Illustration of fully-connected and broken Erdős–Rényi networks
The Erdős–Rényi model could capture the occasional long-range connections that occurred in real networks, but it couldn’t reproduce the clustering of interactions. This discrepancy was resolved in 1998, when mathematicians Duncan Watts and Steven Strogatz developed the concept of a ‘small-world’ network, in which most links were local but a few were long-range. They found that such networks cropped up in all sorts of places: the electricity grid, neurons in worm brains, co-stars in film casts, even Erdős’s academic collaborations.[57] It was a remarkable finding, and more discoveries were about to follow.
The small-world idea had addressed the issue of clustering and long-range links, but physicists Albert-László Barabási and Réka Albert spotted something else unusual about real-life networks. From film collaborations to the World Wide Web, they’d noticed that some nodes in the network had a huge number of connections, far more than typically appeared in the Erdős–Rényi or small-world networks. In 1999, the pair proposed a simple mechanism to explain this extreme variability in connections: new nodes that joined the network would preferentially attach to already popular ones.[58] It was a case of the ‘rich get richer’.
The following year, a team at the University of Stockholm showed that the number of sexual partnerships in Sweden also appeared to follow this rule: the vast majority of people had slept with at most one person in the past year, whereas some reported dozens of partners. Researchers have since found similar patterns of sexual behaviour in countries ranging from Burkina Faso to the United Kingdom.[59]
What effect does this extreme variability in number of partners have on outbreaks? In the 1970s, mathematician James Yorke and his colleagues noticed there was a problem with the ongoing gonorrhea epidemic in the United States. Namely, it didn’t seem possible. For the disease to keep spreading, the reproduction number needed to be above one. That meant infected people should on average have at least two recent sexual partners: one who gave the infection to them, and another who they passed it on to. But a study of patients with gonorrhea had found that they’d had only 1.5 recent partners on average.[60] Even if the probability of transmission during sex was very high, it suggested that there simply weren’t enough encounters for the disease to persist. What was going on?
If we just take the average number of partners, we are ignoring the fact that not everyone’s sex lives are the same. This variability is important: if someone has a lot of partners, we’d expect them to be both more likely to get infected and more likely to pass the infection on. We therefore need to account for the fact that they can contribute to transmission in these two different ways. Yorke and his colleagues argued that this might explain why there could be a gonorrhea epidemic, despite people having few partnerships on average: people with lots of contacts might be contributing disproportionality to the spread, pushing the reproduction number above one. Anderson and May would later show that the more variation there was in the number of partners people had, the higher we’d expect the reproduction number to be.
Identifying people who are at higher risk – and finding ways to reduce this risk – can help stop an outbreak in its early stages. In the late 1980s, Anderson and May suggested that STIs would initially spread quickly through such high-risk groups, even though the overall outbreak would be smaller than we’d expect if everyone mixed at random.[61]
By breaking contagion down into its basic DOTS components – duration, opportunities, transmission probability, susceptibility – and thinking about how network structure affects contagion, we can also estimate the risk posed by a new STI. In 2008, an American scientist returned home to Colorado after a month working in Senegal. A week later, he’d fallen ill with a headache, extreme tiredness, and a rash on his torso. Soon after, his wife – who hadn’t travelled – developed the same symptoms. Subsequent lab tests indicated both had been exposed to the Zika virus. Prior Zika research had focused on transmission from mosquitoes, but the Colorado incident suggested the virus had access to another route: it could infect people during sexual encounters.[62] As Zika spread around the globe in 2015–16, more reports of sexual transmission would follow, fueling speculation about a new type of outbreak. ‘Zika: The Millennials’ S.T.D.?’ asked one opinion piece in the New York Times during 2016.[63]
Based on the DOTS for Zika, our research group estimated that the reproduction number for sexual transmission was below one; the virus would probably not cause an STI epidemic. Zika could potentially cause small outbreaks in groups with a lot of sexual contacts, but it was unlikely to pose a major risk in areas without mosquitoes.[64] Unfortunately, the same has not been true for other STIs.
Gaëtan dugas was blond, charming, and had a lot of sex. A Canadian flight attendant, he’d slept with over two hundred men a year prior to March 1984, when he died of aids a few weeks after his 31st birthday. Three years later, journalist Randy Shilts featured Dugas in his bestselling book And the Band Played On. Shilts suggested that Dugas had played a central part in the early spread of the disease. He dubbed Dugas ‘patient zero’, a term still used today to refer to the first case in an outbreak. Shilts’ book fuelled speculation that Dugas was the person who introduced the epidemic to North America. The New York Post called him ‘The Man Who Gave Us aids’; the National Review said he was ‘the Columbus of aids’.
