March 11, 2020

# What’s the Risk of Death from Corona-virus?

I’m writing this because I have heard many people say something along the lines of:

“Many more people died from the Common Flu last year in the United States than have died the Coronavirus, so the Coronavirus is a much smaller risk than Common Flu.”

In this article I’m going to explain why I think this viewpoint greatly under-estimates the risk of the Coronavirus and give some ideas for other ways to interpret the available information.

If you believe the risk of the Coronavirus is low because you have heard that the total number of deaths from the Coronavirus is lower than the number of deaths from the Common Flu each year in the United States (or any particular country), I would highly encourage you to read this article.

This article also provides guidelines for comparing risk of death from the Corona virus and also applies to other comparisons of risk, such as the risk of riding a roller coaster compared going to the beach, or flying in an airplane (or helicopter) compared to driving.

# Total Death Data

The numbers are changing rapidly, and also depend on which country we are talking about, on January 24 China had reported 41 deaths from the Coronavirus

On March 3rd, the United States reported 9 deaths from the Coronavirus, and as of March 10th 2020, the United States has reported deaths 30 from the Coronavirus.

By February 1st (of 2020), 304 people had died of the Coronavirus in China.

These are my sources:

In comparison, in the 2017–2018 Flu season, the CDC estimates that between 46,000 and 95,000 people died of the flu, and best estimate is 61,000 deaths.
So on February 9th or earlier, people would say things like “The Corona virus has killed under 1,000 people in China so, and in 2017–2018 over 50,000 people died of the flu in the United States, so the Coronavirus is a much smaller threat than the Common Flu that appears every year so we really don’t need to worry about the Coronavirus.”

I have heard several Medical Doctors and News Anchors make statements like these on national TV, so I believe many people heard something similar.

A Harvard Blog on the Coronavirus even mentioned that the flu kills more people than the Coronavirus without explicitly mentioning what I believe are the high risks involved with the Coronavirus.
https://www.health.harvard.edu/diseases-and-conditions/coronavirus-resource-center#q14
So it is a true statement that the number of people who have died so far in the United States and China of the Coronavirus is lower than the number of people who die of the Common Flue each year in each of these countries.

Keep in mind, the number of cases and deaths have been increasing rapidly, so the number of deaths keeps going up, so the specific figures are subject to change, but let’s consider the general argument that compares the total number of deaths that have occurred (Total Deaths) between the Coronavirus and the Common Flu as a basis for assessing the overall danger of the Coronavirus.

I have heard people make the same argument when comparing the risk of skydiving or riding a roller coaster (or another activity), and it goes something like this: more people die every year in the United States in car accidents than skydiving, (or riding a roller coaster) so skydiving (or another activity) is safer than driving.

However, I believe that that comparing Total Deaths that have occurred isn’t the best metric to use to assess relative risk, and I think Potential Total Deaths from the Coronavirus is a better metric. That is, I think we should care about the total number of people who could die from the Coronavirus (what I call Potential Total Deaths), and I will try to quantify this.

The Total Deaths from the Common Flu generally range from about 30,000 per year to 60,000 pear year.

From my perspective, here are things about the Coronavirus that make the Potential Total Deaths from the Coronavirus much higher than Potential Total Deaths for the Common Flu:

• Death Rate Is 10 Times Higher for the Coronavirus than for the Common Flu (for patients who receive adequate medical care)
• The Death Rate 50 Will Be Times Higher for Many Because there Is Limited Medical Capacity and Many People will Likely be Infected Very Quickly!
• Nearly Everyone Could Contract the Coronavirus Whereas Not Everyone Catches the Common Flu

All three of these facts make the Potential Total Deaths from to the Coronavirus much higher than the Potential Total Deaths from the Common Flu.

In fact, I estimate that Potential Total Deaths from the could be 100 times higher than the Deaths from the Common Flu in the 2017–2018 season.

I estimate that there will likely be over 9 Million Potential Total Deaths from the Coronavirus in the United States alone if there is a wide outbreak compared to 61,000 Deaths from the Common Flu in the 2017–2018 season. 9 Million people is more than the population of the state of Colorado, and more than the population of most US States.

These are potential deaths if no action is taken. Luckily, as of March 16th 2020, many US cities have taken measures that will reduce the spread of the virus-so this is not likely anymore. But these are the potential Deaths if no action was take — and they are much higher than annual Deaths form the Common Flu.

