and Newton – regretting his hasty sale – reinvested. When the bubble burst a few months later, he lost £20,000, equivalent to around £20 million in today’s money.[1]

Another person to join the Federal Reserve discussions was Robert May, who had previously supervised Sugihara’s PhD. An ecologist by training, May had worked extensively on analysis of infectious diseases. Although May was drawn into financial research largely by accident, he would go on to publish several studies looking at contagion in financial markets. In a 2013 piece for The Lancet medical journal, he noted the apparent similarity between disease outbreaks and financial bubbles. ‘The recent rise in financial assets and the subsequent crash have rather precisely the same shape as the typical rise and fall of cases in an outbreak of measles or other infection,’ he wrote. May pointed out that when an infectious disease epidemic rises it’s bad news, and when it falls, it’s good news. In contrast, it’s generally seen as positive when financial prices rise and bad when they fall. But he argued that this is a false distinction: rising prices are not always a good sign. ‘When something is going up without a convincing explanation about why it’s going up, that really is an illustration of the foolishness of the people,’ as he put it.[14]

It soon became clear the reproduction number could vary a lot between different populations. For example, diseases like measles can spread to a lot of people if it hits a community with limited immunity, but we rarely see outbreaks in countries with high levels of vaccination. The R of measles can be 20 in populations where everyone is at risk, but in highly vaccinated populations, each infected person generates less than one secondary case on average. In other words, R is below one in these places. We can therefore use the reproduction number to work out how many people we need to vaccinate to control an infection. Suppose an infection has an R of 5 in a fully susceptible population, as smallpox did, but we then vaccinate four out of every five people. Before vaccination, we’d have expected a typical infectious person to infect five other people. If the vaccine is 100 per cent effective, four of these people will now be immune on average. So each infectious person would be expected to generate only one additional case.

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.

Viewing at-risk people as special or different can encourage a ‘them and us’ attitude, leading to segregation and stigma. In turn, this can make epidemics harder to control. From hiv/aids to Ebola, 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.

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]