This article is from the source 'nytimes' and was first published or seen on . It last changed over 40 days ago and won't be checked again for changes.

You can find the current article at its original source at https://www.nytimes.com/2020/04/23/world/europe/coronavirus-R0-explainer.html

The article has changed 29 times. There is an RSS feed of changes available.

Version 6 Version 7
R0, the Messy Metric That May Soon Shape Our Lives, Explained R0, the Messy Metric That May Soon Shape Our Lives, Explained
(3 days later)
World leaders and public health experts are poised to spend the coming months or years obsessed with a variable known as R0.World leaders and public health experts are poised to spend the coming months or years obsessed with a variable known as R0.
Pronounced “R-naught,” it represents the number of new infections estimated to stem from a single case.Pronounced “R-naught,” it represents the number of new infections estimated to stem from a single case.
In other words, if R0 is 2.5, then one person with the disease is expected to infect, on average, 2.5 others.In other words, if R0 is 2.5, then one person with the disease is expected to infect, on average, 2.5 others.
An R0 below 1 suggests that the number of cases is shrinking, possibly allowing societies to open back up. An R0 above 1 indicates that the number of cases is growing, perhaps necessitating renewed lockdowns or other measures.An R0 below 1 suggests that the number of cases is shrinking, possibly allowing societies to open back up. An R0 above 1 indicates that the number of cases is growing, perhaps necessitating renewed lockdowns or other measures.
But R0 is messier than it might look. It is built on hard science, forensic investigation, complex mathematical models — and often a good deal of guesswork. It can vary radically from place to place and day to day, pushed up or down by local conditions and human behavior.But R0 is messier than it might look. It is built on hard science, forensic investigation, complex mathematical models — and often a good deal of guesswork. It can vary radically from place to place and day to day, pushed up or down by local conditions and human behavior.
Yet for all its vagaries, R0 is expected to shape our world in the coming months and possibly years as governments and health experts treat it as the closest thing to a compass in navigating the pandemic.Yet for all its vagaries, R0 is expected to shape our world in the coming months and possibly years as governments and health experts treat it as the closest thing to a compass in navigating the pandemic.
What follows is a simple guide to how this metric works, why it matters and how to think about it.What follows is a simple guide to how this metric works, why it matters and how to think about it.
The term is borrowed from the study of demographics, where it is used to describe birthrates.The term is borrowed from the study of demographics, where it is used to describe birthrates.
R refers to reproduction and 0 to the zeroth generation, as in patient zero. Together, they are typically called the basic reproduction number.R refers to reproduction and 0 to the zeroth generation, as in patient zero. Together, they are typically called the basic reproduction number.
It is calculated from innate features of a disease, like how easily it jumps from one person to the next, along with elements of human behavior that shape how often sick and susceptible people will come into contact.It is calculated from innate features of a disease, like how easily it jumps from one person to the next, along with elements of human behavior that shape how often sick and susceptible people will come into contact.
The resulting number is meant to help model an outbreak’s possible trajectory.The resulting number is meant to help model an outbreak’s possible trajectory.
Say that 1,000 people have a seasonal flu whose R0 is estimated at 1.3.Say that 1,000 people have a seasonal flu whose R0 is estimated at 1.3.
They would be expected to infect 1,300 people. That second generation would go on to infect another 1,690.They would be expected to infect 1,300 people. That second generation would go on to infect another 1,690.
That can add up. By the 10th generation, about 30 days time, 42,621 people would have caught the flu.That can add up. By the 10th generation, about 30 days time, 42,621 people would have caught the flu.
But any R0 is just an estimate and, epidemiologists stress, an imperfect one.But any R0 is just an estimate and, epidemiologists stress, an imperfect one.
A paper published last year in Emerging Infectious Diseases, an academic journal, described the metric as important but warned that it can be “easily misrepresented, misinterpreted and misapplied.”A paper published last year in Emerging Infectious Diseases, an academic journal, described the metric as important but warned that it can be “easily misrepresented, misinterpreted and misapplied.”
There is no consensus for how to measure it. Much of the underlying math relies, by necessity, on educated guesses and on human factors that can change unpredictably.There is no consensus for how to measure it. Much of the underlying math relies, by necessity, on educated guesses and on human factors that can change unpredictably.
