The Rules of Contagion

all know of new stories and ideas that have spread widely online, but we also know of posts – perhaps including our own – that have fizzled away without notice. So how common is popularity online? What does a typical outbreak even look like?

The rumours about the higgs boson spread gradually at first. On 1 July 2012, Twitter users started speculating that the elusive particle – nicknamed the ‘God particle’– had finally been discovered. Originally suggested by Peter Higgs in 1964, the boson was a crucial missing piece in the subatomic jigsaw. The laws of particle physics said it should exist, but it was yet to be observed in reality.

That would soon change. The rumours on Twitter initially claimed that physicists had discovered the boson at the Tevatron particle accelerator in Illinois. The rumour outbreak grew at a rate of about one new user per minute during this period. The next day, researchers at the Tevatron announced that they’d found promising – but not quite definitive – evidence that the Higgs boson existed. The Twitter outbreak accelerated, with more and more users joining, and attention turned to the Large Hadron Collider at CERN. These latest rumours would prove true: two days later, CERN researchers announced they had indeed found the boson. As media interest in the discovery grew, more joined the Twitter outbreak. It grew by over five hundred users per minute for the next day or so, before peaking soon after. By 6 July, five days after the first rumour emerged, interest in the story had declined dramatically.[39]

When the Higgs rumours started, some users posted about the potential discovery, while others retweeted these comments to their own followers. If we look at how the first few hundred of these retweets were connected, there is a huge amount of variation in transmission (see figure on next page). Most tweets didn’t go very far, only spreading the news to one or two others. But in the middle of the transmission network, there is a large chain of retweets, including two large-scale transmission events, with single users spreading the rumour to many other people.

This sort of diversity in transmission is common in online sharing. In 2016, Duncan Watts, then based at Microsoft Research, worked with collaborators at Stanford University to look at ‘cascades’ of sharing on Twitter. The group tracked over 620 million pieces of content, noting which users had reposted links shared by others. Some links passed between multiple users in a long chain of transmission. Others sparked but faded away much faster. Some didn’t spread at all.[40]

Initial retweets about the Higgs boson rumour, 1 July 2012. Each dot represents a user, with lines showing retweets

Data: De Domenico et al., 2013

For infectious diseases, we’ve seen there are two extreme types of outbreaks. ‘Common source’ transmission occurs when every­one gets infected from the same source, like food poisoning. At the other extreme, a propagated outbreak spreads from person-to-person over several generations. There is a similar diversity in online cascades. Sometimes content will spread to lots of people from a single source – known in marketing as a ‘broadcast’ event – whereas on other occasions it will propagate from user to user. The Stanford and Microsoft researchers found that broadcasts were a crucial part of the largest cascades. About one in a thousand Twitter posts got more than 100 shares, but only a fraction of these spread because of propagated transmission. Of the posts that spread, there was generally a single broadcast event behind its success.

When we talk about online contagion, it’s tempting to focus only on things that have become popular. However, this ignores the fact that the vast majority of things do not take off. The Microsoft team found that around 95 per cent of Twitter cascades consisted of a single tweet that nobody else shared. Of the remaining cascades, most didn’t go any further than one additional step in terms of sharing. The same is true of other online platforms: it’s extremely rare to get something that spreads, and even when it does, it doesn’t spread beyond a few generations of transmission. Most content just isn’t that contagious.[41]

In the previous chapter, we looked at outbreaks of shootings in Chicago, where transmission generally ended after a small number of events. Several diseases also stumble and stutter in human populations like this. For example, strains of bird flu like H5N1 and H7N9 have caused large outbreaks in poultry, but don’t spread well among people (at least, not for the moment).

What sort of outbreaks should we expect if something doesn’t spread very effectively? We’ve already looked at how we can use the reproduction number, R, to assess whether an infectious disease has the potential to spread or not; if R is above the critical value of one, there is potential for a large epidemic to occur. But even if R is below one, there’s still a chance an infected person will pass the disease on to someone else. It might be unlikely, but it’s possible. Unless the reproduction number is zero, we should therefore expect to get some secondary cases occasionally. These new cases may generate further generations of infection before the outbreak eventually stutters to an end.

If we know the reproduction number of a stuttering infection, can we predict how big an outbreak will be on average? It turns out that we can, thanks to a handy piece of mathematics. As well as becoming a crucial part of outbreak analysis, it’s an idea that would shape how Jonah Peretti and Duncan Watts approached viral marketing in the early days of Buzzfeed.[42]

Suppose an outbreak starts with one infectious person. By definition, this first case will generate R secondary cases on average. Then these new infections will generate R more cases each – which translates into R² new cases – and so on:

Outbreak size = 1 + R + R² + R³ + …

We could try and add up all these values to work out the expected outbreak size. But fortunately there’s