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August 23 - August 25, 2020
out that, in most situations, neither explanation was correct.[35] Like Ross, Kermack and McKendrick started by developing a mathematical model of disease transmission. For simplicity, they assumed the population mixed randomly in their model. Like marbles being shaken in a jar, everyone in the population has an equal chance of meeting everyone else. In the model, the epidemic sparks with a certain number of infectious people, and everyone else susceptible to infection. Once someone has recovered from infection, they are immune to the disease. We can therefore put the population into one of
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meet one. To illustrate the effect, Kermack and McKendrick showed how the SIR model could reproduce the dynamics of a 1906 outbreak of plague in Bombay (now Mumbai). In the model, the pathogen remains equally infectious over time; it is the shifting numbers of susceptible and infectious people that lead to the rise and fall.
The crucial change happens at the peak of the epidemic. At this point, there are so many immune people – and so few susceptible – that the epidemic cannot continue to grow. The epidemic will therefore turn over and start its decline.
When there are enough immune people to prevent transmission, we say that the population has acquired ‘herd immunity’.
Likewise, herd immunity meant that the population as a whole could block transmission, even if some individuals were still susceptible.
nowhere. 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.
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’.
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.
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.
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.
R = Duration × Opportunities × Transmission probability × Susceptibility
One example is food poisoning: outbreaks can often be traced to a specific meal or person. The most infamous case is that of Mary Mallon – often referred to as ‘Typhoid Mary’ – who carried a typhoid infection without symptoms. In the early twentieth century, Mallon was employed as a cook for several families around New York City, leading to multiple outbreaks of the disease and several deaths.[53]
His note suggested that the financial network might be robust in some situations and extremely fragile in others. The idea was well-established in ecology: the structure of a network might make it resilient to minor shocks, but the same structure could also leave it vulnerable to complete collapse if put under enough stress. Think about a team at work. If most people are doing well, weaker members can get away with mistakes because they are linked to high performers. However, if most of the team are struggling, the same links will instead drag strong members down. ‘The basic point was that all
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The variability in links wasn’t the only problem. It was also how these big banks fitted into the rest of the network. 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. This results in an outbreak that spreads quickly through these clusters of high-risk individuals, but struggles to reach the other, less connected, parts of the network. In contrast, a
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When multiple banks invest in the same asset, it creates a potential route of transmission between them. If a crisis hits and one bank starts selling off its assets, it will affect all the other firms who hold these investments. 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]
The spread of scientific concepts would inspire some of the first research into the transmission of ideas. During the early 1960s, US mathematician William Goffman suggested that the transfer of information between scientists worked much like an epidemic.[3] Just as diseases like malaria spread from person to person via mosquitoes, scientific research often passed from scientist to scientist via academic papers. From Darwin’s theory of evolution to Newton’s laws of motion and Freud’s psychoanalytic movement, new concepts had spread to ‘susceptible’ scientists who came into contact with them.
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’.
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.
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 study also demonstrated that social norms could emerge in wild animals. 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.’
humans. In the process, he’d come up with a set of rules – or ‘postulates’ – to identify whether a particular germ is responsible for a disease. To start with, he thought that it should always be possible to find the germ inside someone who has the disease. Then, if a healthy host – like a laboratory animal – was exposed to this germ, it should develop the disease too. Finally, it should be possible to extract a sample of the germ from the new host once they fall ill; this germ should be the same as the one they were originally exposed to.[40]
There is a long-standing paradox in medicine: people who have a heart attack or stroke while surrounded by relatives take longer to get medical care. This may well be down to the structure of social networks. There’s evidence that close-knit groups of relatives tend to prefer a wait-and-see approach after witnessing a mild stroke, with nobody willing to contradict the dominant view. In contrast, ‘weak ties’ – like co-workers or non-relatives – can bring a more diverse set of perspectives, so flag up symptoms faster and call for help sooner.[47]
exposures. For example, in Christakis and Fowler’s analysis of smoking, they noted that people were more likely to quit if lots of their contacts stopped as well. Researchers have also identified complex contagion in behaviours ranging from exercise and health habits to the uptake of innovations and political activism.
it. Take fire alarms. As well as signaling there might be a fire, alarms make it acceptable for everyone to leave the building. One classic 1968 experiment had students sit working in a room as it slowly filled with fake smoke.[49] If they were alone, they would generally respond; if they were with a group of studious actors, they would continue to work, waiting for someone else to react.
there are benefits to having Pixar-style overlaps between groups to get innovations out to a wider audience.[50]
One is the lag between exposure and symptoms. Just like an infection, violence can have an incubation period; we might not see symptoms straight away. Sometimes a violent event will lead to another one soon after: for example, it might not take long for one gang to retaliate against another. On other occasions it may take much longer for knock-on effects to emerge.
