Sunday, March 15, 2020

Wrapping Your Head Around the Coronavirus Epidemic

I wrote this because I needed a compendium of information I could share quickly with everyone I know, and I realized that it might be of wider use.  Please share it with those you think are not taking the coronavirus epidemic seriously or who may still not understand the importance of social distancing.  If you find errors in this article, or if important information is missing, please alert me and I will make corrections.

Update on 03/17/20: I have made a few corrections, brought some information up to date, and noted a few new developments.  Thanks go to Professor William Johnston of Wesleyan University and Professor Lyle Ungar of The University of Pennsylvania for their helpful comments.  Remaining errors of fact or emphasis are my own.


The barrage of information surrounding the coronavirus outbreak is bewildering, and as the number of infected individuals increases, so will the information assault.  What is it truly important to understand?  The goal of this post is to walk you through some vital information; feel free to browse.  If you find the information consolidated here useful, please share it with others.  The future course of the disease depends on actions taken right now.

Much of the information in this article comes from a superb blog post by Tomas Pueyo entitled "Coronavirus: Why You Must Act Now".  That article goes into greater depth than this one, and it has been updated repeatedly.   I strongly encourage you to read it.  In fact, if you consider yourself already well informed, skip the present article and click on the link right away.  It has already had tens of millions of views.

Most of us have no experience weathering an epidemic.  When so little is happening, it is hard to take drastic action.  But it is action taken now, when the need to do so is not obvious, that will make the greatest difference once the need becomes clear.

This article is written so that it may be skimmed or browsed.  Skip ahead to the recommendations if you wish and start there.

What is the coronavirus?

Most are aware that the coronavirus - officially named SARS-CoV-2 - emerged in China in December, in Hubei province.  SARS-Cov-2 belongs to a group of viruses named after their crown-like shape; some cause minor infections such as colds.  Others have been responsible for very bad illnesses, such as SARS (Severe Acute Respiratory Syndrome, also know as SARS-CoV) and MERS (Middle East Respiratory Syndrome, MERS-CoV), which were contained through prompt, concerted action.  The novel coronavirus causes a disease, named COVID-19 by the World Health Organization (WHO), that has caused outbreaks worldwide, first in China and then all over the world, most virulently in South Korea, Italy and Iran.  Last week, the WHO declared that the worldwide outbreaks constituted a pandemic.  That means that it's pretty much everywhere now.

If it's everywhere, why don't we see it?

As the graphic below makes clear, the virus circulated for weeks in Hubei province before action was taken.  During that time, infected individuals - many of whom had no symptoms - spread the virus widely (grey-green bars).  By the time a few cases have been identified (yellow bars) in a given jurisdiction, there are many undiagnosed cases, each of them communicating the disease to others.
detail from infographic in "Coronavirus: Why You Must Act Now", by Tomas Pueyo
We are in the early stages of the explosive stage of the epidemic in the U.S. right now.  If the experience of Hubei province is a guide, there are probably tens of thousands of domestic infections that have yet to be diagnosed.  In Connecticut, there are likely hundreds of cases.

There is a hopeful message in the graphic above: as soon as drastic action was taken, the number of new infections ceased to climb.  The number of reported cases continued to increase, but it too peaked after two weeks.  The impact of the drastic actions being taken now should become apparent by the end of next week.

What does it do?

In about 80% of cases, symptoms are mild to moderate.  Mild cases include flu-like symptoms: fever, respiratory symptoms, aches and pains, and a dry cough.  Most of these cases resolve with rest and do not require medical intervention.  Moderate cases involve fever above 100.4 F, chills, and lack of energy -- like a bad case of the flu.  They also involve shortness of breath.  Some mild-to-moderate cases will result in mild pneumonia, which can still clear up without medical intervention.  But in older individuals and those with underlying conditions, this needs supportive treatment.  Dehydration is also a risk, again requiring supportive treatment in severe cases.  Cases that are mild to moderate in severity clear up in approximately two weeks.  There are apparently cases in which the patient, though able to communicate the disease to others, does not have strong enough symptoms to feel sick at all.

About 14% of cases are severe, requiring medical intervention to support breathing, typically in the form of supplemental oxygen.

Some 6% of cases become critical.  Organ failure is possible, or a form of pneumonia that results in lung damage, either by the virus itself or by a massive immune response to the infection ("cytokine storm").  It is these cases that most commonly lead to death, and survival for most will depend upon access to advanced health care.

The actual death rate is lower than 6%, largely due to medical interventions that prevent systemic collapse while the individual fights the illness.  It has varied from about 0.5% in well-prepared jurisdictions in which everyone who needs it can get treatment, to about 4% where the health care system is unable to meet the demand for treatment.

