Monday, April 20, 2020

1910-11 Plague in China

In 1911, another epidemic swept through China. That time, the world came together

A railway cutting through the hills of Manchuria, circa 1906.
(CNN)In 1911, a deadly epidemic spread through China and threatened to become a pandemic. Its origins appeared to be related to the trade in wild animals, but at the time no one was sure.
Lockdowns, quarantine measures, the wearing of masks, travel restrictions, the mass cremation of victims, and border controls were deployed to try to lower the infection rate. Yet more than 60,000 people died in modern-day northeast China, making it one of the world's largest epidemics at the time.
When the disease was eventually brought under control, the Chinese government convened the International Plague Conference in the northern city of Shenyang -- close to the epicenter of the outbreak.
    In attendance were virologists, bacteriologists, epidemiologists and disease experts from many of the world's major powers -- the United States, Japan, Russia, the United Kingdom and France.
    Illustration of the Reaper (allegory of Death) above Manchuria, which was published in Le Petit Journal, in  France, in 1911.
    The purpose of the conference was to find the cause of the outbreak, learn which suppression techniques were most effective, discover why the disease had spread so far so fast, and assess what could be done to prevent a second wave. While the conference was not without some finger pointing, it was mostly a genuine attempt to learn.
    As the world now faces a pandemic characterized by a lack of a globally co-ordinated response and multilateral effort on the part of political leaders, the collaborative aspects of the 1911 conference in north-eastern China are worth reconsidering.
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    Today, the World Health Organization (WHO) appears compromised, the virus has been racialized, major nations are angry with each other and competing for resources and control of the narrative, while poorer countries are left to fend largely for themselves.
    Compared to 1911, we appear a polarized and divided world.

    Marmots and plague

    The Great Manchurian Plague that broke out across northeastern China in 1910 was devastating.
    From the autumn of 1910, until the outbreak was finally suppressed the following year, an estimated 63,000 people died. The epidemic hit international headlines when it reached the northeastern city of Harbin, in today's Heilongjiang province. Harbin was then part of what was known as Manchuria, a vast, agriculturally important but sparsely populated region situated on the juncture of the Chinese, Japanese and Russian spheres of influence. The majority of the territory was Chinese-governed, with Japan controlling the port area around Dalian and Russia running Manchuria's railways.
    Harbin was an international city, home to many Russians who worked for the China Eastern Railway (CER), which connected the Trans-Siberian Railway to the Japanese-controled port city of Dalian. The city was also home to large communities of Japanese, Americans and Europeans engaged in trades connected to the railway.
    That included the fur trade, and it was from this industry that the disease most likely came.
    Tarbagan marmot (Marmota sibirica), a species of rodent in the family Sciuridae, in steppes around Khukh Lake, Mongolia.
    The Tarbagan marmot was a species of rodent that lived mostly on the grasslands and steppe of Mongolia and neighboring Manchuria. European, American and Japanese furriers had long purchased sable, mink and otter furs from local hunters, but had never been interested in the coarse fur of the Tarbagan marmot. But new dying techniques at the start of the century allowed marmot fur to pass as an affordable alternative for better-quality furs.
    Thousands of nomadic local hunters were tasked by foreign buyers with bringing marmot hides, which soared in value in the years before the virus. Rural hunters had long avoided using diseased marmots for food, but did not think to cast aside the hides of sick animals -- especially not when they were worth so much.
    Pinpointing the initial outbreak of the plague is hard, but it was first officially noted by Russian doctors in Manzhouli, an Inner Mongolian town on the Chinese-Russian border, which had grown up around the CER. The symptoms were alarming -- fever followed by haemoptysis (the coughing up of blood). In Manzhouli, the dead were left in the street and railway freight cars were turned into quarantine wards.
    A picture of victims of the Great Manchurian Plague.
    Just as viruses spread fast along airline routes today, back then the railways facilitated the spread. Fear in Manzhouli meant many people followed the routes the marmot hides had taken along the CER to the Heilongjiang city of Qiqihar, and then on to Harbin.
    Cases of the pneumonic plague appeared in major rail termini -- Tianjin, Beijing and along the Beijing to Wuhan railway. Even Shanghai, almost 2,000 miles from Manzhouli, reported a case and considered a lockdown of the city to prevent wider infection. In the crowded slums of Harbin, the disease took hold swiftly. By November 8, 1910, Harbin had a death toll of 5,272.

