The Rules of Contagion

Why Things Spread--And Why They Stop


By Adam Kucharski

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One of the Best Books of 2020 — Financial Times
One of the "Most 2020 Books of 2020" — Washington Post
One of the Best Science Books of 2020 — The Times of London
One of the Best Science Books of 2020 — The Guardian

From fake news to COVID-19, a "smart and engaging" (New York Times) look at why the science of outbreaks is the science of modern life

It’s undeniable that we live in a world shaped by outbreaks. Whether it’s pandemic disease, misinformation, or violence, grasping why exactly some things spread is essential for understanding the world around us. In The Rules of Contagion, Adam Kucharski uncovers the crucial factors driving outbreaks, exploring what it actually means for something to “go viral.” He offers compelling insights into human behavior, ultimately showing us how we can all get better at predicting outbreaks—and how they can be stopped. Revised in light of the COVID-19 pandemic, this is a comprehensive and essential guide to our times. 



A theory of happenings

WHEN I WAS THREE YEARS OLD, I lost the ability to walk. It happened gradually at first: a struggle to stand up here, a lack of balance there. But things soon deteriorated. Short distances became tricky, while slopes and stairs were near impossible. One Friday afternoon in April 1990, my parents took me and my failing legs to the Royal United Hospital in Bath. By the next morning I was seeing a neurological specialist. The initial suspect was a spinal tumour. Several days of tests followed; there were X-rays, blood samples, nerve stimulation, and a lumbar puncture to extract spinal fluid. As the results came in, the diagnosis shifted towards a rare condition known as Guillain-Barré syndrome (GBS). Named after French neurologists Georges Guillain and Jean Alexandre Barré, GBS is the result of a malfunctioning immune system. Rather than protecting my body, it had started attacking nerves, spreading paralysis.

Sometimes the sum of human wisdom is to be found, as writer Alexandre Dumas put it, within the words ‘wait and hope’.1 And that was to be my treatment, to wait and to hope. My parents were given a multicoloured party horn to check the strength of my breathing (there was no home equipment small enough for a toddler). If the horn failed to unroll when I blew, it meant the paralysis had reached the muscles that pumped air into my lungs.

There is a photo of me sitting on my grandfather’s lap around this time. He is in a wheelchair. He’d caught polio in India aged twenty-five, and had been unable to walk since. I’d only ever known him like that, his strong arms wheeling uncooperative legs. In a way, it brought familiarity to this unfamiliar situation. Yet what linked us was also what separated us. We shared a symptom, but the mark of his polio was permanent; GBS, for all its misery, was usually a temporary condition.

So we waited and we hoped. The party horn never failed to unroll, and a lengthy recovery began. My parents told me GBS stood for ‘Getting Better Slowly’. It was twelve months before I could walk, and another twelve before I could manage anything resembling a run. My balance would suffer for years to come.

As my symptoms faded, so did my memories. Events became distant, left behind to another life. I can no longer remember my parents giving me chocolate buttons before the needles. Or how I subsequently refused to eat them–even on a normal day–fearing what would come next. The memories of games of tag at primary school have faded too, with me spending all of lunchtime as ‘it’, my legs still too weak to catch the others. For the twenty-five years that followed my illness, I never really spoke about GBS. I left school, went to university, completed a PhD. GBS seemed too rare, too meaningless to bring up. Guillain-what? Barré who? The story, which I never told anyway, was over for me.

Except it wasn’t quite. In 2015, I was in the Fijian capital Suva when I encountered GBS again, this time professionally. I’d been in the city to help investigate a recent dengue fever epidemic.2 Transmitted by mosquitoes, the dengue virus causes sporadic outbreaks on islands like Fiji. Although symptoms are often mild, dengue can come with a severe fever, potentially leading to hospitalisation. During the first few months of 2014, over 25,000 people showed up at health centres in Fiji with a suspected dengue infection, putting a huge burden on the health system.

If you’re imagining an office perched on a sunny beach, you’re not picturing Suva. Unlike Fiji’s resort-laden Western division, the capital is a port city in the southeast of the main island, Viti Levu. The two main roads of the city loop down into a peninsula, forming the horseshoe shape of a magnet, with the area in the middle attracting plenty of rain. Locals who were familiar with British weather told me that I’d feel right at home.