So about 20% of cases require medical attention.  It is important to recognize that in a massive outbreak, 20% of a large number is a large number.  It is in this way that the health care system in Hubei province, and now in Lombardy, Italy, became overwhelmed.

Whom does it target?

Everyone can catch the disease.  The death rate among children is low, though no age group is truly safe from serious illness.  The death rate is high among seniors, however.  The graph below from Business Insider compares the mortality rates within different age groups to the seasonal influenza.

from; data from CDC and Korean CDC.
Takeaways include:
  • The mortality rate rises with age; it is 8% for those aged 70 and older and 15% for those 80 and older.
  • COVID-19 is far more dangerous than the seasonal flu, about twenty times more dangerous.  This is why it must be taken seriously.  And bear in mind that the mortality rates shown above are for South Korea, a nation that has dealt with the epidemic effectively.

Is this epidemic unprecedented?

No.  One hundred years ago, the "Spanish Flu" infected more than a quarter of the world's population, with a mortality rate estimated between 1% and 5%, leaving between 17 million and 100 million dead worldwide.  Fatalities included the President of Brazil.  It was called "Spanish Flu" only because the media in other countries suppressed news of the disease, making Spain look particularly hard hit.  Robust young GIs on their way home from World War I were decimated.

emergency hospital at Camp Funston at Fort Riley, KS (from

We can learn something important from the 1918 influenza pandemic.  Two cities treated the outbreak differently.  Philadelphia experienced its first victims on 17 September, but did not initiate efforts to suppress the disease until 3 October.  By that time, a parade honoring the end of the war had occurred, resulting in the infection of many.  The death rate in Philadelphia spiked in mid-October.

By contrast, St. Louis experienced its first case on 5 October and took steps on 7 October.  As the graph below shows, there was no sharp spike in mortality the way there was in Philadelphia.

From The Microbial Menagerie,

It must be said that Philadelphia's outbreak commenced earlier, and so St. Louis had a few more days to observe and learn from the situation.  That said, we have numerous "Philadelphias" to inform us about the current disease outbreak.  There is no excuse for not being a "St. Louis" at the present time.

How bad will it be here?

It is unknown how hard Middletown, the state of Connecticut, and the United States in general will be hit.  Working against us is the criminally negligent posture adopted initially by the federal government, wasting precious time to help citizens and states prepare.  Working for us could be the viral spread of information about how to take sensible steps to protect ourselves and others; that is why Pueyo and I wrote these articles.  Here is what will determine how bad things will be.

Each infected person can infect others.  If the average number of others is less than one, the disease outbreak declines exponentially.  If the number of others is greater than one, the outbreak grows exponentially.  Individuals infected with SARS-CoV-2 appear to infect an additional 2.2 victims on average, resulting in explosive exponential growth.

Few understand the extraordinary power of the exponential function and its "gradually and then all at once" nature.  For the present purposes, note that if everyone infects two others, the infection progression starting with "patient zero" is 1-2 4-8-16-32-64-128-256-512-1024...  This is the way videos go viral, and there is a good reason this name was chosen.  It is the mathematics behind pyramid scams, compound interest, chain reactions, population explosions and other explosions, and a host of other processes.

By taking steps that lower the rate of infection, the exponential rise in the number of infections can be "flattened", as shown below.  For this reason, effective public health measures are said to "flatten the curve".

The New York Times published an interactive tool in an article entitled "How Much Worse the Coronavirus Could Get, in Charts".   You can use it to experiment with different scenarios to see how important early intervention is.  The model they use is crude, but it gets the point across: early dramatic intervention saves many lives.  Those complaining about the disappointment of athletic competition being canceled should be helped to understand that it is during the nearly invisible stage of the disease that we will make the biggest gains in terms of human life.  It is all about compounding, in the same way that early deposits in one's retirement account have a much greater impact at retirement time than later deposits.

Schools can serve as incubators of infection, and children, who are not strongly at risk, can nevertheless serve as vectors, bringing home the disease and sharing it with more vulnerable groups such as parents and grandparents.  It is for this reason that the City of Middletown was wise to close its schools.  The disruption to education is potentially severe.  And there are children whose lives are organized by school -- indeed, whose prospect for a nutritious meal depends upon school.  Our municipal leaders need to give thought to how these unwanted effects can be mitigated.  But we owe them our thanks for acting when they did.

According to a presentation at Stanford Medical School by Michal Tal, we can expect the number of cases to double every 7-10 days in the U.S., ultimately resulting in 96 million cases of COVID-19 and 480,000 deaths.  This would make it more than ten times more deadly than a bad flu season (such as the current one, which has resulted in 22,000-55,000 deaths nationwide so far, according to the Centers for Disease Control and Prevention).  In fact, the number of cases has recently been doubling every 3-4 days.