    Initial response and debates

    The response to the outbreak was rapid, given the logistical constraints at the start of the 20th century.
    Quarantine centers were established, mostly in converted rail freight cars, for people the authorities thought had have come into contact with the disease -- relatives of the dead plus those in the fur trapping and trading business.
    If the quarantined didn't show symptoms within five-to-10 days they were released with a wire wristband fastened with a lead seal stating they were plague free. But if symptoms did show, the entire freight car was essentially doomed, given the disease's staggering near 100% mortality rate. Burials were forbidden; mass cremations were enforced.
    In Harbin, the Chinese authorities' lead doctor Wu Lien-teh, a Malaysia-born ethnic-Chinese medic educated at Cambridge University, was managing to contain the outbreak.
    This photo taken sometime between 1910 and 1915 shows Dr. Wu Lien-teh, a Cambridge-educated Chinese physician who pioneered the use of masks during the Manchurian Plague of 1910-11.
    Wu began post-mortem exams of victims and crucially established that the disease was pneumonic plague and not bubonic (the difference between the forms of plague is the location of infection; in pneumonic plague the infection is in the lungs, in bubonic plague, the lymph nodes). He also heavily recommended the wearing of face masks.
    By early 1911, China had mobilized doctors and epidemiologists from across China to converge on Harbin. Wu knew there was a big deadline looming. Chinese New Year was officially January 30 and Wu knew that limiting travel would be almost impossible during the annual migration home for so many Chinese people.
    If the infection rate wasn't brought down, then it risked becoming a nationwide epidemic.
    The response was sometimes harsh -- any lodging house where an infection appeared was burnt to the ground. But overall Wu's anti-plague measures worked. So-called "sanitary zones," quarantines, lockdowns, isolation, travel restrictions and face masks were all implemented and appear to have brought the infection rate in Harbin down by the end of January.
    Infections had spread, however, along the rail line. By the start of January 1911, Shenyang had over 2,571 deaths. Eventually, quarantining and travel restrictions in Shenyang began to take effect and the infection rate fell. But the rail line extended onwards and several towns close to the major port city of Dalian reported cases.
    In Dalian itself, mass inspections of train and ship passengers were instituted, the line was then shut, and ferries from Dalian ordered to remain in port. This meant the plague never reached Dalian.
    Though cases continued to pop up across Manchuria and occasionally beyond, in Harbin, Wu declared the plague suppressed at the end of January 1911, with a final mass cremation of victims.
    It was time to convene an international conference to try to find out why the outbreak had been so severe and widespread -- and which anti-plague measures had worked best.

    A conference in Shenyang

    Yale professor William C Summers notes in his 2012 study of the Great Manchurian Plague that: "By the end of January 1911, the momentum for some sort of international consortium of 'experts' to come together in China was building rapidly."
    The conference was not without risk for the Chinese.
    China had a Russian-controlled rail line running through a vast swathe of its territory, Japan was ensconced in Dalian and controlling China's major northern seaport, and the European powers and US had treaty ports up and down the country.
    Kitajskaya street in Harbin circa 1932.
    Still, they pushed ahead with hosting, which helped China avoid the charge of doing nothing in the aftermath of the epidemic. All attendees pledged that the conference was primarily concerned with scientific investigation, and not with imposing any further controls on China from outside.
    By April 3, 1911, Shenyang's Shao Ho Yien palace had been turned into a conference center that included meeting rooms, laboratories for experiments and living quarters for the delegates. As well as the principal countries mentioned, Italy, Mexico, the Netherlands, Germany and Austria-Hungary all sent experts. Many were from prestigious institutes.
    The main body of the conference sought to deal with eliminating the bad science and gossip, and getting to the scientific root of the bacteria. It was high-level science for the day -- bacterial toxins, surface agglutinins, variant strains. There was also discussion of modes of contagion such as coughing and false theories such as the passing of the bacillus on food. There even was talk of what we would now call asymptomatic patients and super-spreaders.
    Containment was a major theme. What had worked best? Emergency quarantine and travel measures, certainly. Also, the early use of face masks which predated Wu's discovery of the bacillus as pneumonic. Additionally, the rapid construction of plague hospitals to isolate the infected and potentially infected from ordinary hospital patients.
    Harbin Railway Station, taken in about 1900.
    The conference wrapped on April 28, 1911, with closing remarks by Wu. Ultimately, China's fears that Russia, Japan or the European powers would use the conference to advance their political aims against China didn't materialize.
    The conference's conclusions and resolutions dealt with the science of the plague, the need for sanitary improvements, quarantine regulations and the unwitting cause of the epidemic, the Tarbagan marmot.
    Closing the conference Dr Wu urged that: "Every effort should be made to secure effective medical education in China."