Another, much older, reminder of home was to follow soon after. During an introductory meeting, a colleague at the World Health Organization (WHO) mentioned that clusters of GBS had been appearing on Pacific Islands. Unusual clusters. The annual par for the disease was 1 or 2 cases per 100,000 people, but in some places they’d seen double figures.3

Nobody ever worked out why I got GBS. Sometimes it follows an infection–GBS has been linked to flu and pneumonia, as well as other diseases4–but sometimes there’s no clear trigger. In my case, the syndrome was just noise, a random blip in the grand scheme of human health. But in the Pacific during 2014/15, GBS represented a signal, just like birth defects would soon do in Latin America.

Behind these new signals lay the Zika virus, named after the Zika Forest in southern Uganda. A close relative of the dengue virus, Zika was first identified in the forest’s mosquitoes in 1947. In the local language, Zika means ‘overgrown’5 and grow it would, from Uganda to Tahiti to Rio de Janeiro and beyond. Those signals in the Pacific and Latin America in 2014 and 2015 would gradually become clearer. Researchers found increasing evidence of a link between Zika infection and neurological conditions: as well as GBS, Zika seemed to lead to pregnancy complications. The main concern was microcephaly, where babies develop a smaller brain than usual, resulting in a smaller skull.6 This can cause a host of serious health issues, including seizures and intellectual disabilities.

In February 2016, triggered by the possibility that Zika was causing microcephaly,7 WHO announced that the infection was a Public Health Emergency of International Concern, or PHEIC (pronounced ‘fake’). Early studies had suggested that for every 100 Zika infections during pregnancy, there could be between 1 and 20 babies with microcephaly.8 Although microcephaly would become the primary concern about Zika, it was GBS that first brought the infection into health agencies’ focus, as well as into mine. Sitting in my temporary office in Suva in 2015, I realised that this syndrome, which had shaped so much of my childhood, was one I knew almost nothing about. My ignorance was mostly self-inflicted, with some (entirely understandable) assistance from my parents: it was years before they told me GBS could be fatal.

At the same time, the health world was facing a much deeper ignorance. Zika was generating a huge volume of questions, few of which could yet be answered. ‘Rarely have scientists engaged with a new research agenda with such a sense of urgency and from such a small knowledge base,’ wrote epidemiologist Laura Rodrigues in early 2016.9 For me, the first challenge was to understand the dynamics of these Zika outbreaks. How easily did the infection spread? Were the outbreaks similar to dengue ones? How many cases should we expect?

To answer these questions, our research group started to develop mathematical models of the outbreaks. Such approaches are now commonly used in public health, as well as appearing in several other fields of research. But where do these models originally come from? And how do they actually work? It’s a story that starts in 1883 with a young army surgeon, a water tank and an angry staff officer.

RONALD ROSS HAD WANTED to be a writer, but his father pushed him into medical school. His studies at St Bartholomew’s in London struggled to compete with his poems, plays and music, and when Ross took his two qualifying exams in 1879, he passed only the surgery one. This meant he could not join the colonial Indian Medical Service, his father’s preferred career path.10

Unable to practice general medicine, Ross spent the next year sailing the Atlantic as a ship’s surgeon. Eventually he passed his remaining medical exam and scraped into the Indian Medical Service in 1881. After two years in Madras, Ross moved to Bangalore to take up a post as Garrison Surgeon in September 1883. From his comfortable colonial viewpoint, he claimed it was a ‘picture of pleasure’, a city of sun, gardens and pillared villas. The only problem, as he saw it, was the mosquitoes. His new bungalow seemed to attract far more than the other army rooms. He suspected it was something to do with the water barrel sitting outside his window, which was surrounded by the insects.

Ross’s solution was to tip over the tank, destroying the mosquitoes’ breeding ground. It seemed to work: without the stagnant water, the insects left him alone. Spurred on by his successful experiment, he asked his staff officer if they could remove the other water tanks too. And while they were at it, why not also get rid of the vases and tins that lay scattered around the mess? If the mosquitoes had nowhere to breed, they would have little option but to move on. The officer wasn’t interested. ‘He was very scornful and refused to allow men to deal with them,’ Ross later wrote, ‘for he said it would be upsetting to the order of nature, and as mosquitoes were created for some purpose it was our duty to bear with them.’