There are now nearly 5000 cases diagnosed in the United States (as of 17 March).  With a doubling time of a several days, we can expect a million cases before May.  This is a recipe for overwhelmed hospitals and inadequate care, as the recent experiences of China and Italy demonstrate.  See "The Extraordinary Decisions Facing Italian Doctors" for the grim details, if you need persuading.
triage section of a hospital in Lombardy, Italy (from an article in Atlantic)
And the number of actual infections (as opposed to diagnosed cases) is much larger, as I have pointed out already.  Pueyo's article walks the reader through an estimate of the infection-to-deaths ratio during the early stages of the disease.  It is about 800:1.  With close to 100 deaths nationwide so far (as of 17 March), this translates to 80,000 active infections at the present time, most of them undiagnosed.

Unfortunately, there are fewer than three hospital beds per 1000 individuals in the United States, fewer than in Italy, and four times fewer than in Japan or South Korea.  And about two thirds of those are already occupied at any given time.  This makes a strong case for slowing the infection rate to make it more manageable.

What can be done?

Reducing the transmission rate through all available means is what societies must try to do, the pronouncements of some ill-informed national leaders notwithstanding.  Containment is the first line of defense: identify, trace, and isolate every case in an effort to prevent the spread of the disease.  The era of containment has come to an end in the U.S., and mitigation is now the order of the day: slow the transmission rate to the extent possible.  This consists of travel bans, containment zones, quarantines, and changes in personal behavior.  Precious time has been lost in the U.S., and some options are no longer on the table.  Travel bans are useful when the arrival of even a few diseased individuals means a significant increase in disease transmission.  Now that the virus is being transmitted between individuals within the U.S., the value of international travel bans is lower, as shown in detail in the article linked at the beginning of this post.

Internal restrictions are the next line of defense.  Once the city of Wuhan halted travel, the cycle of infection was dramatically reduced.  New cases developed, making it hard to be sure, but within a couple weeks the situation began to improve.  Containment zones are a burden on the citizenry; just ask someone within the New Rochelle containment zone.  But they are an essential component to slow the spread of the virus once it has taken hold.  New Jersey has instituted a "soft curfew", and similar actions are beginning to snowball in other jurisdictions.

These actions are examples of social distancing - minimizing infection by minimizing interpersonal contact.  No one knows who carries the virus and who doesn't, so the only sure-fire way to prevent infection is isolation.  Every individual can also practice social distancing to reduce their personal risk and contribute to lowering the risk of everyone else.

It is likely that social distancing will not dramatically reduce the proportion of Americans ultimately infected.  What it can do is two things:
  • "flatten the curve": slow the rate at which infection occurs so that the number of very ill individuals at any one time is no greater than our hospitals can accommodate;
  • by delaying infection, buy time for the development of a vaccine, which could confer protection on those who have not yet been infected.  Vaccines ordinarily take years to develop.  The timeline of a year to eighteen months being discussed in the media is optimistic and will require an unprecedented approach.
The animation below shows the result of social distancing: the "curve" of infection is "flattened", resulting in fewer infections at the same time and (ideally) keeping the total number of serious cases to within what the hospitals can handle.

infographic by Alexander Radtke,

Nations that have "flattened the curve" include Hong Kong, Singapore, and Taiwan.  Each of them is small and can protect itself more easily; moreover, each of them experienced the SARS epidemic in 2003 and learned from it.  Individual provinces in China outside the main outbreak zones have also flattened the curve.  As China returns to work, the infection rate will likely rise again.

Everyone should read the article "Why outbreaks like coronavirus spread exponentially, and how to 'flatten the curve'" in the 15 March Washington Post.  The simulations it contains illustrate the value of extensive social distancing and show how dramatically it can slow the spread of disease.

The urgency of action is illustrated by the similarity between the disease trajectory in the United States and that in jurisdictions such as China and Italy:
Cumulative COVID-19 cases in a number of nations (from The Financial Times)
In an article released on 16 March by the Imperial College COVID-19 Response Team, the U.S. epidemic is predicted to peak in late June and result in 2.2 million deaths - far more than the Michal Tal prediction, and enough to get the attention of U.S. leadership.

It is simply a reality that many will die.  It is also true that a sufficiently draconian remedy to prevent any transmission -- quarantining everyone for weeks -- is out of the question; many would die in this scenario as well.  Public health officials are attempting to balance these realities to minimize mortality.  Significant, perhaps crippling economic impacts are inevitable.  The pandemic will be a particular challenge in nations that have attempted to dismantle critical parts of their bureaucratic infrastructure, perhaps in the belief that private action always outperforms concerted government action.