    Global responses

    In 1911 there was no WHO.
    The response to the epidemic, the job of trying to limit its spread and suppress it, was left to individual nations, often nations with political antagonisms.
    There were no politicians in Shenyang, only scientists who saw the need for a global intergovernmental response -- and a global health organization. That did begin to emerge after the First World War with the League of Nations formed in the wake of the 1919 Paris Peace Conference. The League took on matters relating to health through its Health Bureau, formed by an executive section of medical experts.
    The bureau targeted the eradication of leprosy, malaria and yellow fever and successfully helped to contain epidemics of typhus in Russia and various outbreaks of cholera and typhoid in China between the wars. After World War II, the League's successor, the United Nations, created the WHO.
    The Great Manchurian Plague did not ultimately spread in any serious way to the rest of China, Mongolia or Russia. The shutdown of Dalian port stopped the spread out from Manchuria to major destinations in Japan, Korea, Hong Kong and elsewhere in Asia.
    From there it could have moved by ocean liner to Europe, America and throughout the world. But it didn't.
    Summers, the historian, said that containment was down to a joined up response.
    "Such a conjunction of the right knowledge, the right resources, and the right people has not always been the case in other global challenges of epidemic disease," he said.
    Measures taken today around the world -- specially constructed quarantine hospitals, mask wearing ordinances, enhanced sanitary practices, travel restrictions, grounded planes and dedicated teams of healthcare workers -- in many ways replicate those taken 110 years ago in northeastern China.
    However, the major players today -- the US, China, the nations of the European Union, and Japan -- seemingly have little interest in a coordinated response to the health crisis and prospects of any apolitical conference seem remote.
      In 1911, the world's leading disease experts were eager to get to China.
      Perhaps that is what needs to happen at some point after the coronavirus pandemic: the world's scientists could circumvent the politicians to find a way to meet, share and discuss Covid-19 in an open forum.
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      How Malaysian plague fighter Wu Lien-teh laid down lessons for Wuhan virus