Here is some more detail on each of the above factors:

Death Rate Is 5 to10 Times Higher
The Death Rate for the Coronavirus is estimated to be 5 to 10 out of 1,000 (0.5% to 1%), or higher, for patients who receive necessary medical treatment very quickly compared to 1 out of 1000 for the Common Flu. Therefore, the Coronavirus has a Death Rate for treated patients 5 to 10 times higher than the Death Rate of the Common Cold. This alone could make Deaths from the Coronavirus 5 to 10 times as large as Deaths from the Common Flu.

The Death Rate Will Be About 50 Times Higher for Many
A significant portion of Coronavirus patients are have severe infections causing significant damage to their lungs which leads to difficulty breathing; these patients require significant amounts of medical attention (what we will call Intensive Care) and access to medical equipment like ventilators. However, medical care and ventilators are in limited supply. When Coronavirus patients don’t have access to the necessary treatment, the Death Rate increases dramatically, and reaches approximately 50 out of 1,000 for all Coronavirus patients (not just those with severe infections) compared to 1 out of 1,000 for the Common Flu. Therefore, Death Rates for the Coronavirus can be 50 times the Death Rate of the Common Flu.

Some sources Estimate that 5% — 10% of Coronavirus patients require Intensive Care.
Death Rate in the US is already estimated to be 4% to 5%. In Italy, the Death Rate is estimated to be 4%.

Highly Contagious, People Aren’t Immune, and no Vaccine:
Given that Coronavirus is very easy to spread, people aren’t immune to it, and there is no vaccine for the Coronavirus this will likely cause many people to get sick at once and overwhelm the medical system making the Death Rate higher for many people.

Nearly Everyone Could Contract the Coronavirus
Only about 30 Million to 40 Million people catch the Common Flu every year in the United States out of a population of about 330 Million. This is because some people are immune to the Flu and because there are vaccines, so the Common Flu does not infect all people who come into contact with people who are already infected. Therefore the people with immunity do not catch the Common Flu and do not infect other people. This is sometimes called Herd Immunity.

The same conditions that will make the Coronavirus spread quickly (easily spread, no immunity and no vaccine) will mean that most people in the United States are likely to contract the Coronavirus if significant measures aren’t take to reduce the spread. Some experts estimate that 50—70% of the population is likely to be infected which is 165 Million to 230 Million people which is much larger than the number infected by the Common Flu every year in the United States (30 Million to 40 Million) which means and the Death Rate will apply to more people leading to more Total Deaths from the Coronavirus. These factors (easily spread, no immunity and no vaccine) will increase the number of people who are sick at any given time, which will overload the medical system which increase the number of people for whom the higher Death Rate applies because they do not receive needed. medical treatment.

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#### Why Total Deaths that Have Occurred Isn’t the Best Metric for Measuring Risk of The Coronavirus (or Other Dangers)

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## Slowing the Spread Will Save Lives

New information is still coming in which will give us more accurate values for the elevate Rates (rates of Severe Infections requiring Intensive Care, and Death Rates), but it is important to understand the primary idea.

Given that a significant percentage of people infected with the Coronavirus will have Severe Infections that require Intensive Care, the limited capacity of hospitals and ventilators, and the higher Death Rate for people who don’t have access to medical treatment, slowing the spread will reduce the number of people who are sick at once, which will save lives — likely Millions of lives.

See the graph below for an illustration:

Slowing the spread of the virus will reduce the number of people who are sick at the same time (time is illustrated horizontally on this graph, with number of sick people indicated vertically).

Given that there is limited capacity for medical care and limited ventilators, when too many people are sick at the same time the overall Death Rate for the Coronavirus patients who don’t have access to treatment will likely increase from about 1% to about 5%.

In the graph above the area under the curve represents an amount of people.

The dotted line represents the limited medical capacity.

Everybody above the dotted line will have a higher Death Rate that those below the dotted line. Death Rates for those above the dotted line is likely 5% or higher compared to about 1% for those below the line. Thus, slowing the spread of the disease means a flatter curve in terms of the number of people who are sick at any given time, and increase the number of people who receive proper medical care, which will save Millions of lives. I believe it is likely that at least 5 Million people in the United States would be saved.

More detail on this later in the article.

## Comparing Total Deaths (that have occurred)

This section discuss what measuring Total Annual Deaths or Total Deaths that have occurred misses, and what other information I think should considered.

