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The Coronavirus, by the Numbers The Coronavirus, by the Numbers
(3 days later)
Adam Kucharski studies how diseases spread, but he’s not handling viruses in the lab or treating sick people in the hospital. He’s a mathematician at the London School of Hygiene & Tropical Medicine, and he uses math to understand outbreaks of diseases like Ebola, SARS, influenza and now Covid-19. His goal is to design better ways to control outbreaks.Adam Kucharski studies how diseases spread, but he’s not handling viruses in the lab or treating sick people in the hospital. He’s a mathematician at the London School of Hygiene & Tropical Medicine, and he uses math to understand outbreaks of diseases like Ebola, SARS, influenza and now Covid-19. His goal is to design better ways to control outbreaks.
In an eerie coincidence, he wrote a book called “The Rules of Contagion,” before the current outbreak, which has been published in Britain and will be released in September in the United States. In it he talks about the math of contagion involving not only physical diseases, but also ideas, rumors and even financial crises.In an eerie coincidence, he wrote a book called “The Rules of Contagion,” before the current outbreak, which has been published in Britain and will be released in September in the United States. In it he talks about the math of contagion involving not only physical diseases, but also ideas, rumors and even financial crises.
In a recent experiment for the 100th anniversary of the 1918 flu, he worked with another mathematician and BBC presenter, Hannah Fry, of University College London, and collaborators at the University of Cambridge, to create a documentary, “Contagion: The BBC Four Pandemic,” using a phone app to track social contacts and map how an infection might spread.In a recent experiment for the 100th anniversary of the 1918 flu, he worked with another mathematician and BBC presenter, Hannah Fry, of University College London, and collaborators at the University of Cambridge, to create a documentary, “Contagion: The BBC Four Pandemic,” using a phone app to track social contacts and map how an infection might spread.
The news of coronavirus epidemics around the world involves a flood of numbers that are a challenge for any nonscientist to digest. I asked Dr. Kucharski to help us navigate some of these numbers, and to tell us which ones we should pay attention to. We talked on the phone and corresponded by email this week. This is an edited version of our back and forth.The news of coronavirus epidemics around the world involves a flood of numbers that are a challenge for any nonscientist to digest. I asked Dr. Kucharski to help us navigate some of these numbers, and to tell us which ones we should pay attention to. We talked on the phone and corresponded by email this week. This is an edited version of our back and forth.
We hear a lot about the percentage of sick people who are dying. Is that the case fatality rate?We hear a lot about the percentage of sick people who are dying. Is that the case fatality rate?
The case fatality rate measures the risk that someone who develops symptoms will eventually die from the infection.The case fatality rate measures the risk that someone who develops symptoms will eventually die from the infection.
And how is that rate calculated?And how is that rate calculated?
Ideally, we would monitor a large group of people from the point at which they develop symptoms until they later die or recover, then calculate the proportion of all these cases who had died.Ideally, we would monitor a large group of people from the point at which they develop symptoms until they later die or recover, then calculate the proportion of all these cases who had died.
So can we just look at the total number of deaths and the current number of cases?So can we just look at the total number of deaths and the current number of cases?
The problem with just dividing the total number of deaths and total number of cases is that it doesn’t account for unreported cases or the delay from illness to death. The delay is crucial: If 100 people arrive at hospital with Covid-19 on a given day, and all are currently still alive, it obviously doesn’t mean that the fatality rate is 0 percent. We need to wait until we know what happens to them eventually.The problem with just dividing the total number of deaths and total number of cases is that it doesn’t account for unreported cases or the delay from illness to death. The delay is crucial: If 100 people arrive at hospital with Covid-19 on a given day, and all are currently still alive, it obviously doesn’t mean that the fatality rate is 0 percent. We need to wait until we know what happens to them eventually.
Any deaths will be people who got sick two to three weeks ago, so it’s not simply deaths at the moment divided by cases at the moment. Plus some cases might be missed: If you have two deaths from two cases, as happened in Iran last month, that most likely means you’ve missed a bunch of cases.Any deaths will be people who got sick two to three weeks ago, so it’s not simply deaths at the moment divided by cases at the moment. Plus some cases might be missed: If you have two deaths from two cases, as happened in Iran last month, that most likely means you’ve missed a bunch of cases.