For this reason, most diseases are given a range, rather than a single figure. SARS is usually described as having an R0 of 2 to 5 — an enormous difference.For this reason, most diseases are given a range, rather than a single figure. SARS is usually described as having an R0 of 2 to 5 — an enormous difference.
Tellingly, scientists are still disputing and revising estimates for diseases that have been studied for years; R0 figures for measles have ranged from 3.7 to 203.Tellingly, scientists are still disputing and revising estimates for diseases that have been studied for years; R0 figures for measles have ranged from 3.7 to 203.
Still, for all its flaws, it’s useful shorthand for both experts studying the disease and leaders trying to manage it.Still, for all its flaws, it’s useful shorthand for both experts studying the disease and leaders trying to manage it.
In practice, there is no such thing as a fixed R0. It’s better to think of this number as a starting point for the virus’s behavior in the absence of real-world human or environmental factors.In practice, there is no such thing as a fixed R0. It’s better to think of this number as a starting point for the virus’s behavior in the absence of real-world human or environmental factors.
New figures are coming out all the time. But, generally, studies now estimate that the pathogen that causes Covid-19 has an R0 of 2 to 2.5.New figures are coming out all the time. But, generally, studies now estimate that the pathogen that causes Covid-19 has an R0 of 2 to 2.5.
That’s significantly higher than the flu and within lower-end ranges for SARS, another coronavirus.That’s significantly higher than the flu and within lower-end ranges for SARS, another coronavirus.
To know how quickly a virus spreads, you also need its serial interval, or average time between each successive infection. Some studies estimate the coronavirus’s at 4 to 4.5 days. That’s almost twice as fast as SARS, which is why the coronavirus spreads so much more quickly.To know how quickly a virus spreads, you also need its serial interval, or average time between each successive infection. Some studies estimate the coronavirus’s at 4 to 4.5 days. That’s almost twice as fast as SARS, which is why the coronavirus spreads so much more quickly.
The serial interval, though, is considered more or less fixed. People can heavily influence R0, which is why it receives so much more attention than other metrics.The serial interval, though, is considered more or less fixed. People can heavily influence R0, which is why it receives so much more attention than other metrics.
The term can also be used to describe a snapshot in time: an estimate of how the virus is reproducing on the ground in a given time and place.The term can also be used to describe a snapshot in time: an estimate of how the virus is reproducing on the ground in a given time and place.
For example, during China’s initial outbreak, one study estimated, the virus spread with an R0 of 5.7 — a catastrophically high figure.For example, during China’s initial outbreak, one study estimated, the virus spread with an R0 of 5.7 — a catastrophically high figure.
Governments increasingly use R0 as a metric for whether their country’s cases are growing faster than they can manage or shrinking as quickly as they’d like.Governments increasingly use R0 as a metric for whether their country’s cases are growing faster than they can manage or shrinking as quickly as they’d like.
Interest in R0 has grown so intense that a video of Angela Merkel, the restrained German chancellor rarely associated with viral videos, explaining the variable has been viewed nearly nine million times.Interest in R0 has grown so intense that a video of Angela Merkel, the restrained German chancellor rarely associated with viral videos, explaining the variable has been viewed nearly nine million times.
“We are now at about a reproduction factor of 1, so one person is infecting another one,” Ms. Merkel said at a press event last week. “If we get to the point where everybody infects 1.1 people, then by October we will reach the capacity of our health care system.”“We are now at about a reproduction factor of 1, so one person is infecting another one,” Ms. Merkel said at a press event last week. “If we get to the point where everybody infects 1.1 people, then by October we will reach the capacity of our health care system.”
When a country has more patients than intensive care beds, death rates can spike drastically.When a country has more patients than intensive care beds, death rates can spike drastically.
At an R0 of 1.2, Ms. Merkel went on, Germany would cross that threshold in July. At an R0 of 1.3, it would happen in June.At an R0 of 1.2, Ms. Merkel went on, Germany would cross that threshold in July. At an R0 of 1.3, it would happen in June.
“So that’s where you see how small the margin is,” she said.“So that’s where you see how small the margin is,” she said.