The experiment would turn out to be the first in a lifelong analysis of mosquitoes. The second study would come over a decade later, inspired by a conversation in London. In 1894, Ross had travelled back to England for a one-year sabbatical. The city had changed a lot since his last visit: Tower Bridge had been completed, Prime Minister William Gladstone had just resigned, and the country was about to get its first film parlour.11 When Ross arrived, though, his mind was focused elsewhere. He wanted to catch up on the latest malaria research. In India, people regularly fell ill with the disease, which could lead to fever, vomiting, and sometimes death.

Malaria is one of the oldest diseases known to humanity. In fact, it may have been with us for our entire history as a species.12 However, its name comes from Medieval Italy. Those who caught a fever would often blame ‘mala aria’: bad air.13 The name stuck, as did the blame. Although the disease was eventually traced to a parasite called Plasmodium, when Ross arrived back in England the cause of its spread was still a mystery.

In London, Ross called on biologist Alfredo Kanthack at St Bartholomew’s, hoping to learn about developments he may have missed while in India. Kanthack said that if Ross wanted to know more about parasites like malaria, he should go and speak to a doctor called Patrick Manson. For several years, Manson had researched parasites in southeastern China. While there, he had discovered how people get infected with a particularly nasty family of microscopic worms called filariae. These parasites were small enough to get into a person’s bloodstream and infect their lymph nodes, causing fluid to accumulate within the body. In severe cases, a person’s limbs could swell to many times their natural size, a condition known as elephantiasis. As well as identifying how the filariae caused disease, Manson had shown that when mosquitoes fed on infected humans, they could also suck up the worms.14

Manson invited Ross into his lab, teaching him how to find parasites like malaria in infected patients. He also pointed Ross to recent academic papers he’d missed while out in India. ‘I visited him often and learnt all he had to tell me,’ Ross later recalled. One winter afternoon, they were walking down Oxford Street, when Manson made a comment that would transform Ross’s career. ‘Do you know,’ he said, ‘I have formed the theory that mosquitoes carry malaria just as they carry filariae.’

Other cultures had long speculated about a potential link between mosquitoes and malaria. British geographer Richard Burton noted that in Somalia, it was often said that mosquito bites brought on deadly fevers, though Burton himself dismissed the idea. ‘The superstition probably arises from the fact that mosquitoes and fevers become formidable about the same time,’ he wrote in 1856.15 Some people had even developed treatments for malaria, despite not knowing what caused the disease. In the fourth century, Chinese scholar Ge Hong described how the qinghao plant could reduce fevers. Extracts of this plant now form the basis for modern malaria treatments.16 (Other attempts were less successful: the word ‘abracadabra’ originated as a Roman spell to ward off the disease.17)

Ross had heard the speculation linking mosquitoes and malaria, but Manson’s argument was the first to really convince him. Just as mosquitoes ingested those tiny worms when they fed on human blood, Manson reckoned that they could also pick up malaria parasites. These parasites then reproduced within the mosquito before somehow making their way back into humans. Manson suggested that drinking water might be the source of infection. When Ross returned to India, he set out to test the idea, with an experiment that would be unlikely to pass a modern ethics board.18 He got mosquitoes to feed on an infected patient then lay eggs in a bottle of water; once the eggs had hatched, he paid three people to drink the water. To his disappointment, none of them got malaria. So how did the parasites get into people?

Ross eventually wrote to Manson with a new theory, suggesting that the infection might spread through mosquito bites. The mosquitoes injected some saliva with each bite: maybe this was enough to let the parasites in? Unable to recruit enough human volunteers for another study, Ross experimented with birds. First, he collected some mosquitoes and got them to feed on the blood of an infected bird. Then he let these mosquitoes bite healthy birds, which soon came down with the disease as well. Finally, he dissected the saliva glands of the infected mosquitoes, where he found malaria parasites. Having discovered the true route of transmission, he realised just how absurd their previous theories had been. ‘Men and birds don’t go about eating dead mosquitoes,’ he told Manson.