We’ve seen all sorts of numbers for fatality rates. Does the latest estimate of 3.4 percent globally make sense?We’ve seen all sorts of numbers for fatality rates. Does the latest estimate of 3.4 percent globally make sense?
Early on, people looked at total current cases and deaths, which, as I said, is a flawed calculation, and concluded that the case fatality rate must be 2 percent based on China data. If you run the same calculation on yesterday’s totals for China, you get an apparent CFR (case fatality rate) of near 4 percent. People are speculating that something is happening with the virus, where it actually is just this statistical illusion that we’ve known about from Day 1. I’d say on best available data, when we adjust for unreported cases and the various delays involved, we’re probably looking at a fatality risk of probably between maybe 0.5 and 2 percent for people with symptoms.Early on, people looked at total current cases and deaths, which, as I said, is a flawed calculation, and concluded that the case fatality rate must be 2 percent based on China data. If you run the same calculation on yesterday’s totals for China, you get an apparent CFR (case fatality rate) of near 4 percent. People are speculating that something is happening with the virus, where it actually is just this statistical illusion that we’ve known about from Day 1. I’d say on best available data, when we adjust for unreported cases and the various delays involved, we’re probably looking at a fatality risk of probably between maybe 0.5 and 2 percent for people with symptoms.
I had a short Twitter thread explaining this (and predicting the rise) a couple of weeks ago:I had a short Twitter thread explaining this (and predicting the rise) a couple of weeks ago:
What about another number we hear about all the time, R, the reproductive number, or how many people a given patient is likely to infect. Why is it important and what goes into calculating it?What about another number we hear about all the time, R, the reproductive number, or how many people a given patient is likely to infect. Why is it important and what goes into calculating it?
At its simplest, R is the answer to the question: How worried should we be about infection? If R is above one, each case, on average, is giving it to at least one other person. You’re going to see growth.At its simplest, R is the answer to the question: How worried should we be about infection? If R is above one, each case, on average, is giving it to at least one other person. You’re going to see growth.
If it’s less than one, then a group of infected people are generating less infection. From a policy-planning point of view, it gives you a very clear objective. For example, in the Ebola response in 2014, it was a really prominent part of the response. The aim was to get R below one.If it’s less than one, then a group of infected people are generating less infection. From a policy-planning point of view, it gives you a very clear objective. For example, in the Ebola response in 2014, it was a really prominent part of the response. The aim was to get R below one.
That seems very simple and straightforward, but you write that it’s more complicated than it seems. In your book you say that to calculate R you’ve got to know duration, opportunity, transmission probability and susceptibility (the “DOTS”). Let’s take them one by one. What is duration?That seems very simple and straightforward, but you write that it’s more complicated than it seems. In your book you say that to calculate R you’ve got to know duration, opportunity, transmission probability and susceptibility (the “DOTS”). Let’s take them one by one. What is duration?
How long someone is infectious. If someone is infectious twice as long, then that’s twice as long that they are around to spread infection.How long someone is infectious. If someone is infectious twice as long, then that’s twice as long that they are around to spread infection.
Do we know what the duration is for this coronavirus?Do we know what the duration is for this coronavirus?
On average, we’d probably be looking at a week or two. Of course, if people get hospitalized, then they’re not in the community spreading infection in the same way.On average, we’d probably be looking at a week or two. Of course, if people get hospitalized, then they’re not in the community spreading infection in the same way.
The second component is opportunity. How do you determine that?The second component is opportunity. How do you determine that?
That’s a measure of how many people you come into contact with for every day you’re infectious. With something like flu, you’re not infectious very long but a lot of your interactions could potentially spread it. Whereas with something like HIV, the duration is much longer but the number of sexual partners you have relative to the number of conversations you have is obviously much lower.That’s a measure of how many people you come into contact with for every day you’re infectious. With something like flu, you’re not infectious very long but a lot of your interactions could potentially spread it. Whereas with something like HIV, the duration is much longer but the number of sexual partners you have relative to the number of conversations you have is obviously much lower.
And transmission probability?And transmission probability?
This is a measure of the chance the infection will get across during an interaction. For example, during a sexual encounter, the virus won’t necessarily get across.This is a measure of the chance the infection will get across during an interaction. For example, during a sexual encounter, the virus won’t necessarily get across.
Finally there’s susceptibility. How do you determine that?Finally there’s susceptibility. How do you determine that?
