Don’t “Flatten the Curve,” squash it!

You have all seen a version of this curve of COVID-19 case loads by now:

Or this one:

Or this, which made it even into the New York Times:

Or this:

There are many more. What all these diagrams have in common:

  1. They have no numbers on the axes. They don’t give you an idea how many cases it takes to overwhelm the medical system, and over how many days the epidemic will play out.

The Curve Is a Lie

These suggestions are dangerously wrong, and if implemented, will lead to incredible suffering and hardship. Let’s try to understand this by putting some numbers on the axes.

What is the capacity of the healthcare system?

This is a difficult question and cannot be answered in a short post like this. The US has about 924,100 hospital beds (2.8 per 1000 people). California has only 1.8. Countries like Germany have 8. South Korea has 12. (Their hospital system got overloaded nonetheless.) Most of these beds are in use, but we can create more, using improvisation (for instance using hotels and school gyms) and strategic resources of the military, national guard and other organizations.

Based on Chinese data, we can estimate that about 20% of COVID-19 cases are severe and require hospitalization. However, many severe cases will survive if they can be adequately provided for at home (which may include oxygen, IVs and isolation).

More important is the number of ICU beds, which by some estimates can be stretched to about a 100,000, and of which about 30,000 may be available. About 5% of all COVID-19 cases need intensive care, and without it, all of them will die. We can also increase the number of ICU beds somewhat, but the equipment that we need to deal with sepsis, kidney, liver and heart failure, severe pneumonia etc. cannot be stretched arbitrarily between them.

An important part of the equation are ventilators. Most of the critically ill COVID-19 cases die of an infection of the lungs that makes it impossible to breathe and even destroys so much tissue that the blood can no longer be sufficiently oxygenated. These patients need intubation and/or mechanical ventilation to give them a chance of survival, or even an ECMO machine, which oxygenates the blood directly. About 6% of all cases need a ventilator, and if hospitals put all existing ventilators to use, we have 160,000 of them. In addition, the CDC has a strategic stockpile of 8900 ventilators that can be deployed in hospitals that need them.

If we take the number of ventilators as a proximate limit on the medical resources, it means we can take care of up to 170,000 critically ill patients at the same time. (Not all patients in intensive care will need ventilation, and not all patients needing ventilation will be in intensive care, but there is a large overlap, and both groups will die without intervention.)

How many people will get infected?

Without containment, the virus becomes endemic, and leading epidemiologists like Marc Lipsitch (Harvard) and virologist Christian Drosten (Charité Berlin) estimate that between 40% and 70% of the population get infected until we develop some degree of herd immunity. (Unfortunately, we do not know how long this immunity lasts. We already observe multiple strains of COVID-19, and will see many more, due to the large number of carriers.) In a population like the US (327 million), that means between 130 million and 230 million. Let’s assume that 55% of the US population (the middle ground) get infected between March and December, and we are looking at 180 million people.

What about undetected mild and asymptomatic cases?

In the early days of the infection, many outside observers were highly skeptical of the Chinese numbers, and thought that they might hide magnitudes of undetected mild and asymptomatic cases, which means that the mortality is much lower than reported. The WHO delegation to China, led by Bruce Aylward, found this not to be the case. Aylward maintains that once enough resources were available, the Chinese testing was very thorough and only a fraction of infected cases have been missed. (Even mild and asymptomatic cases of COVID-19 are infectious, so they matter.)

How many people will get critically ill?

Of the 180 million, 80% will be regarded as “mild” cases. Some of them will have no symptoms at all, many will come down with a flu like disease that lasts for two weeks, and which may include pneumonia, but they will get better on their own, usually within 2–3 weeks. About 20% will develop a severe case and need medical support to survive. Severe cases tend to take about 3–6 weeks to recover. And about 6% may need intubation and/or ventilation, because they can no longer breathe on their own. Most of the difference in death rates between Wuhan (5.8%) and the rest of China (0.4% to 0.7%) stems from the difference in ability to provide care for the critical cases. (Update March 17th, 2020: The numbers for hospitalization rate and intensive care rate are taken from an early Chinese report. In Italy, the ICU rate is currently at 16%, but most mild cases are probably still undetected. Since the Diamond Princess Cruise ship data show that half of all infected cases remained asymptomatic, a better estimate of the hospitalization rate may be 10%, with the number of patients requiring intensive care 2%-3%. However, the real case fatality rates of the coronavirus are still in dispute at this point.)

Once a person is on the ventilator, it often takes about 4 weeks for them to get out of intensive care again. That’s a very slow turnaround! If we set this as our estimate, we can calculate how many people are simultaneously in need of medical resources.

The Curve with numbers

If we assume that 55% of Americans catch COVID-19 until the end of 2020, and 6% (10.8 million) of them will need ventilators at some point, and we furthermore simplify the model into a normal distribution (a symmetric bell curve with a steep exponential onset, a gradual flattening once most people are infected or immune, and a gradual falloff as cases resolve), we get the following diagram:

The brown line near the bottom: that’s our limited supply of ventilators and intensive care beds! The red curve does not contain all cases of COVID-19, but only those 6% that will die if we cannot put them on a ventilator for something like four weeks. In this scenario, it means that the maximum number of cases needing care on the same day, without any kind of mitigation, is around 3 million! It’s clear that we need to desperately flatten this curve, because it means that for much of the year, the vast majority of cases will not even get assessed for intubation and critical care.