In 1902, Ross received the second ever Nobel Prize for medicine for his work on malaria. Despite contributing to the discovery, Manson did not share the award. He only found out that Ross had won when he saw it in a newspaper.19 The once close friendship between mentor and student gradually splintered into a sharp animosity. Though he was a brilliant scientist, Ross could be a divisive colleague. He got into a series of disputes with his rivals, often involving legal action. In 1912, he even threatened to sue Manson for libel.20 The offence? Manson had written a complimentary reference letter for another researcher, who was taking up a professorship that Ross had recently vacated. Manson did not rise to the argument, choosing to apologise instead. ‘It takes two fools to make a quarrel,’ as he later put it.21

Ross would continue to work on malaria without Manson. In the process, he’d find a new outlet for his single-minded stubbornness, and a new set of opponents. Having discovered how malaria spread, he wanted to demonstrate that it could be stopped.

MALARIA ONCE HAD A MUCH BROADER reach than it does today. For centuries, the disease stretched across Europe and North America, from Oslo to Ontario. Even as temperatures dropped during the so-called Little Ice Age in the seventeenth and eighteenth centuries, the biting cold of winter would still be followed by the biting mosquitoes of summer.22 Malaria was endemic in many temperate countries, with ongoing transmission and a regular stream of new cases from one year to the next. Eight of Shakespeare’s plays include mentions of ‘ague’, a medieval term for malarial fever. The salt marshes of Essex, northeast of London, had been a notorious source of disease for centuries; when Ronald Ross was a student, he’d treated a woman who picked up malaria there.

Having made the link between insects and infections, Ross argued that removing mosquitoes was the key to controlling malaria. His experiences in India–like the experiment with the water tank in Bangalore–had persuaded him that mosquito numbers could be reduced. But the idea went against popular wisdom. It was impossible to get rid of every last mosquito, went the argument, which meant there would always be some insects left, and hence potential for malaria to spread. Ross acknowledged that some mosquitoes would remain, but he believed that malaria transmission could still be stopped. From Freetown to Calcutta, his suggestions were at best ignored and at worst derided. ‘Everywhere, my proposal to reduce mosquitoes in towns was treated only with ridicule,’ he later recalled.

In 1901, Ross had led a team to Sierra Leone to try and put his mosquito control ideas into practice. They cleared away cartloads of tins and bottles. They poisoned the standing water mosquitoes loved to breed in. And they filled potholes so ‘death-dealing street-puddles’, as Ross called them, couldn’t form on the roads. The results were promising: when Ross visited again a year later, there were far fewer mosquitoes. However, he had warned health authorities the effect would only last if the control measures continued. Funding for the clean up had come from a wealthy Glaswegian donor. When the money ran out, enthusiasm waned, and mosquito numbers increased once again.

Ross had more success advising the Suez Canal Company the following year. They’d been seeing around 2,000 malaria cases a year in the Egyptian city of Ismailia. After intensive mosquito reduction efforts, this number fell below a hundred. Mosquito control was also proving effective elsewhere. When the French had attempted to build a canal in Panama during the 1880s, thousands of workers had died from malaria, as well as yellow fever, another mosquito-borne infection. In 1905, with the Americans now leading the Panama project, US Army Colonel William Gorgas oversaw an intensive mosquito control campaign, making it possible to complete the canal.23 Meanwhile further south, physicians Oswaldo Cruz and Carlos Chagas were spearheading anti-malaria programmes in Brazil, helping to reduce cases among construction workers.24

Despite these projects, many remained sceptical about mosquito control. Ross would need a stronger argument to persuade his peers. To make his point, he would eventually turn to mathematics. During those early years in the Indian Medical Service, he’d taught himself the subject to a fairly advanced level. The artist in him admired its elegance. ‘A proved proposition was like a perfectly balanced picture,’ he later suggested. ‘An infinite series died away into the future like the long-drawn variations of a sonata.’ Realising how much he liked the subject, he regretted not studying it properly at school. He was now too far into his career to change direction; what use was mathematics to someone working in medicine? ‘It was the unfortunate passion of a married man for some beautiful but inaccessible lady,’ as he put it.