But real-time R0 estimates like Germany’s are, however sophisticated, highly speculative. It is an estimate built on other estimates, some more informed than others.But real-time R0 estimates like Germany’s are, however sophisticated, highly speculative. It is an estimate built on other estimates, some more informed than others.
Still, it is one of our only metrics for guessing at how well lockdowns and other policies are working — and therefore for determining whether and when those policies are worth their enormous economic and social costs.Still, it is one of our only metrics for guessing at how well lockdowns and other policies are working — and therefore for determining whether and when those policies are worth their enormous economic and social costs.
No. It means, assuming the numbers are correct, that the virus’s spread has been paused.No. It means, assuming the numbers are correct, that the virus’s spread has been paused.
Where R0 drops below 1, this means that every, say, 100 sick people will infect fewer than 100 others. Each successive generation of infections will be smaller than the last.Where R0 drops below 1, this means that every, say, 100 sick people will infect fewer than 100 others. Each successive generation of infections will be smaller than the last.
But people can still get sick, and people can still die. It can take a long time for countries to see the virus fully recede, especially if the initial outbreak was bad.But people can still get sick, and people can still die. It can take a long time for countries to see the virus fully recede, especially if the initial outbreak was bad.
Updated June 5, 2020 Updated June 12, 2020
Touching contaminated objects and then infecting ourselves with the germs is not typically how the virus spreads. But it can happen. A number of studies of flu, rhinovirus, coronavirus and other microbes have shown that respiratory illnesses, including the new coronavirus, can spread by touching contaminated surfaces, particularly in places like day care centers, offices and hospitals. But a long chain of events has to happen for the disease to spread that way. The best way to protect yourself from coronavirus — whether it’s surface transmission or close human contact — is still social distancing, washing your hands, not touching your face and wearing masks.
So far, the evidence seems to show it does. A widely cited paper published in April suggests that people are most infectious about two days before the onset of coronavirus symptoms and estimated that 44 percent of new infections were a result of transmission from people who were not yet showing symptoms. Recently, a top expert at the World Health Organization stated that transmission of the coronavirus by people who did not have symptoms was “very rare,” but she later walked back that statement.So far, the evidence seems to show it does. A widely cited paper published in April suggests that people are most infectious about two days before the onset of coronavirus symptoms and estimated that 44 percent of new infections were a result of transmission from people who were not yet showing symptoms. Recently, a top expert at the World Health Organization stated that transmission of the coronavirus by people who did not have symptoms was “very rare,” but she later walked back that statement.
A study by European scientists is the first to document a strong statistical link between genetic variations and Covid-19, the illness caused by the coronavirus. Having Type A blood was linked to a 50 percent increase in the likelihood that a patient would need to get oxygen or to go on a ventilator, according to the new study.A study by European scientists is the first to document a strong statistical link between genetic variations and Covid-19, the illness caused by the coronavirus. Having Type A blood was linked to a 50 percent increase in the likelihood that a patient would need to get oxygen or to go on a ventilator, according to the new study.
The unemployment rate fell to 13.3 percent in May, the Labor Department said on June 5, an unexpected improvement in the nation’s job market as hiring rebounded faster than economists expected. Economists had forecast the unemployment rate to increase to as much as 20 percent, after it hit 14.7 percent in April, which was the highest since the government began keeping official statistics after World War II. But the unemployment rate dipped instead, with employers adding 2.5 million jobs, after more than 20 million jobs were lost in April.The unemployment rate fell to 13.3 percent in May, the Labor Department said on June 5, an unexpected improvement in the nation’s job market as hiring rebounded faster than economists expected. Economists had forecast the unemployment rate to increase to as much as 20 percent, after it hit 14.7 percent in April, which was the highest since the government began keeping official statistics after World War II. But the unemployment rate dipped instead, with employers adding 2.5 million jobs, after more than 20 million jobs were lost in April.