As of March 10th, 30 people have died in the United Stats from the Coronavirus, which is a small fraction of the approximately 40,000 people who died in the United States last year from the Common Flu. In fact, for the last 10 years, the CDC estimates that on average over 30,000 people died form the Common Flu in the United States.

Now determining an exact number of people who died form the Common Flu is difficult because it’s not always clear when a death is attributable to the flu, so the CDC gives a range of numbers.

As a comparable piece of data, over 39,400 people died in car accidents in the United States in 2018. The number of car accident deaths annually in the United States has been between 30,000 and 50,000 since 1982,

Now, when doing quantitive analysis it’s often useful to change the numbers or the values of parameters involved. To do this, let’s consider different activities what have different levels of banter (risk), and compare them to car accident deaths in the United States which were about 40,000 in 2018.

In 2018 there were 18 deaths of US soldiers in Afghanistan — does that mean it’s more dangerous to drive in the United States than to be deployed to Afghanistan?!

In 2019 one person died from jumping into the Grand Canyon— does that mean it’s more dangerous to drive in the United States than to jump into the Grand Canyon?!

If you judged danger by looking at Total Annual Deaths that have occurred in any given year, you would conclude that driving in the United States was more dangerous than jumping into the Grand Canyon, which is over 6,800 feet deep (over 2,000 meters for those on the metric system). That is, the Grand Canyon is over 1 mile deep (or over two kilometers deep).

Intuitively we know that jumping into the Grand Canyon and serving in a war zone are more dangerous than driving, so these examples should demonstrate that Total Annual Deaths isn’t the best metric to look at to compare risk.

Jumping into the Grand Canyon has a very high chance of death — let’s assume it’s 100% chance of death— so it’s very dangerous!

My main point is that looking at total deaths per year (Total Annual Deaths, or TAD) is not the best metric to compare the risk of different activities.

That is, when comparing the danger or risk of different activities, we shouldn’t look at the Total Annual Deaths, but look at the likelihood of death (or injury or other negative outcome) given that we engage in a certain behavior, or that certain things happen to us.

You will generally want to use the same sort of metric or comparable metrics for comparing the risk of two behaviors or events, and probably compare a ratio that consists of number of deaths (or injuries incurred) compared to the number of times you participate in an activity or the total amount of time spent doing an activity.

For example, jumping into the Grand Canyon would have a Fatality Rate 1 death per 1 jump, which can be expressed as the ratio “1 to 1” (abbreviated as 1:1), or 100% (100% of Jumps result in a Death).

### Ratios Review

This section gives a brief math review for those who don’t primary work in quantitive fields, or may not consider themselves “math people” — don’t worry, I’ll make it understandable, I promise!

When dealing with randomness, odds, and probability, it’s really important to have a clear definitions and an understanding of the basics of percentages, and terms like “likelihood” and “probability.”

To illustrate the concepts, let’s take the scenario where doctors perform heart surgery, and the patients either survive or die. Let’s say that the Death Rate is 20% for all surgeries. We’ll assume that this is a purely random process that is not affected by the health of the patient or other factors (such as how many hours the doctor worked that day which would affect fatigue).

A Death Rate of 20% means that for every 100 times the surgery is performed (Surgeries) 20 patients die, and the other 80 survive. Now, 20% is a Ratio: it is the Ratio of the total number of patients who die (Deaths), compared to the total number of times the Surgery is performed (Surgeries).

Let’s assume that each patient is only operated on once. Then the number of Surgeries is the number of Patients.

The Death Rate as a percentage is the Number of Deaths (Deaths) divided by the Number of Surgery Patients (Patients).

$\text{Death Rate}=\dfrac{\text{Deaths}}{\text{Patients}}=20\%=0.2$

As a percentage, the Death Rate is 20%; as a decimal the Data Rate is 0.2 (that’s 20% as a decimal). As a Ratio, it is 20 out of 100, which is 1 out of 5.

Note that the numbers in a Ratio can be multiplied (or divided) by the same number and the Ratio remains the same.

So 20 Deaths out of 100 Patients is the Death Rate expressed as a Ratio, which we can abbreviate by writing “20:100”.

Now this is a Ratio, so if we double the number of Patients, the number of Deaths should also Double. So we would expect 40 Deaths out of 200 Patients. We can also divide the number of Patients by two, which should also Divide the Number of Deaths by two, so we would expect 10 Deaths out of 50 Patients.