Ross put the intellectual affair behind him for a while, but returned to the subject after his mosquito discovery. This time, he found a way to make his mathematical hobby useful to his professional work. There was a vital question he needed to answer: was it really possible to control malaria without removing every mosquito? To find out, he developed a simple conceptual model of malaria transmission. He started by calculating how many new human malaria infections there might be each month, on average, in a given geographic area. This meant breaking down the process of transmission into its basic components. For transmission to occur, he reasoned, there first needs to be at least one human in the area who is infectious with malaria. As an example, he picked a scenario where there was one infectious person in a village of 1,000. For the infection to pass to another human, an Anopheles mosquito would have to bite this infectious human. Ross reckoned only 1 in 4 mosquitoes would manage to bite someone. So if there were 48,000 mosquitoes in an area, he’d expect only 12,000 to bite a person. And because only 1 person in 1,000 was initially infectious, on average only 12 of those 12,000 mosquitoes would bite that one infectious person and pick up the parasite.

It takes some time for the malaria parasite to reproduce within a mosquito, so these insects would also have to survive long enough to become infectious. Ross assumed only 1 in every 3 mosquitoes would make it this far, which meant that of the 12 mosquitoes with the parasite, only 4 would eventually become infectious. Finally, these mosquitoes would need to bite another human to pass on the infection. If, again, only 1 in 4 of them successfully fed off a human, this would leave a single infectious mosquito to transmit the virus. Ross’s calculation showed that even if there were 48,000 mosquitoes in the area, on average they would generate only one new human infection.

If there were more mosquitoes, or more infected humans, by the above logic we’d expect more new infections per month. However, there is a second process that counteracts this effect: Ross estimated that around 20 per cent of humans infected with malaria would recover each month. For malaria to remain endemic in the population, these two processes–infection and recovery–would need to balance each other out. If the recoveries outpaced the rate of new infections, the level of disease eventually would decline to zero.

This was his crucial insight. It wasn’t necessary to get rid of every last mosquito to control malaria: there was a critical mosquito density, and once the mosquito population fell below this level, the disease would fade away by itself. As Ross put it, ‘malaria cannot persist in a community unless the Anophelines are so numerous that the number of new infections compensates for the number of recoveries.’

Ross calculated that even if there were 48,000 mosquitoes in a village that contained someone infected with malaria, it might only result in one additional human case

When he wrote up the analysis in his 1910 book The Prevention of Malaria, Ross acknowledged that his readers might not follow all of his calculations. Still, he believed that they would be able to appreciate the implications. ‘The reader should make a careful study of those ideas,’ he wrote, ‘and will, I think, have little difficulty in understanding them, though he may have forgotten most of his mathematics’. Keeping with the mathematical theme, he called his discovery the ‘mosquito theorem’.

The analysis showed how malaria could be controlled, but it also included a much deeper insight, which would revolutionise how we look at contagion. As Ross saw it, there were two ways to approach disease analysis. Let’s call them ‘descriptive’ and ‘mechanistic’ methods. In Ross’s era, most studies used descriptive reasoning. This involved starting with real-life data and working backwards to identify predictable patterns. Take William Farr’s analysis of a London smallpox outbreak in the late 1830s. A government statistician, Farr had noticed that the epidemic grew rapidly at first, but eventually this growth slowed until the outbreak peaked, then started to decline. This decline was almost a mirror image of the growth phase. Farr plotted a curve through case data to capture the general shape; when another outbreak started in 1840, he found it followed much the same path.25 In his analysis, Farr didn’t account for the mechanics of disease transmission. There were no rates of infection or rates of recovery. This isn’t that surprising: at the time nobody knew that smallpox was a virus. Farr’s method therefore focused on what shape epidemics take, not why they take that shape.26

In contrast, Ross adopted a mechanistic approach. Rather than taking data and finding patterns that could describe the observed trends, he started by outlining the main processes that influenced transmission. Using his knowledge of malaria, he specified how people became infected, how they infected others, and how quickly they recovered. He summarised this conceptual model of transmission using mathematical equations, which he then analysed to make conclusions about likely outbreak patterns.

Because his analysis included specific assumptions about the transmission process, Ross could tweak these assumptions to see what might happen if the situation changed. What effect might mosquito reduction have? How quickly would the disease disappear if transmission declined? Ross’s approach meant he could look forward and ask ‘what if?’, rather than just searching for patterns in existing data. Although other researchers had made rough attempts at this type of analysis before, Ross brought the ideas together into a clear, comprehensive theory.27 He showed how to examine epidemics in a dynamic way, treating them as a series of interacting processes rather than a set of static patterns.