Mass protests against police brutality that have brought thousands of people onto the streets in cities across America are raising the specter of new coronavirus outbreaks, prompting political leaders, physicians and public health experts to warn that the crowds could cause a surge in cases. While many political leaders affirmed the right of protesters to express themselves, they urged the demonstrators to wear face masks and maintain social distancing, both to protect themselves and to prevent further community spread of the virus. Some infectious disease experts were reassured by the fact that the protests were held outdoors, saying the open air settings could mitigate the risk of transmission.Mass protests against police brutality that have brought thousands of people onto the streets in cities across America are raising the specter of new coronavirus outbreaks, prompting political leaders, physicians and public health experts to warn that the crowds could cause a surge in cases. While many political leaders affirmed the right of protesters to express themselves, they urged the demonstrators to wear face masks and maintain social distancing, both to protect themselves and to prevent further community spread of the virus. Some infectious disease experts were reassured by the fact that the protests were held outdoors, saying the open air settings could mitigate the risk of transmission.
Exercise researchers and physicians have some blunt advice for those of us aiming to return to regular exercise now: Start slowly and then rev up your workouts, also slowly. American adults tended to be about 12 percent less active after the stay-at-home mandates began in March than they were in January. But there are steps you can take to ease your way back into regular exercise safely. First, “start at no more than 50 percent of the exercise you were doing before Covid,” says Dr. Monica Rho, the chief of musculoskeletal medicine at the Shirley Ryan AbilityLab in Chicago. Thread in some preparatory squats, too, she advises. “When you haven’t been exercising, you lose muscle mass.” Expect some muscle twinges after these preliminary, post-lockdown sessions, especially a day or two later. But sudden or increasing pain during exercise is a clarion call to stop and return home.Exercise researchers and physicians have some blunt advice for those of us aiming to return to regular exercise now: Start slowly and then rev up your workouts, also slowly. American adults tended to be about 12 percent less active after the stay-at-home mandates began in March than they were in January. But there are steps you can take to ease your way back into regular exercise safely. First, “start at no more than 50 percent of the exercise you were doing before Covid,” says Dr. Monica Rho, the chief of musculoskeletal medicine at the Shirley Ryan AbilityLab in Chicago. Thread in some preparatory squats, too, she advises. “When you haven’t been exercising, you lose muscle mass.” Expect some muscle twinges after these preliminary, post-lockdown sessions, especially a day or two later. But sudden or increasing pain during exercise is a clarion call to stop and return home.
States are reopening bit by bit. This means that more public spaces are available for use and more and more businesses are being allowed to open again. The federal government is largely leaving the decision up to states, and some state leaders are leaving the decision up to local authorities. Even if you aren’t being told to stay at home, it’s still a good idea to limit trips outside and your interaction with other people.States are reopening bit by bit. This means that more public spaces are available for use and more and more businesses are being allowed to open again. The federal government is largely leaving the decision up to states, and some state leaders are leaving the decision up to local authorities. Even if you aren’t being told to stay at home, it’s still a good idea to limit trips outside and your interaction with other people.
Touching contaminated objects and then infecting ourselves with the germs is not typically how the virus spreads. But it can happen. A number of studies of flu, rhinovirus, coronavirus and other microbes have shown that respiratory illnesses, including the new coronavirus, can spread by touching contaminated surfaces, particularly in places like day care centers, offices and hospitals. But a long chain of events has to happen for the disease to spread that way. The best way to protect yourself from coronavirus — whether it’s surface transmission or close human contact — is still social distancing, washing your hands, not touching your face and wearing masks.
Common symptoms include fever, a dry cough, fatigue and difficulty breathing or shortness of breath. Some of these symptoms overlap with those of the flu, making detection difficult, but runny noses and stuffy sinuses are less common. The C.D.C. has also added chills, muscle pain, sore throat, headache and a new loss of the sense of taste or smell as symptoms to look out for. Most people fall ill five to seven days after exposure, but symptoms may appear in as few as two days or as many as 14 days.Common symptoms include fever, a dry cough, fatigue and difficulty breathing or shortness of breath. Some of these symptoms overlap with those of the flu, making detection difficult, but runny noses and stuffy sinuses are less common. The C.D.C. has also added chills, muscle pain, sore throat, headache and a new loss of the sense of taste or smell as symptoms to look out for. Most people fall ill five to seven days after exposure, but symptoms may appear in as few as two days or as many as 14 days.