The idea of Dugas as patient zero was certainly attention-grabbing, and has been repeated often in the decades since. But it turned out to be fiction. In 2016, a team of researchers published an analysis of hiv viruses from a range of patients, including men diagnosed with aids in the 1970s and Dugas himself. Based on the genetic diversity of these viruses and the rate of hiv evolution, the team estimated that hiv had arrived into North America in 1970 or 1971. However, they found no evidence that Dugas had introduced hiv to the US. He was just another case in a much wider epidemic.[65]
So how did the patient zero designation come about? In the original outbreak investigation, Dugas hadn’t actually been listed as ‘Patient 0’, but rather as ‘Patient O’, the ‘O’ short for ‘Outside California’. In 1984, William Darrow, a researcher with the Centers for Disease Control and Prevention (CDC), had been assigned to investigate a cluster of deaths among gay men in Los Angeles.[66] The CDC generally gave each case a number based on the order in which they had been reported, but the cases had been relabelled for the LA analysis. Before Dugas had been linked to the Los Angeles cluster, he was simply ‘Patient 057’.
When investigators traced how the cases were linked, it suggested that the deaths might be the result of an as-yet-unknown STI. Dugas appeared prominently in the network, with links to multiple cases in New York and LA. This was in part because he’d tried to help the investigators, naming 72 of his partners in the preceding three years. Darrow pointed out that this had always been the aim of the investigation: to understand how cases were linked, rather than find out who had started the outbreak. ‘I never said that he was the first case in the United States,’ he later commented.
When investigating outbreaks, we face a gap between what we want to know and what we can measure. Ideally, we’d have data on all the ways in which people are connected, and how infection has spread through these links. What we can actually measure is very different. A typical outbreak investigation will reconstruct some of the links between people who were infected. Depending on which cases and links are reported, the resulting network won’t necessarily look like the actual transmission route. Some people might appear more prominent than they really were, while some transmission events might be missed.
When Randy Shilts came across the CDC diagram while researching his book, his attention was drawn to Dugas. ‘In the middle of that study was a circle with an O next to it, and I always thought it was Patient O,’ he later recalled. ‘When I went to the CDC, they started talking about Patient Zero. I thought, “Ooh, that’s catchy”.’[67]
It’s easier to tell a story w
hen it has a clear antagonist. According to historian Phil Tiemeyer, it was Shilts’s editor Michael Denneny who suggested they make Dugas the villain in the book and accompanying publicity. ‘Randy hated the idea,’ Denneny told Tiemeyer. ‘It took me almost a week to argue him into it.’ The decision – which Denneny later said he regretted – came because the media seemed to have little interest in aids otherwise. ‘They were not going to review a book that was an indictment of the Reagan administration and the medical establishment.’[68]
When discussing outbreaks that involve superspreading events, there is a tendency to place all attention on the people apparently at the centre of them. Who are these ‘superspreaders’? What makes them different from everyone else? However, such attention can be misplaced. Take that story of the Belgrade teacher who arrived in hospital with smallpox. There was nothing intrinsically unusual about him or his behaviour. He had acquired the disease through a chance encounter, had tried to get medical care at an appropriate place – a hospital – and the outbreak spread because nobody initially suspected smallpox was the cause. This is true of many outbreaks: it’s often difficult to predict in advance what role a specific individual will play.
Even if we can identify situations that create a risk of disease transmission, it won’t necessarily lead to the outcome we expect. On 21 October 2014, at the height of the Ebola epidemic in West Africa, a two-year-old girl arrived at a hospital in the city of Kayes, Mali. Following the death of her father, who had been a healthcare worker, the girl had travelled over 1,200 km from neighbouring Guinea with her grandmother, uncle and sister. At the Kayes hospital, the girl tested positive for Ebola, and would die of the disease the next day. She was Mali’s first case of Ebola, and health authorities began to search for people who may have come into contact with her. During her trip, she’d taken at least one bus and three taxis, potentially interacting with dozens if not hundreds of people. She’d already been displaying symptoms when she arrived at the hospital; based on the nature of Ebola transmission, there was a good chance she could have passed the virus on. Investigators eventually managed to track down over one hundred of the girl’s contacts and placed them in quarantine as a precaution. However, none of them came down with Ebola. Despite her long journey, the girl hadn’t infected anyone.[69]
When Ebola superspreading events did occur during 2014–15, our team noticed there was one feature that stood out. Unfortunately, it wasn’t a particularly helpful one: the cases most likely to be involved in superspreading were the ones that couldn’t be linked to existing chains of transmission. Put simply, the people driving the epidemic were generally the ones the health authorities didn’t know about. These people went undetected until they sparked a new set of infections, making it near impossible to predict superspreading events.[70]
With enough effort, we can often trace some of the path of infection during an outbreak, reconstructing who might have infected whom. It can be tempting to construct a narrative as well, speculating about why certain people transmitted more than others. However, just because an infection is capable of superspreading doesn’t necessarily mean the same people are always the superspreaders. Two people might behave in almost the same way, but by chance one of them spreads infection and the other does not. When history is written, one is blamed and the other ignored. Philosophers call it ‘moral luck’: the idea that we tend to view actions with unfortunate consequences as worse than equal actions without any repercussions.[71]
Sometimes the people involved in an outbreak do behave differently, but not necessarily in the way we might assume. In his book The Tipping Point, Malcolm Gladwell describes an outbreak of gonorrhea in Colorado Springs, Colorado, during 1981. As part of the outbreak investigation, epidemiologist John Potterat and his colleagues had interviewed 769 cases, asking whom they’d recently had sexual contact with. Of these cases, 168 people had at least two contacts who were also infected. This suggested they were disproportionately important in the outbreak. ‘Who were those 168 people?’ Gladwell asked. ‘They aren’t like you or me. They are people who go out every night, people who have vastly more sexual partners than the norm, people whose lives and behaviour are well outside of the ordinary.’