Descriptive and mechanistic methods–one looking back and the other forward–should in theory converge to the same answer. Take the descriptive approach. With enough real-life data, it would be possible to estimate the effect of mosquito control: tip over a water tank, or remove mosquitoes in some other way, and we can observe what happens. Conversely, the predicted effect of mosquito control in Ross’s mathematical analysis should ideally match the real impact of such measures. If a control strategy genuinely works, both methods should tell us that it does. The difference is that with Ross’s mechanistic approach, we don’t need to knock over water tanks to estimate what effect it might have.

Mathematical models like Ross’s often have a reputation for being opaque or complicated. But in essence, a model is just a simplification of the world, designed to help us understand what might happen in a given situation. Mechanistic models are particularly useful for questions that we can’t answer with experiments. If a health agency wants to know how effective their disease control strategy was, they can’t go back and rerun the same epidemic without it. Likewise, if we want to know what a future pandemic might look like, we can’t deliberately release a new virus and see how it spreads. Models give us the ability to examine outbreaks without interfering with reality. We can explore how things like transmission and recovery affect the spread of infection. We can introduce different control measures–from mosquito removal to vaccination–and see how effective they might be in different situations.

In the early twentieth century, this approach was exactly what Ross needed. When he announced that Anopheles mosquitoes spread malaria, many of his peers were unconvinced that mosquito control would reduce the disease. This made descriptive analysis problematic: it’s tricky to assess a control measure if it’s not being used. Thanks to his new model, however, Ross had convinced himself that long-term mosquito reduction would work. The next challenge was convincing everyone else.


  • "In this smart and engaging tour of epidemiology, written before the pandemic, Kucharski makes a convincing case that just as the arc of an epidemic depends on the transmissibility of a virus and a population's susceptibility to infection, so online contagions obey similar rules."—New York Times Book Review
  • "The Rules of Contagion is a fascinating and richly detailed excursion into a science as old as biblical plagues and as current as today's headlines: the science of contagion, of disease, of ideas, of emotions, of everything. This is a book you'll want to spread to your friends."— Jordan Ellenberg, author of How Not to Be Wrong
  • "Perfect timing.... Prepares the ground comprehensively for readers to make sense of what is happening today, by distilling the wisdom gathered by studying previous epidemics over more than a century."—Financial Times
  • "Learned and lucid.... Coronavirus has prompted hot-headed public and media reaction; this book offers comfort in the form of cold, hard facts."—The Prospect
  • "A fascinating exploration of the mathematics of things that go viral--not least of them viruses.... Kucharski takes his readers down provocative detours, such as the use of public-health models of disease transmission to examine how social networks figure in urban gun violence, with algorithms that take into account such things as 'age gang affiliations, and prior arrests.'... Utterly timely and readable."—Kirkus Reviews
  • "It is hard to imagine a more timely book ... much of the modern world will make more sense having read it."—The Times (UK)
  • "This is a hell of a moment for a book like this to come out ... the principles of contagion, which, Kucharski argues, can be applied to everything from folk stories and financial crises to itching and loneliness, are suddenly of pressing interest to all of us."—Sunday Times (UK)
  • "The Rules of Contagion is popular science at its best. The prose is sparkling and clear. The subject is deeply fascinating and highly relevant. Touching on psychology, medicine, network theory and mathematics, epidemiologist Adam Kucharski has written a brilliant and authoritative guide to the hidden laws of how things spread - from ideas and memes, to violence and deadly viruses. An example of its subject matter, this book is also highly contagious: once you have read it, you will want to make sure others read it too."
    Alex Bellos, author of Alex's Adventures in Numberland
  • "Rich in stories, The Rules of Contagion is a down-to-earth account of how mathematical approaches can help us better understand and, in turn, better respond to contagion in all its dynamic forms. Tackling issues from pandemics and gun violence, to financial crises and misinformation, Adam Kucharski inspires us all to think like mathematicians. A must read for anybody interested in epidemics and other crises."—Peter Piot, director of the London School of Hygiene & Tropical Medicine

On Sale
Sep 7, 2021
Page Count
352 pages
Basic Books

Adam Kucharski

About the Author

Adam Kucharski is an associate professor and a Sir Henry Dale fellow at the London School of Hygiene and Tropical Medicine, where he works on analysis of infectious disease outbreaks. He is also the author of The Perfect Bet. He lives in London.

Learn more about this author