How far would we need to spread a normal distribution to make sure that it fits below the limit of our medical resources?

The “flattening the curve” idea suggests that if we wash our hands and stay at home while being sick aggressively enough, we won’t have to stop the virus from becoming endemic and infecting 40% to 70% of all people, but we can slow the spread of the infection so much that out medical system can deal with the case load. This is how our normally distributed curve looks like when it contains 10.8 million patients, of which no more than 170,000 are ill at the same time:

Dampening the infection rate of COVID-19 to a level that is compatible with our medical system means that we would have to spread the epidemic over more than a decade! (Far to the left, you see our unmitigated distribution for comparison.) I am pretty confident that we will have found effective treatments until then, but you get the idea: reducing the infectivity of the new corona virus to a manageable level is simply not going to be possible by mitigation, it will require containment.

My curves are not correct!

My back-of-the-envelope calculation is not a proper simulation, or a good model of what’s going on either. Don’t cite it as such! In reality, the spread of a disease does not follow a normal distribution. The main bump of the curve will be on the left, with a long tail on the right. There is always going to be some effective mitigation (prevention of public gatherings, conferences, non-essential travel). The model is quite sensitive to the length of the stay in the ICU. If we get that down, fewer people will need these resources simultaneously, and the peaks of the curves will come down. We may be able to fight the inflammation during pneumonia, and reduce the number of critical cases. The available medical resources will increase over time to deal with the need. Regulations will be dropped, new treatments will be explored, and some of them will work. At some point in the near future, we may have to blow into a tube before we enter an airplane or an important public building, and a little screen tells us within seconds if our airways hold COVID-19, H1N1 or the common flu. But the point of my argument is not that we are doomed, or that 6% of our population has to die, but that we must understand that containment is unavoidable, and should not be postponed, because later containment is going to be less effective and more expensive, and leads to additional deaths.

Containment works

China has demonstrated to us that containment works: the complete lockdown of Wuhan did not lead to starvation or riots, and it has allowed the country to prevent the spread of large number of cases into other regions. This made it possible to focus more medical resources on the region that needed it most (for instance, by sending more than 10000 extra doctors to Wuhan and the Hubei region). Wuhan, the epicenter of the outbreak, now observes less than 10 cases per day. The rest of the Hubei region registered no new cases for over a week now. It is possible to stop the virus!

China has learned its lesson: after the lockdown of Hubei, other regions implemented effective containment measures as soon as the first cases emerged. The same happened in Singapore and Taiwan. South Korea was tracking its first 30 cases very well, until patient 31 infected over 1000 others on a church congregation.

For some reason, Western countries refused to learn the lesson. The virus spread in Italy, until their hospitals collapsed under the load. According to reports from the crisis region, resources became so scarce that older people or those with a history of cancer, organ transplants or diabetes were excluded from access to critical care. The US, UK and Germany are not yet at this point: they try to “flatten the curve” by implementing ineffective or half hearted measures that are only meant to slow down the spread of the disease, instead of containing it.

There will be some countries that do not have the necessary infrastructure to implement severe containment measures, which include widespread testing, quarantines, movement restrictions, travel restrictions, work restrictions, supply chain reorganization, school closures, childcare for people working in critical professions, production and distribution of protective equipment and medical supplies. This means that some countries will stomp out the virus and others will not. In a few months from now, the world will turn into red zones and green zones, and almost all travel from red zones into green zones will come to a halt, until an effective treatment for COVID-19 is found.

Flattening the curve is not an option for the United States, for the UK or Germany. Don’t tell your friends to flatten the curve. Let’s start containment and stop the curve.

Update (March 17th, 2020):

A lot has happened since I wrote this post. Lots of people have sent comments, criticism and encouragement. I am especially grateful to my friend Nicholas Della Penna, to Professor Michael Lin from Stanford, to André Miede for a German translation, to Djalel Chefrour, who did a translation into Arabic, to Nima Behravan for a Farsi translation, and to Sean Scherer for organizing communication efforts.

Alison Hill has build a wonderful online simulator app that lets you try different scenarios and plug in different numbers.

Alison Hill’s Interactive Simulation

The Imperial College in London has released a study that is (unlike by back-of-the-envelope calculation above) based on proper simulations. It uses higher numbers for the infection rate than my best guess, and somewhat lower numbers for hospitalization, average length of ICU stay and fatality rates, and arrives at the same conclusion: the number of cases during the peak of the infection exceeds the available medical resources not by a small factor, but by a magnitude. That is also the case if we mild mitigation measures. To have a real effect, we need to drastically reduce the number of cases, using lockdowns of affected regions.

Mitigation strategy scenarios for GB showing critical care (ICU) bed requirements. (Ferguson et al.: Impact of non-pharmaceutical interventions (NPIs) to reduce COVID19 mortality and healthcare demand)

In response to this study, a review by Chen Shen, Nassim Nicholas Taleb and Yaneer Bar-Yam points out that this does not mean that we only have a choice between perpetual intervals of lockdowns and continued spread of the disease in the intervals, until we develop an effective vaccine or course of treatment. China has demonstrated that a combination of lockdowns, door-to-door testing and contact tracing can fully eradicate the virus.



Artificial Intelligence, Cognitive Architectures, Computationalism, occasional consumption of caffeinated beverages

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Joscha Bach

Artificial Intelligence, Cognitive Architectures, Computationalism, occasional consumption of caffeinated beverages