Unfortunately, outlets often ignore these guidelines. Researchers at Columbia University noted a 10 per cent rise in suicides in the months following the death of comedian Robin Williams.[14] They pointed to a potential contagion effect, given that many media reports about Williams’ death did not follow who guidelines, and the largest increase in suicides occurred in middle-aged men using the same method as Williams. There can be a similar effect with mass shootings; one study estimated that for every ten US mass shootings, there are two additional shootings as a result of social
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behaviour among workers who are still at high risk.[19] The first Cure Violence project started in 2000, in West Garfield Park in Chicago. Why did they pick that location? ‘It was the most violent police district in the country at the time,’ Slutkin said. ‘It has always been my bias – as it is for many epidemiologists – to head for the middle of the epidemic, because it’s your best test and you can affect the greatest impact.’
McCluskey’s findings – and accompanying recommendations – led to the creation of the Violence Reduction Unit, which she would head up for the following decade. Borrowing techniques from Cure Violence and other US projects, such as Boston’s Operation Ceasefire, the unit introduced a range of public health ideas to tackle the spread of violence.[29]
A friend suggested that she could still pursue a literary career alongside this role. Nightingale was not interested. ‘You ask me why I do not write something,’ she replied. ‘I think one’s feelings waste themselves in words; they ought all to be distilled into actions and into actions which bring results.’[37]
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]
But what if the situation were slightly different? Say the person with a threshold of 1 had a threshold of 2. This time, the first person would start rioting, but there would be nobody else with a low enough threshold to be triggered. Although the crowds in each situation are near identical, the behaviour of one person could be the difference between a riot and a tantrum. Granovetter suggested personal thresholds could apply to other forms of collective behaviour too, from going on strike to leaving a social event.[55]
really prevent over 1.3 million cases?[67] In the field of public health, people often refer to disease control measures as ‘removing the pumphandle.’ It’s a nod to John Snow’s work on cholera, and the removal of the handle on the Broad Street pump. There’s just one problem with this phrase: when the pumphandle came off on 8 September 1854, London’s cholera outbreak was already well in decline. Most of the people at risk had either caught the infection already, or fled the area.
and jobs – of having large numbers of people with drug addiction. Because the success of different control strategies can vary between the three stages of a drug epidemic, it’s crucial to know what stage we’re currently in. In theory, it should be possible to work this out by estimating the annual numbers of new users, existing users, and heavy users. But the complexity of the opioid crisis – with its mix of prescription and illegal use, makes it very difficult to pick these things apart. There are some useful data sources – such as visits to emergency rooms and results of post-arrest drug
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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.[31]
Looking at how design influences people’s behaviour is not necessarily unethical. Indeed, medical organisations regularly run randomised experiments to work out how to encourage healthy behaviour. For example, they might send one type of reminder about cancer screening to some people and a different one to others, and then see which gets the best response.[34] Without these kinds of experiments, it would be difficult to work out how much a particular approach actually shifted people’s behaviour.
In biology, this arms race is known as the ‘Red Queen effect’, after the character in Lewis Carroll’s Through the Looking-Glass. When Alice complains that running in the looking-glass world doesn’t take her anywhere new, the Red Queen replies that, ‘here, you see, it takes all the running you can do, to keep in the same place.’
We could try and add up all these values to work out the expected outbreak size. But fortunately there’s an easier option. In the nineteenth century, mathematicians proved that there’s an elegant rule we can apply to sequences like the one above. If R is between 0 and 1, the following equation is true: 1 + R + R2 + R3 + … = 1/(1–R) In other words, as long as the reproduction number is below 1, the expected outbreak size is equal to 1/(1–R).
Researchers at MIT have found that false news tends to spread further and faster than true news. Maybe this is because high-profile people with lots of followers are more likely to spread falsehoods? The researchers actually found the opposite: it was generally people with fewer followers who spread the false news. If we think of contagion in terms of the four DOTS, this suggests false information spreads because the transmission probability is high, rather than there being more opportunities for spread.
from a single source. This means that complex contagion – such as nuanced political views – can have a major disadvantage on the internet. Rather than encouraging users to develop challenging, socially complex ideas, the structure of online social interactions instead favours simple, easy-to-digest content. So perhaps it’s not surprising that this is what people are choosing to produce.
‘When a measure becomes a target, it ceases to be a good measure’ as economist Charles Goodhart reportedly once said.[74]
Rewarding success based on a simple performance metric creates a feedback loop: people start chasing the metric rather than the underlying quality it is trying to assess.
When Alexandre Dumas first wrote The Three Musketeers in serialised form, his publisher paid him by the line. Dumas therefore added the servant character Grimaud, who spoke in short sentences, to stretch out the text (then killed him off when the publisher said that short lines didn’t count).[75]
Ultimately, it’s a question of cost-effectiveness. 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.[81]
Other companies have since followed suit. ‘We’re competing with sleep,’ joked Netflix CEO Reed Hastings in 2017.[86]
What we can do, though, is try and make media outlets, political organisations, and social media platforms – not to mention ourselves – more resistant to manipulation. To start with, that means having a much better understanding of the transmission process. It’s not enough to concentrate on a few groups, or countries, or platforms. Like disease outbreaks, information rarely respects boundaries.
Yet most coders don’t create everything from scratch. To save time, they use tools that others have developed and shared. Many of them do this by searching an online resource called ‘npm’, which collects together handy bits of code like left-pad. In some cases, people incorporate these existing tools into new programs, which they subsequently share.