Multiplying or dividing both numbers in a Ratio by the same number will give us new numbers for a Ratio that I will call an Equivalent Ratio. So 20 out of 100; 40 out of 200 (multiplied by 2); and 10 out of 50 (divided by 2) are all Equivalent Ratios.

As another example, if we start with the Ratio 20 out of 100 if we multiply these numbers by 10, we get 200 out of 1,000 which is an Equivalent Ratio.

Starting with the Ratio 20 out of 100 Starting, dividing both the number of Deaths, and the Number of Patients by 20, gives the Equivalent Ratio 1 Death out of 5 Patients, which we can write as: “1 : 5” or “1 out of 5”.

If we operated on 10,000 patients, we would multiply the numbers in the Ratio 200 out of 1,000 by 10 to get 2,000 Deaths out of 10,000 Patients

To predict the number of Deaths for any given number of Patients we can multiply any of the Equivalent Ratios by the number needed to bring our number of patients to the desired level.

For example, if we want to know the number of Deaths if 20,000 surgeries are performed, we already determined that we would have 2,000 Deaths out of 10,000 Patients; and 20,000 is 2 times 10,000, so to determine (calculate) the number of Deaths, we would take 2,000 and multiply by 2, which is 4,000.

Note that we can multiply any of the Equivalent Ratios we already calculated by the appropriate number (what I’ll call a Multiplier) to determine the number of Deaths for a given number of Surgeries.

In the prior example, we multiplied 2,000 out of 10,000 by 2 to get 4,000 out of 20,000. We could also multiply the Equivalent Ratio of 20 out of 100 by 200 (200 is the Multiplier) to also get 4,000 out of 20,000. Clearly starting with the Ratio of 2,000 out of 10,000 is easier to do.

Using this method (the Multiplier Method) to calculate Equivalent Ratios requires being able to determine the appropriate Multiplier, which is done by comparing the values of the total Patients in question. That is, to get from 10,000 patients to 20,000 patients requires multiplying by 2.

Question: what is the number of deaths if there are a Million surgeries? Note that a Million is a Thousand times a Thousand.

Well, we can take our Ratio of 2,000 out of 10,000 and multiply by 100 to get 200,000 out of 1,000,000 our 200 Thousand out of one Million.

We can also predict the number of Deaths for a given number of Patients (Surgeries) by multiplying the Death Rate (as a decimal or fraction) by the Number of Patients.

If we want to predict the number of Deaths if we operated on 1,500 patients, we can multiply 1,500 by the Death Rate of 20% (which is 0.2 as a decimal) and the result is 300.

We can also use the Multiplier Method and multiply 200 out of 1,000 by 1.5 to get 300 out of 1,500.

When comparing Death Rates (or any Rates) it’s very useful to compare the number of Deaths (or number of different outcomes) for a fixed number of Patients as a reference value. In the United States, we often use the reference number of 100, and express various rates as a certain number per 100, which is how the word “Percentage” is defined, and which uses the symbol “ % ”.

For example if every year 3 out of every 100 people in the United States contract a disease, we would say that 3 percent or 3% of people contract the disease.

When the Death Rate is a number like 20% that is easy to multiply by, it is often easier to multiply the Death Rate by the number of patients. 20% is 2 for every 10, so the simplest way to multiply by 20% is to divide by 10, and then multiply the result by 2.

Now let’s say the Death Rate for lung surgery is 3.72%. How many Deaths would you expect for 30,000 patients? How about 300,000 patients?

Well, 4.72% is 4.72 out of 100. If we multiply these numbers by 100, we get:

472 out of 10,000

Now if we multiply these numbers by 3 we get:

1,416 out of 30,000

Now if we multiply this by 10 we get:

14,160 out of 300,000

My point is that when the Death Rate is a number with more digits like 4.72%, to calculate the number of Deaths for 300,000 patients, instead of multiply 300,000 by 4.72% (which we can do by dividing by 100 and multiplying by 4.72), we can simply multiply 1416 by 10, as we know we will have 1416 Deaths out of 30,00 surgeries, and multiplying this Ratio by 10 will bring us to 300,000 surgeries, which is why number of surgeries we want determine the Deaths for.