If air travel is unavoidable, there are some steps you can take to protect yourself. Most important: Wash your hands often, and stop touching your face. If possible, choose a window seat. A study from Emory University found that during flu season, the safest place to sit on a plane is by a window, as people sitting in window seats had less contact with potentially sick people. Disinfect hard surfaces. When you get to your seat and your hands are clean, use disinfecting wipes to clean the hard surfaces at your seat like the head and arm rest, the seatbelt buckle, the remote, screen, seat back pocket and the tray table. If the seat is hard and nonporous or leather or pleather, you can wipe that down, too. (Using wipes on upholstered seats could lead to a wet seat and spreading of germs rather than killing them.)If air travel is unavoidable, there are some steps you can take to protect yourself. Most important: Wash your hands often, and stop touching your face. If possible, choose a window seat. A study from Emory University found that during flu season, the safest place to sit on a plane is by a window, as people sitting in window seats had less contact with potentially sick people. Disinfect hard surfaces. When you get to your seat and your hands are clean, use disinfecting wipes to clean the hard surfaces at your seat like the head and arm rest, the seatbelt buckle, the remote, screen, seat back pocket and the tray table. If the seat is hard and nonporous or leather or pleather, you can wipe that down, too. (Using wipes on upholstered seats could lead to a wet seat and spreading of germs rather than killing them.)
Taking one’s temperature to look for signs of fever is not as easy as it sounds, as “normal” temperature numbers can vary, but generally, keep an eye out for a temperature of 100.5 degrees Fahrenheit or higher. If you don’t have a thermometer (they can be pricey these days), there are other ways to figure out if you have a fever, or are at risk of Covid-19 complications.Taking one’s temperature to look for signs of fever is not as easy as it sounds, as “normal” temperature numbers can vary, but generally, keep an eye out for a temperature of 100.5 degrees Fahrenheit or higher. If you don’t have a thermometer (they can be pricey these days), there are other ways to figure out if you have a fever, or are at risk of Covid-19 complications.
The C.D.C. has recommended that all Americans wear cloth masks if they go out in public. This is a shift in federal guidance reflecting new concerns that the coronavirus is being spread by infected people who have no symptoms. Until now, the C.D.C., like the W.H.O., has advised that ordinary people don’t need to wear masks unless they are sick and coughing. Part of the reason was to preserve medical-grade masks for health care workers who desperately need them at a time when they are in continuously short supply. Masks don’t replace hand washing and social distancing.The C.D.C. has recommended that all Americans wear cloth masks if they go out in public. This is a shift in federal guidance reflecting new concerns that the coronavirus is being spread by infected people who have no symptoms. Until now, the C.D.C., like the W.H.O., has advised that ordinary people don’t need to wear masks unless they are sick and coughing. Part of the reason was to preserve medical-grade masks for health care workers who desperately need them at a time when they are in continuously short supply. Masks don’t replace hand washing and social distancing.
If you’ve been exposed to the coronavirus or think you have, and have a fever or symptoms like a cough or difficulty breathing, call a doctor. They should give you advice on whether you should be tested, how to get tested, and how to seek medical treatment without potentially infecting or exposing others.If you’ve been exposed to the coronavirus or think you have, and have a fever or symptoms like a cough or difficulty breathing, call a doctor. They should give you advice on whether you should be tested, how to get tested, and how to seek medical treatment without potentially infecting or exposing others.
If you’re sick and you think you’ve been exposed to the new coronavirus, the C.D.C. recommends that you call your healthcare provider and explain your symptoms and fears. They will decide if you need to be tested. Keep in mind that there’s a chance — because of a lack of testing kits or because you’re asymptomatic, for instance — you won’t be able to get tested.If you’re sick and you think you’ve been exposed to the new coronavirus, the C.D.C. recommends that you call your healthcare provider and explain your symptoms and fears. They will decide if you need to be tested. Keep in mind that there’s a chance — because of a lack of testing kits or because you’re asymptomatic, for instance — you won’t be able to get tested.
Italy, for example, recently estimated that its social and economic restrictions had pushed the virus’s R0 down to 0.8 — a huge achievement won at a heavy cost.Italy, for example, recently estimated that its social and economic restrictions had pushed the virus’s R0 down to 0.8 — a huge achievement won at a heavy cost.
How long might it take Italy to resemble South Korea, which is tentatively reopening as it confirms about 10 new cases per day?How long might it take Italy to resemble South Korea, which is tentatively reopening as it confirms about 10 new cases per day?