What should we do?

We as individuals have a number of things we can and must do:

  • WASH YOUR HANDS.  Clean hands protect you and those around you -- a win-win.
  • Stop touching your face.  This is harder than washing your hands, but it is a part of the hygiene that can reduce the rate of transmission.  My graduate student Jake has invented "scorpion pepper hand sanitizer", with the idea that once your touch your eye after using this product, you will stop doing it forever.  I don't think the product will become available in time to do us any good, so you'll have to try another method.  If you have a catcher's or goalie's mask, try wearing it.  (I am joking here, but if it works for you, it is worth considering.)
  • Practice social distancing to the extent you possibly can.  This involves avoiding public events of all sorts, and in fact minimizing human contact.  At its logical extreme, it becomes solitary confinement, which is a recipe for insanity.  So each of us will have to ride the line that preserves our sanity while minimizing our chance of spreading the disease or having it communicated to us.
  • Stay home if you feel unwell.  Now is not the time to be a hero by showing up even though you feel like death warmed over.  Now is the time to be a hero by not showing up, even though your fever is mild and you could probably soldier on.  See this Washington Post editorial, "You are the hero we are waiting for".
  • Share information on what must be done and why.  Just as a few anti-vaxxers can hitch a free ride on the "herd immunity" of a mostly-vaccinated group, a few careless individuals will not lead to greater disease spread if the rest of us are using safe practices.  But the number that can be supported is small.  That means that we need to get as many as possible to practice extensive social distancing, right now.
  • Understand that the closings of schools, libraries, and other public meeting places are an important step in flattening the curve.  Support the efforts of your beleaguered (and soon-to-be-overwhelmed) public officials and encourage stronger, not weaker, action.  Don't expect Middletown's schools to reopen in two weeks.
  • Tend to the emotional needs of yourself and those you live with.  This will last months.  We cannot afford to exhaust our stores of resilience in the early stages of the epidemic.
These measures are optional, when viewed from a personal point of view: protecting oneself is always an individual choice.  But when viewed from the point of view of society, these measures don't seem so optional.  Who am I to put others at risk, especially those for whom a negative outcome is more likely than it is for me?

Social distancing is what we as individuals can do.  Flattening the curve is why we do it - to keep the disease from spiking in such as way as to overwhelm the health care system.  We do it to save lives.  Government forces us to do some social distancing by closing schools, canceling public meetings, and regulating what remains.  The rest is up to us.  Remember that if the number of people infected on average by each individual is less than one, the epidemic dies away.  And remember that we are doing this for ourselves, yes, but even more so for those at greater risk than ourselves.  As Tomas Pueyo put it, "This is probably the one time in the last decade the sharing an article might save lives.  They need to understand this to avert a catastrophe.  The moment to act is now."
Handwashing explained (from an article at


Tree Fanatic said...

Bravo, Brian -- Very useful to have all that data in one place. Thank you.

Elisabeth Holder said...

I have been keeping track of Corona virus cases in Connecticut since last Friday. Here is the data: Friday 6, Saturday 12, Sunday 20, Monday 41. Note that we are close to doubling the number of cases every day, which would be an extremely fast rate. Most Western Countries are in the 2 -5 day range. However, we have so little testing that these numbers reflect more about our testing than about the course of the disease itself.

While the Connecticut Department of Health has been trying to follow up on every possible case, as of this morning (March 17th), there is still no local testing in Middlesex County. We should be aware that the exceedingly rapid rise in cases likely reflects the very large number of hidden cases that are all around us. We won't truly know what's going on until there is widespread testing. Here is the classic case of understanding that the absence of information is not information about absence.

Please take all the precautions that are being widely publicized. Get your information from reputable sources. I have already received one email that is full of erroneous information. Support your family and friends by communicating via phone and email. Donate to organizations on the front lines of this crisis. Let's be a modern-day St. Louis and a compassionate community.

Ana Perez-Girones said...

Thanks so much, Brian.
Because all my family is in Spain, I follow their news as much as ours here. It's scary and it's coming. Please, if you can stay home, don't leave home. Not just so you stay healthy--so that people who cannot get sick won't. Think of your parents, grandparents, younger people with health issues. There won't be enough hospital care for them. And remember to appreciate our health care providers--there are going to be many heroes among them.

Michael Harris said...

Great article. Thank you.

Kathleen White said...

Thanks, Brian, for this and for the links to the Pueyo articles. Everyone needs to read them.