These same mathematical methods and techniques will help you calculate the number of Deaths from the Corona virus and potentially negative outcomes from other dangerous activities and environmental dangers.

An understanding or Ratios and percentages is essential when assessing risks of things like the Corona virus.

To compare Death Rates, since there were about 40,000 Deaths from car accidents in the United States in 2018 and a population of about 320 Million, that means the Death Rate from car accidents is about 1 in 8,000, or 125 in 1 Million.

The US had 13,000 soldiers in Afghanistan in 2018 and 18 deaths, so the Death Rate for soldiers in Afghanistan was 1.4 for every 1,000 soldiers or 1,400 for every Million. This is over ten times more dangerous per person than driving in the United States.

There were also about 40,000 Deaths from the Common Flu in 2018 so the overall Death Rate from the Common Flu for all persons in the United States (not just those infected) is similar to the Death Rate from Car accidents, at about 1 in 8,000.

The above assumed things were completely random, and not affected by the actions we take. That is, the Death Rate for a surgery wasn’t impacted by the health of the patient or the skill of doctor.

We also assumed a the Death Rate was a fixed ratio. If a surgery has a 20% Death Rate you expect 20 out of 100, or 1 in 5 patients to die. However, in reality, if the Death Rate is 20% (and it’s truly random) and you operate on 5 people, there is a chance that all 5 people survive which is  . When you are eagling with numbers in the tens of thousands the number of people who actually die will almost always be very close to the Death Rate times the number of Patients.

In practice, for the numbers involved with Coronavirus (thousands and millions of patients), the number of Deaths will be very close to the Death Rate times the number of Patients.

It’s also true that the Death Rate for the Coronavirus changes based on the amount of medical care that people receive.

So the Number of Deaths from something doesn’t really tell us much about the inherent danger or risk of that thing, whether it be an activity or a disease. People usually think about Risk as the likelihood of something bad happening.

As discussed, jumping into the Grand Canyon is very dangerous as we think you’ll die with 100% chance (100 out of 100 people who jump will die). Describing it as “Risky” isn’t even appropriate because you’ll die with 100% certainty (or near certainty).

Just because the number of people who die from jumping into the Grand Canyon is low does not mean that we can jump into he Grand Canyon and expect to live — as we discussed we think we’ll die with near 100% certainty.

So we should really look at the Death Rate for the Coronavirus, and how many people we think might contract the Coronavirus in the United States or around the World, which will then tell us the potential total number of people who could die from Corona-virus.

Looking at the total number of people who have died from Corona-virus and seeing that it is only a few hundred in the United States (or a few hundred in China as of a few months ago) doesn’t tell us much about the total number of people who could die and the overall risks involved.

Just like looking at the total number of people who have died from jumping into the Grand Canyon and seeing it was 1 person last year, doesn’t tell us much about the total number of people who could die if many people jumped or fell into the Grand Canyon. Given that the Death Rate of jumping into the Grand Canyon is high, if lots of people fell into the Grand Canyon, lots of people would die.

We therefore need to look at the overall Death Rates or Ratios for things like the Coronavirus  and other dangers and the number of people they might affect to determine the number of people who could die, which I think is the number we should really care about.

Note that we do need to define what values we are most interested in measuring and reducing. I think Total Deaths that are likely in a given country over a time period or for the out-break is the metric we should look to minimize. This is different than Total Deaths that have occurred. I will call the Total Deaths that are likely to occur the Total Potential Deaths.

## Many Coronavirus Patients Require Ventilators and Significant Medical Care

You may have heard that the Death Rates for Coronavirus are perhaps slightly higher than the Common Flu and so for healthy people there isn’t much to worry about.

I do not believe that this is accurate.

I think the most important thing to point out is that reports I have read indicate that the Death Rate increases substantially from about 1% for patients who have access to medical care (things like ventilators) to about 5% for those who do not have access to adequate proper medical care and medical equipment like ventilators.
https://www.weforum.org/agenda/2020/03/suddenly-the-er-is-collapsing-a-doctors-stark-warning-from-italys-coronavirus-epicentre/
These are my findings based on researching reports by Medical staff from Italy, where information is more freely available.

Coronavirus attaches and kills cells in the lungs. The immune response often further destroys lung tissue. The result is that a certain percentage of those infected require hospitalization, which we will call the Hospitalization Rate, and which some sources estimate around 14%.