Italy reported 15,918 new cases in the past five days, a workable shorthand for the number of people who might still be infectious. At an R0 of 0.8, it would take 26.8 generations of the virus for Italy’s new infections to pace South Korea’s.Italy reported 15,918 new cases in the past five days, a workable shorthand for the number of people who might still be infectious. At an R0 of 0.8, it would take 26.8 generations of the virus for Italy’s new infections to pace South Korea’s.
At four days per generation, that’s about 100 days, or early August. And that’s only if the status quo — lockdown — is maintained.At four days per generation, that’s about 100 days, or early August. And that’s only if the status quo — lockdown — is maintained.
Three and a half more months of social restrictions would be costly for Italy’s already-strained society and economy. And it would not be a guarantee. Even South Korea has measures in place to reimpose lockdowns if cases resurge.Three and a half more months of social restrictions would be costly for Italy’s already-strained society and economy. And it would not be a guarantee. Even South Korea has measures in place to reimpose lockdowns if cases resurge.
This is why some experts believe that, in the coming months or years, government measures will not be aimed at simply driving down R0 as low as possible, but at managing it within acceptable levels.This is why some experts believe that, in the coming months or years, government measures will not be aimed at simply driving down R0 as low as possible, but at managing it within acceptable levels.
In such a scheme, social and economic restrictions would be lifted and reimposed in response to fluctuations in the R0. But no one knows what the right balance would be, much less how to achieve it.In such a scheme, social and economic restrictions would be lifted and reimposed in response to fluctuations in the R0. But no one knows what the right balance would be, much less how to achieve it.
A Harvard University study estimated that keeping new cases within what the health care system can manage could require calibrating off-and-on lockdowns through mid-2022.A Harvard University study estimated that keeping new cases within what the health care system can manage could require calibrating off-and-on lockdowns through mid-2022.
Official efforts to track R0 are spotty but growing more common.Official efforts to track R0 are spotty but growing more common.
Several European countries now report estimates below 1, but levels of success remain uncertain.Several European countries now report estimates below 1, but levels of success remain uncertain.
Germany puts its own at 0.9, up from a recent low of 0.7, which had led Ms. Merkel to ease restrictions. Governments face gut-wrenching dilemmas over whether to accept such upticks as necessary evils.Germany puts its own at 0.9, up from a recent low of 0.7, which had led Ms. Merkel to ease restrictions. Governments face gut-wrenching dilemmas over whether to accept such upticks as necessary evils.
One study from France estimated that timely lockdowns pushed R0 down to 0.5 from 3.3, a stunning transformation.One study from France estimated that timely lockdowns pushed R0 down to 0.5 from 3.3, a stunning transformation.
Still, French cases jumped the day after the study was published, in part because nursing home infections had not previously been recorded, a reminder that R0 estimates are imperfect shorthand.Still, French cases jumped the day after the study was published, in part because nursing home infections had not previously been recorded, a reminder that R0 estimates are imperfect shorthand.
India, whose enormous population and rickety health care system make it one of the pandemic’s most-watched countries, estimates its R0 to have declined to 1.36 from 1.55. That’s low, but still above 1 — meaning case numbers are growing.India, whose enormous population and rickety health care system make it one of the pandemic’s most-watched countries, estimates its R0 to have declined to 1.36 from 1.55. That’s low, but still above 1 — meaning case numbers are growing.
It is difficult to assign the United States a single R0 figure. The country has multiple concurrent outbreaks, each with its own dynamics and each at a different point in its life cycle.It is difficult to assign the United States a single R0 figure. The country has multiple concurrent outbreaks, each with its own dynamics and each at a different point in its life cycle.
The former founders of Instagram set up a website that estimates state-by-state Rt values, a variation on R0 that accounts for rates of transmission. Though it is not associated with professional epidemiologists or public health experts, it has received heavy attention, reflecting the hunger for information on this useful but fuzzy metric.The former founders of Instagram set up a website that estimates state-by-state Rt values, a variation on R0 that accounts for rates of transmission. Though it is not associated with professional epidemiologists or public health experts, it has received heavy attention, reflecting the hunger for information on this useful but fuzzy metric.