      • A century ago, Wu stopped a pneumonic plague that killed 60,000 in northeast China using preventive measures considered ahead of their time
      • Wu’s lessons still hold relevance in modern medicine today, a Singapore professor says
      Wu Lien-teh helped to contain a plague in Harbin in 1910. Photo: HandoutWu Lien-teh helped to contain a plague in Harbin in 1910. Photo: Handout
      Wu Lien-teh helped to contain a plague in Harbin in 1910. Photo: Handout
      As the number of 
      coronavirus cases
       continues to rise in China and elsewhere, the efforts of a Malaysian doctor who ended a pneumonic plague that killed 60,000 in northeast China a century ago bears lessons for the current pandemic, according to a professor in Singapore.
      Wu Lien-teh, a doctor from Penang, was called to Harbin in 1910 to combat a plague, which he found was being transmitted from diseased animals to humans amid a bustling fur trade. More than 95 per cent of infected patients died.
      Wu implemented preventive measures to contain the outbreak at a time when antibiotics were not available, including setting up quarantine units, imposing travel bans, and convincing Russian and Japanese authorities to shut railway services to Harbin. Patients who had succumbed to the plague were also cremated in large numbers in hygienic locations.
      Wu’s records of his containment efforts – found today at the library of the National University of Singapore (NUS) – formed the basis for accurate clinical decisions in terms of treatment and infection prevention, said Paul Tambyah, President of the Asia Pacific Society of Clinical Microbiology and Infection.
      “They also provided valuable information for policymakers who had to make decisions about quarantine, shutting down sections of cities and the allocation of resources,” said Tambyah, a professor of medicine.
      The trans-Siberian railway, which carried both passengers and goods for trade to Europe – including fur from Siberian marmots, a species of rodent, harvested in northeast 
      China
       – had facilitated the transmission of the plague. Someone with the disease could board a train in Harbin and in a matter of days be in Paris or Berlin, Tambyah said.
      “This dramatic escalation of global travel highlighted the perils of emerging infectious diseases,” he said.
      Wu’s notes contained principles that had been known since medieval times when plagues afflicted 
      Asia
       and 
      Europe
      , but he published them in a form which has been used by modern public health officials since, Tambyah said.
      “It is important not to draw too many parallels from a very different time and situation, but in my opinion, the scientific approach is always critical,” Tambyah said.
      “The key is international cooperation, transparent sharing of data and not being afraid of rejecting measures that do not work,” he said. “That is the best way to limit the damage from these emerging infectious diseases, and it has been for the last 100 years or more.”
      By March 1911, the pandemic was contained, earning 32-year-old Wu a reputation as a plague fighter. A month later, he chaired the International Plague Conference in Shenyang, which was attended by scientists from Britain, China, France, Germany, the United States and other nations.
      Wu’s efforts to battle the Harbin plague earned him a nomination for the Nobel Prize for medicine in 1935 – making him the first person from what is now Malaysia to be nominated – although he did not win the prestigious award.
      Nevertheless, he remained well regarded as an infectious diseases expert by Chinese Malaysians and within China.
      Coronavirus: how China builds two hospitals at top speed at the heart of the virus outbreak
      Born in 1879 to a Guangdong father and Penang-born Chinese mother, Wu was the first ethnic Chinese person to read medicine at the University of Cambridge. He worked in the government health service after leaving Britain for Kuala Lumpur in 1903, then ran a private practice the following year.
      In 1910, he moved to Harbin to investigate the plague at the invitation of the Chinese imperial government of the Qing dynasty.
      Wu fled China in 1937 during the Japanese occupation and moved to Ipoh in northwestern Malaysia, where he opened a general practice.
      Charles Toh*, 89, a Singapore doctor, was among the patients who went to Wu’s clinic.
      “Whenever I had a fever or sore throat or any other sickness, my parents would take me to see him,” Toh said, adding that the clinic was always busy due to Wu’s fame.
      “In those days, when knowledge of infectious diseases was so backwards ... and there were no antibiotics available, it was amazing he could save so many lives [in Harbin],” Toh said.
      “He was a good communicator. He had no airs. His clinic was packed with patients because he was so famous and he had extensive expertise in infectious diseases,” he said.
      Wu died in Penang in 1960. A museum in Harbin is dedicated to him. He was awarded honorary degrees from many universities including the University of Hong Kong, Tokyo University and Johns Hopkins University in the US.
      *Charles Toh is the author’s father, who was born and raised in Ipoh, Malaysia where Wu was based. Toh Han Shih is a Singaporean writer in Hong Kong.

      Thursday, April 9, 2020

      Coronavirus Cases Came From Europe, Genomes Show




      Travelers seeded multiple cases starting as early as mid-February, genomes show.



      Since the first genome of the coronavirus was sequenced in January, researchers around the world have sequenced over 3,000 more, some of which are genetically identical while others carry distinctive mutations.Credit...National Institutes of Health/EPA, via Shutterstock



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      o                                               New research indicates that the coronavirus began to circulate in the New York area by mid-February, weeks before the first confirmed case, and that travelers brought in the virus mainly from Europe, not Asia.

      “The majority is clearly European,” said Harm van Bakel, a geneticist at Icahn School of Medicine at Mount Sinai, who co-wrote a study awaiting peer review.

      A separate team at N.Y.U. Grossman School of Medicine came to strikingly similar conclusions, despite studying a different group of cases. Both teams analyzed genomes from coronaviruses taken from New Yorkers starting in mid-March.

      The research revealed a previously hidden spread of the virus that might have been detected if aggressive testing programs had been put in place.



      On Jan. 31, President Trump barred foreign nationals from entering the country if they had been in China during the prior two weeks.

      It would not be until late February that Italy would begin locking down towns and cities, and March 11 when Mr. Trump said he would block travelers from most European countries. But New Yorkers had already been traveling home with the virus.



      “People were just oblivious,” said Adriana Heguy, a member of the N.Y.U. team.

      Dr. Heguy and Dr. van Bakel belong to an international guild of viral historians. They ferret out the history of outbreaks by poring over clues embedded in the genetic material of viruses taken from thousands of patients.

      Viruses invade a cell and take over its molecular machinery, causing it to make new viruses.

      The process is quick and sloppy. As a result, new viruses can gain a new mutation that wasn’t present in their ancestor. If a new virus manages to escape its host and infect other people, its descendants will inherit that mutation.

      Tracking viral mutations demands sequencing all the genetic material in a virus — its genome. Once researchers have gathered the genomes from a number of virus samples, they can compare their mutations.