Susceptibility measures the chance the person at the other end of the interaction will pick up the infection and become infectious themselves.Susceptibility measures the chance the person at the other end of the interaction will pick up the infection and become infectious themselves.
Once you’ve got numbers for these four components, what’s the equation to come up with R?Once you’ve got numbers for these four components, what’s the equation to come up with R?
If you multiply them together, you get the reproduction number. So if you scale up or scale down any one of these things, it directly affects the value of R.If you multiply them together, you get the reproduction number. So if you scale up or scale down any one of these things, it directly affects the value of R.
Updated June 12, 2020Updated 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.
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.
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.
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.
How does this knowledge help public health planning?How does this knowledge help public health planning?
Generally, susceptibility is the easiest one to reduce if we have things like vaccines. If we don’t, then we have to think about targeting the other aspects of transmission, such as reducing opportunities through social distancing, or probability of transmission during things like handshakes by encouraging hand washing.Generally, susceptibility is the easiest one to reduce if we have things like vaccines. If we don’t, then we have to think about targeting the other aspects of transmission, such as reducing opportunities through social distancing, or probability of transmission during things like handshakes by encouraging hand washing.
What if you’re not in public health, but are thinking about your own personal chances and what your behavior should be?What if you’re not in public health, but are thinking about your own personal chances and what your behavior should be?
If you imagine you’ve got a reproduction number of two, each person’s infecting two others, on average. But some situations are more likely to spread infection than others. We’ve found for things like Covid-19, it’s close-knit interactions that seem to be most important.If you imagine you’ve got a reproduction number of two, each person’s infecting two others, on average. But some situations are more likely to spread infection than others. We’ve found for things like Covid-19, it’s close-knit interactions that seem to be most important.
What we need to think about — and what a lot of our modeling is certainly thinking about — is not just how much transmission is happening, but where is that transmission happening. If you’re going to change your behavior, think how to reduce those risky situations as much as possible.What we need to think about — and what a lot of our modeling is certainly thinking about — is not just how much transmission is happening, but where is that transmission happening. If you’re going to change your behavior, think how to reduce those risky situations as much as possible.
If you were the average person, what would you pay attention to — in terms of the news and the numbers?If you were the average person, what would you pay attention to — in terms of the news and the numbers?
One signal to watch out for is if the first case in an area is a death or a severe case, because that suggests you had a lot of community transmission already. As a back of the envelope calculation, suppose the fatality rate for cases is about 1 percent, which is plausible. If you’ve got a death, then that person probably became ill about three weeks ago. That means you probably had about 100 cases three weeks ago, in reality. In that subsequent three weeks, that number could well have doubled, then doubled, then doubled again. So you’re currently looking at 500 cases, maybe a thousand cases.One signal to watch out for is if the first case in an area is a death or a severe case, because that suggests you had a lot of community transmission already. As a back of the envelope calculation, suppose the fatality rate for cases is about 1 percent, which is plausible. If you’ve got a death, then that person probably became ill about three weeks ago. That means you probably had about 100 cases three weeks ago, in reality. In that subsequent three weeks, that number could well have doubled, then doubled, then doubled again. So you’re currently looking at 500 cases, maybe a thousand cases.
I think the other thing that people do need to pay attention to is the risk of severe disease and fatality, particularly in older groups, in the over-70s, over-80s. Over all we’re seeing maybe 1 percent of symptomatic cases are fatal across all ages. There’s still some uncertainty on that, but what’s also important is that 1 percent isn’t evenly distributed. In younger groups, we’re talking perhaps 0.1 percent, which means that when you get into the older groups, you’re potentially talking about 5 percent, 10 percent of cases being fatal.I think the other thing that people do need to pay attention to is the risk of severe disease and fatality, particularly in older groups, in the over-70s, over-80s. Over all we’re seeing maybe 1 percent of symptomatic cases are fatal across all ages. There’s still some uncertainty on that, but what’s also important is that 1 percent isn’t evenly distributed. In younger groups, we’re talking perhaps 0.1 percent, which means that when you get into the older groups, you’re potentially talking about 5 percent, 10 percent of cases being fatal.
In thinking about social behavior and thinking about your interactions, the question should be, “How do we stop transmission getting into those groups where the impact could be really severe?”In thinking about social behavior and thinking about your interactions, the question should be, “How do we stop transmission getting into those groups where the impact could be really severe?”