Were these people really so promiscuous and unusual? Not particularly, in my view: the researchers found that, on average, these cases reported sexual encounters with 2.3 other infected people. This implies they caught the infection from one person and typically gave it to one or two others. Cases tended to be black or Hispanic, young, and associated with the military; almost half had known their sexual partners for more than two months.[72] During the 1970s, Potterat had begun to notice that promiscuity wasn’t a good explanation for gonorrhea outbreaks in Colorado Springs. ‘Especially striking was the difference in gonorrhea test outcome between sexually adventurous white women from a local upper middle class college and similarly aged black women with modest sexual histories and educational backgrounds,’ he noted.[73] ‘The former were seldom diagnosed with gonorrhea, unlike the latter.’ A closer look at the Colorado Springs data suggested that transmission was likely to be the result of delays in getting treatment among certain social groups, rather than an unusually high level of sexual activity.
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.
Blaming certain groups for outbreaks is not a new phenomenon. In the sixteenth century, the English believed syphilis came from France, so referred to it as the ‘French pox’. The French, believing it to be from Naples, called it the ‘Neopolitan disease’. In Russia, it was the Polish disease, in Poland it was Turkish, and in Turkey it was Christian.[75]
Such blame can stick for a long time. We still refer to the 1918 influenza pandemic, which killed tens of millions of people globally, as the ‘Spanish flu’. The name emerged during the outbreak because media reports suggested Spain was the worst hit country in Europe. However, these reports weren’t quite what they seemed. At the time, Spain had no wartime censorship of news reports, unlike Germany, England and France, who quashed news of disease for fear that it might damage morale. The media blackout in these countries therefore made it appear that Spain had far more cases than anywhere else. (For their part, the Spanish media tried to blame the disease on the French.[76])
If we want to avoid country-specific disease names, it helps to suggest an alternative. One Saturday morning in March 2003, a group of experts gathered at who headquarters in Geneva to discuss a newly discovered infection in Asia.[77] Cases had already appeared in Hong Kong, China and Vietnam, with another reported in Frankfurt that morning. who was about to announce the threat to the world, but first they needed a name. They wanted something that was easy to remember, but which wouldn’t stigmatize the countries involved. Eventually they settled on ‘Severe Acute Respiratory Syndrome’, or sars for short.
The sars epidemic would result in over eight thousand cases and several hundred deaths, across multiple continents. Despite being brought under control in June 2003, the epidemic would cost an estimated $40 billion dollars globally.[78] It wasn’t just the direct cost of treating disease cases; it was the economic impact of closed workplaces, empty hotels and cancelled trade.
According to Andy Haldane, now Chief Economist at the Bank of England, the wider effects of the sars epidemic were comparable with the fallout from the 2008 financial crisis. ‘These similarities are striking,’ he said in a 2009 speech.[79] ‘An external event strikes. Fear grips the system, which, in consequence, seizes. The resulting collateral damage is wide and deep.’
Haldane suggested th
at the public typically respond to an outbreak in one of two ways: flight or hide. In the case of an infectious disease, flight means trying to leave an affected area in the hope of avoiding infection. Because of travel restrictions and other control measures, this generally wasn’t an option during the sars epidemic.[80] Had infected people travelled – rather than being identified and isolated by health authorities – it could have spread the virus to even more locations. The flight response can also happen in finance. Faced with a crash, investors may cut their losses and sell off assets, driving prices even lower.
Alternatively, people may ‘hide’ during an outbreak, dodging situations that could potentially bring them into contact with the infection. If it’s a disease outbreak, they might wash their hands more often, or reduce their social interactions. In finance, banks might hide by hoarding money rather than risking lending to other institutions. However, Haldane pointed out that there is a crucial difference between hide responses in disease outbreaks and financial crises. Hiding behaviour will generally help reduce disease transmission, even if it incurs a cost in the process. In contrast, when banks hoard money it can amplify problems, as happened with the ‘credit crunch’ that hit economies in the run up to the 2008 crisis.
Although the notion of a credit crunch would make headlines during 2007/8, economists first coined the term back in 1966. That summer, US banks had abruptly stopped lending. In the preceding years, there had been high demand for loans, with banks making more and more credit available to keep pace. Eventually, it had got to the point where banks weren’t taking in enough money in savings to continue lending, so the loans stopped. It wasn’t just a matter of banks asking borrowers for higher interest rates. They weren’t lending at all. Banks had reduced the availability of loans before – there were several instances of ‘credit squeezes’ in the US during the 1950s – but some thought ‘squeeze’ was too gentle a word to describe the sudden impact of 1966. ‘A “crunch” is different,’ wrote economist Sidney Homer at the time. ‘It is painful by definition, and it can even break bones.’[81]
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