      Sophisticated computer programs can then figure out how all of those mutations arose as viruses descended from a common ancestor. If they get enough data, they can make rough estimates about how long ago those ancestors lived. That’s because mutations arise at a roughly regular pace, like a molecular clock.


      Image

      Adeline Danneels, left, a technician, and Sandrine Belouzard, virologist and researcher, at work at the Pasteur Institute of Lille, the first European organization to sequence the coronavirus genome, in February.Credit...Sylvain Lefevre/Getty Images

      Maciej Boni of Penn State University and his colleagues recently used this method to see where the coronavirus, designated SARS-CoV-2, came from in the first place. While conspiracy theories might falsely claim the virus was concocted in a lab, the virus’s genome makes clear that it arose in bats.

      There are many kinds of coronaviruses, which infect both humans and animals. Dr. Boni and his colleagues found that the genome of the new virus contains a number of mutations in common with strains of coronaviruses that infect bats.

      The most closely related coronavirus is in a Chinese horseshoe bat, the researchers found. But the new virus has gained some unique mutations since splitting off from that bat virus decades ago.

      Dr. Boni said that ancestral virus probably gave rise to a number of strains that infected horseshoe bats, and perhaps sometimes other animals.

      “Very likely there’s a vast unsampled diversity,” he said.

      Copying mistakes aren’t the only way for new viruses to arise. Sometimes two kinds of coronaviruses will infect the same cell. Their genetic material gets mixed up in new viruses.



      It’s entirely possible, Dr. Boni said, in the past 10 or 20 years, a hybrid virus arose in some horseshoe bat that was well-suited to infect humans, too. Later, that virus somehow managed to cross the species barrier.

      “Once in a while, one of these viruses wins the lottery,” he said.

      In January, a team of Chinese and Australian researchers published the first genome of the new virus. Since then, researchers around the world have sequenced over 3,000 more. Some are genetically identical to each other, while others carry distinctive mutations.

      That’s just a tiny sampling of the full diversity of the virus. As of April 8, there were 1.5 million confirmed cases of Covid-19, and the true total is probably many millions more. But already, the genomes of the virus are revealing previously hidden outlines of its history over the past few months.

      As new genomes come to light, researchers upload them to an online database called GISAID. A team of virus evolution experts are analyzing the growing collection of genomes in a project called Nextstrain. They continually update the virus family tree.

      The deepest branches of the tree all belong to lineages from China. The Nextstrain team has also used the mutation rate to determine that the virus probably first moved into humans from an animal host in late 2019. On Dec. 31, China announced that doctors in Wuhan were treating dozens of cases of a mysterious new respiratory illness.


      Image


      An apoptotic cell heavily infected with coronavirus, yellow.Credit... National Institutes of Health/EPA, via Shutterstock

      In January, as the scope of the catastrophe in China became clear, a few countries started an aggressive testing program. They were able to track the arrival of the virus on their territory and track its spread through their populations.



      But the United States fumbled in making its first diagnostic kits and initially limited testing only to people who had come from China and displayed symptoms of Covid-19.

      “It was a disaster that we didn’t do testing,” Dr. Heguy said.

      A few cases came to light starting at the end of January. But it was easy to dismiss them as rare imports that did not lead to local outbreaks.

      The illusion was dashed at the end of February by Trevor Bedford, an associate professor at the Fred Hutchinson Cancer Research Center and the University of Washington, and his colleagues.

      Using Nextstrain, they showed that a virus identified in a patient in late February had mutation shared by one identified in Washington on Jan. 20.

      The Washington viruses also shared other mutations in common with ones isolated in Wuhan, suggesting that a traveler had brought the coronavirus from China.

      With that discovery, Dr. Bedford and his colleagues took the lead in sequencing coronavirus genomes. Sequencing more genomes around Washington gave them a better view of how the outbreak there got started.

      “I’m quite confident that it was not spreading in December in the United States,” Dr. Bedford said. “There may have been a couple other introductions in January that didn’t take off in the same way.”



      As new cases arose in other parts of the country, other researchers set up their own pipelines. The first positive test result in New York came on March 1, and after a couple of weeks, patients surged into the city’s hospitals.

      “I thought, ‘We need to do this for New York,’” Dr. Heguy said.

      Dr. Heguy and her colleagues found some New York viruses that shared unique mutations not found elsewhere. “That’s when you know you’ve had a silent transmission for a while,” she said.

      Dr. Heguy estimated that the virus began circulating in the New York area a couple of months ago.