Furthermore, a smaller set have very high large amounts of lung tissue destroyed which requires significant medical care and these patients often require ventilators to enable the patient to breathe. We will call situations where patients require ventilators “Severe” Cases.

Some experts estimate that 5% – 10% of infected Patients may be Severe Cases requiring ventilators. Again, these patients will have a much higher Death Rate if they don’t receive ventilators and significant medical care. We will call this rate the Severe Infection Rate (the proportion of those infected who require ventilators).

Note that other sources may have different definitions for the term “Severe” and may use “Critical” instead, or use both terms with “Severe” meaning they require hospitalization, and “Critical” meaning they require treatment in an Intensive Care Unit (Intensive Care).

The Severe Case Rate of 5% – 10% combined with the virus being extremely contagious means that the limited amount of Medical Care Capacity and ventilators is likely to be overwhelmed very quickly, which will increase the overall Death Rate.

For some data, a study estimates that the US has about 62,000 ventilators which are fully-featured and suitable or adults (and another 24,000 for respirators for children, infants, and premature babies). Given this, there are about 190 ventilators per Million adults.
https://www.ncbi.nlm.nih.gov/pubmed/21149215

Some sources predict that over half the US population is likely to contract the Coronavirus (viruses are really good at going viral), with some estimates going to 60% or 70% of the US Population is likely to catch the disease. If we take 50% of the population as a low estimate for the number of people infected with the Coronavirus and use 3% as the a Severe Infection Rate (the proportion of those infected who require ventilators) that becomes 15,000 Severe Infection per Million adults. This is calculated by taking 1 Million adults, estimating half will contract the disease which is 500,000 and then 3% of these will be Severe Infections, which is 15,000 per Million adults.

Now they won’t all be sick at the same time, but if this occurs over the next year, and people remain critical for 1 month, or even 2 weeks, you can see that the 190 ventilators per Million people will not be enough for everybody who needs it.

If there are 15,000 Critical Cases per Million persons in the United States in the next 12 months, this averages to 1,250 per month  . If people require Critical Care for 2 weeks, or half a month, this averages to half of 1,250, which is 625 people, per Million people who require ventilators at any given time, when there are only 190 ventilators per Million.

This is a very quick analysis showing a shortage of ventilators. Things would be worse in reality as ventilators are not easy to transport so there would be regional shortages when an outbreak occurs in a specific location. This analysis also uses a 3% Severe Case Rate, when the Severe Case Rate could actually be much higher.

Again, this is average. Because the number of cases grows quickly over time, we will certainly see dramatic spike in the number of Severe Infections at certain times which will mean that the number of people needing respirators at any time will be higher than 625 per Million persons, and the shortages will be higher. This again means Death Rates will be higher.

We won’t do complex quantitive analysis, but this graphic illustrates the point.

The idea is that if you can decrease the rate that the Coronavirus spreads, you can decrease the number of sick people (what they call Cases) at any given time, which will mean more people can be adequately cared for, and thus decrease the overall Death Rate.

Think of it like this: let’s say you have a food truck or food stand that is popular during the day. If people come at a rate of 5 people per minute, and it takes you a minute to serve each person, then pretty quickly you have a long wait for people to be served. If people leave if the line is longer than 20 minutes that represents lost customers. Perhaps you have 5 people coming per minute for one hour during lunch time, for a total of 300 people during lunch time.

If people leave when the line is longer than 20 minutes, my math says you will only serve 80 people. How can you serve more people if they won’t wait longer than 20 minutes, and you can’t serve them faster?

If you can get them come in over a 3-hour time period, rather than a 1-hour time period, you could serve 200 people, as opposed to 80 if they come in a one hour period. This assumes that people who are in line at the end of the 1 hour or three hour period will wait the additional 20 minutes to be served.

If you can slow down the spread of the virus, you can reduce the number of people who are sick at the peak time, which will increase the number of people who can receive proper medical attention, and therefore increase the Survival Rate for more people.

# Death Rates Compared

So now let’s look at the Death Rates of Corona-virus and the common flu.

The US CDC estimates that in the 2015–2016 flu season that 23,000 people died from the flu in the United States, and that there were 24 Million infections (Symptomatic Illnesses). This is a Death Rate of 1 out of 1,000 or 0.1% (0.1 out of 100).

The Death Rate varies by year, but we’ll use a Death Rate of 1 in 1,000 for the common flu as an average number. It is clearly difficult to determine exactly how many people die of the flu, because people who die often have other illnesses, and at the same time it is hard to determine the number of people who actually catch the flu each year.

Historical data is available here:

No let’s look at the Death Rate of the Coronavirus.

### Theory that Death Rates from the Coronavirus Are Lower than Reported

Before proceeding, I want to address this theory.

Just two weeks ago a university faculty member said that the Death Rates for Coronavirus in China was likely lower than actually reported.

To illustrate the concept, he said that if authorities in China determined that their are 1,000 people who have been infected and 20 people died (at one point in time) then the Death Rate is reported at 20 out of 1,000 which is 2%. These are meant to show a concept and do not represent the actual numbers.

However, he thought that there would be a large number of mild Infections that were not reported or detected but that existed; and these unreported Infections would several times the number of reported Infections.

Therefore, he thought more people than the reported 1,000 people were actually infected and that it was more likely that approximately like 4,000 people would actually be infected (rather than the 1,000 people reported). That is, the actual number of Infected was four times as high as the number of reported Infections.

We would still have 20 deaths, but out of 4,000 Infections rather than 1,000 Infections, so the Death Rate would be 20 out of 4,000 which is 5 out of 1,000 which is 0.5%, instead of the 2% that was reported.

As he said: “The Denominator is Likely Higher”

Even if this is true, this lower Death Rate of 0.5% is still 5 times the Death Rate for the Common Flu, which we estimate at 0.1%, and the the Coronavirus can infect 50% — 100% of the US population, rather than the 40 Million people who catch the Common Flu each year.

I don’t fully believe that the Death Rate from the the Coronavirus is lower than reported because I think that the likelihood that a large number of Coronavirus Cases go un-detected in the long run appears low, as most people do develop symptoms and appear to seek treatment or report their illnesses.

Furthermore, the Death Rate for the Coronavirus for people who don’t receive adequate treatment appears to be about 3% – 5%, and the Death Rate can be reduced to 1% or lower access to medical care and (which has capacity limits as discussed) and preparation to reduce the speed at which the virus spreads.

There are a lot of things that are unknown, but my analysis is based assuming that there are not a lot of un-reported Infections. Another goal of this article is to help people conduct their own analysis based on what they believe to be true.

# Viral Growth of a Virus

Let’s also discuss the rate at which the virus spreads, or the Growth Rate of the number of Infections. I’m going to walk through the calculations so that a broad audience can follow.

The Coronavirus is extremely contagious and can be spread just by being near people who are infected, and doesn’t require physical contact according to the latest research. Furthermore, people can carry the virus for several days or even weeks before showing symptoms; so many people don’t know they’re sick and spread the virus.

This means that a few people who interact with lots of people through their job (like an airport screener in LA, or somebody working in a retail store, or an usher) can become infected from a member of the public and then further infect many other people through their job, especially if they don’t wear protective gear.

If you don’t show symptoms, you can infect a lot of people before you isolate yourself.

Some reports estimate that the number of Coronavirus Infections doubles about ever 3 days in the United States. This seems reasonable for people who may be infected for two weeks before they realize it and take steps to isolate themselves. That is, if somebody is infected, they could easily infect one other person every three days.

We call the amount of time it takes for the number of Infections to double the Doubling Time, or the Doubling Period. Some people have estimated the Doubling Time in the United States to be 6 days.

I’ll walk through the implications of what will occur if Doubling Time is 3 days and if it is 6 days. If the number of Coronavirus Infections doubles (is multiplied by 2) every 3 days, what happens in 30 days?

Well, 30 days is  and if the number of Cases is multiplied by 2 in 3 days, then the number of Infections should be multiplied by   in 630 days. That is, if we have 1,000 Infections today, in 60 days we should have 20,000 Infections — right?

## Wrong!!

This is exponential growth remember.

If we have 1,000 Cases today (Day 0), in 3 days (Day 3) we have 2,000 Cases (Double the 1,000 starting number of Infections. Then in another 3 days (Day 6) we have 4,000 Cases (as  ). Then on Day 9 ( days later) we have 8,000 Cases.

To make the numbering easier let’s count the number of days in the future, so today is Day 0 (rather than Day 1).

Below is a table showing Infections by number the Days in the future starting with 1,000 Cases now (Day 0) and using Doubling Time of 3 days.