      And researchers at Mount Sinai started sequencing the genomes of patients coming through their hospital. They found that the earliest cases identified in New York were not linked to later ones.

      “Two weeks later, we start seeing viruses related to each other,” said Ana Silvia Gonzalez-Reiche, a member of the Mount Sinai team.

      Dr. Gonzalez-Reiche and her colleagues found that these viruses were practically identical to viruses found around Europe. They cannot say on what particular flight a particular virus arrived in New York. But they write that the viruses reveal “a period of untracked global transmission between late January to mid-February.”

      So far, the Mount Sinai researchers have identified seven separate lineages of viruses that entered New York and began circulating. “We will probably find more,” Dr. van Bakel said.



      The coronavirus genomes are also revealing hints of early cross-country travel.

      Dr. van Bakel and his colleagues found one New York virus that was identical to one of the Washington viruses found by Dr. Bedford and his colleagues. In a separate study, researchers at Yale found another Washington-related virus. Combined, the two studies hint that the coronavirus has been moving from coast to coast for several weeks.


      Image


      Cell samples to be infected with coronavirus at The Icahn School of Medicine at Mount Sinai in Manhattan.Credit...Victor J. Blue for The New York Times

      Sidney Bell, a computational biologist working with the Nextstrain team, cautions people not to read too much into these new mutations themselves. “Just because something is different doesn’t mean it matters,” Dr. Bell said.

      Mutations do not automatically turn viruses into new, fearsome strains. They often don’t bring about any change at all. “To me, mutations are inevitable and kind of boring,” Dr. Bell said. “But in the movies, you get the X-Men.”

      Peter Thielen, a virologist at the Applied Physics Laboratory at Johns Hopkins University, likes to think of the spread of viruses like a dandelion seed landing on an empty field.

      The flower grows up and produces seeds of its own. Those seeds spread and sprout. New mutations arise over the generations as the dandelions fill the field. “But they’re all still dandelions,” Dr. Thielen said.

      While the coronavirus mutations are useful for telling lineages apart, they don’t have any apparent effect on how the virus works.

      That’s good news for scientists working on a vaccine.

      Vaccine developers hope to fight Covid-19 by teaching our bodies to make antibodies that can grab onto the virus and block its entry into cells.



      Some viruses evolve so quickly that they require vaccines that can produce several different antibodies. That’s not the case for Covid-19. Like other coronaviruses, it has a relatively slow mutation rate compared to some viruses, like influenza.

      As hard as the fight against it may be, its mutations reveal that things can be a whole lot worse.

      Of course, the coronavirus will continue to mutate as long as it still infects people. It’s possible that vaccines will have to change to keep up with the virus. And that’s why scientists need to keep tracking its history.


      Thursday, April 2, 2020

      WSJ: When a Virus Spreads Exponentially

       https://www.wsj.com/articles/when-a-virus-spreads-exponentially-11585850494



      The key to stopping the Covid-19 pandemic lies in lowering the rate at which infections multiply.

      PHOTO: TOMASZ WALENTA
      • TEXT

      Fighting a pandemic like Covid-19 requires experts in many fields: epidemiologists who study the spread of disease, doctors who treat the sick, scientists who work on finding a vaccine. There is math involved in all of these specialties, but math can also help us to make sense of the barrage of information that we’re receiving daily.

      The starting point is the math of exponential growth. The word “exponential” is sometimes used informally to mean “really fast,” but mathematically it means something very specific: that a quantity is repeatedly multiplied by the same number. When a virus spreads, each infected person goes on to infect a certain number of other people, on average; this is called the reproduction number or R0. Then each newly infected person goes on to infect R0 people, again on average.

      Exponential growth is dangerous, because if each person infects more than one other person, the spread of disease quickly becomes overwhelming. Multiplying by 3, for instance, it only takes 21 steps to reach 10 billion, more than the current population of the world. We start with very low numbers that seem insignificant, but it’s not the absolute numbers that matter, it’s the rate at which they’re increasing, which also increases exponentially. Waiting until an infectious disease feels like a problem is too late to start addressing it.

      MORE EVERYDAY MATH

      One important feature of exponential growth is that it’s not helpful to look at the number of new cases each day. Exponentials increase by multiplication, so it’s more relevant to look at the percentage increase each day. This is what “flattening the curve” is about: reducing the rate of multiplication. Eventually we need the rate to be less than one, so that each infected person infects fewer than one new person, producing exponential decay instead of growth.