Doubling Time: 3 Days.

What this means is that after 30 days we have over 1 Million infections.

That is, in 30 days the number of Infections is multiplied by over 1000 (it is multiplied by 1024).

The Doubling Time is 3 Days, and we Double a total of 10 times.

$2^{10}=1,024$

So the number of Infections is multiple by 1,024 over 10 Doubling Periods, and we have over 1 Million Infections within 1 month. Remember, a Million is a Thousand times a Thousand (a Thousand Thousands).

A good thing to remember is that if somethings grows exponentially, that after 10 Doubling Periods, the final value will be more than 1,000 times the value at the beginning of these Doubling Periods (it will be 1,024 times the initial value).

To reiterate: after 10 Doubling Periods, the value at the end is 1024 times value at the beginning. The table below shows what happens after the first 30 days:

Within another month everybody in the United States would be Infected (the population of the United States is a bout 330 Million) if the number of Infections still double every 6 days (if the Doubling Time is still 6 days).

If you calculate new infections in any given period and estimate that 1% (which is a very low estimate) of new Infections are Severe and will require Ventilators for two weeks, then pretty quickly all the ventilators get used up.

Here’s the math

There are about 62,000 ventilators in the US which adults can use.

If 1% of Infections require ventilators, then 6.2 Million people can be infected in a two week period before the all ventilators are used. As 1% of 6.2 Million is 62,000 (mathematically 62,000 ÷ 1% = 6.2 Million). Dividing by 1% is equivalent to multiplying by 100. That is, if 1 in 100 Infections patents require a ventilator, the total number of infected people that can be handled with 62,000 ventilators is $62,000 \times 100 = 6.2 \text { Million}$.

If Infections Double every 3 days, the the number of new Infections in a 3 day period is equal to the number of Infections at the beginning of the period. That is, if the number of cases goes from 100 to 200 in a certain amount of time, the number of new Infections is equal to 100, which was or number of Cases at the beginning fo the period.

As you can see, the number of Infections reaches 6.2 Million between Day 30 and Day 45. So by Day 42 (in less than two months) if not earlier, all the ventilators in the entire country would be in use.

Unless measures for containment are done, nearly everyone (estimates are 70% of the population) in most cities and towns in the United States will be infected with the Coronavirus. The same applies to most countries where the virus spreads. Of course, if you move to the countryside and limit contact with others, you may avoid infection.

So if the ventilators are used in less than two months when there are more than 6 Million new infections in a 3 day period, nearly everybody who becomes infected after that won’t receive proper medical care, and will have the a higher Death Rate estimated at 5%. If we assume that at least 150 Million people are infected, and 20 Million receive adequate medical care, but 130 Million don’t, then 5% of 130 Million is 6.5 Million Deaths from people who don’t receive proper medial care. Add to this the 1% of 20 Million which is 200,000 and you have 6.7 Million deaths.

This corresponds to everybody coming to your restaurant at once!

If we can at least slow the spread of the virus then we can help ensure that we don’t have 10 Million new infections in a week, which would then consume the ventilators and capacity for medical care.

Note that things get dramatically worse if the rate of Severe Infections (people who require a ventilator) is higher than 1%. If we do the math with a 3% Severe Infection Rate the ventilators become used up after about 2 Million people are infected.

Using a Doubling Time of 6 days doesn’t just the overall outcome very much. It still takes 10 Doubling Periods to grow from over 1,000 Infections to over 1 Million Infections which happens in 60 days instead of 30 days. Essentially the number of days in the future for different events is just multiple by 2 compared to a 3 day Doubling Period.

Doubling Time: 6 Days.

For a 6 Day Doubling Time it takes 4 months before the entire US Population is infected.

# Estimating Potential Deaths

## Author’s Note

This is not so much of a prediction, but an analysis of what is likely to happen, if the United States does not take strong action to close schools, restaurants, gatherings and in person contact.

When I first starting researching information for this article on March 10th 2020, this had not begun to happen in the United States.

As of March 16th 2020, many strong actions to reduce the spread of the virus have been taken by many cities in the United States.

Also, more information is available now that will change the numbers below. For example, we could update the analysis with Death Rates and Ventilation Rates by age group.

I also realize some of the numbers are slightly inconsistent throughout the article which reflects different information being available at different through the writing process. For example, some calculations were done with very low Death Rates of 1% as a Lower Bound on Deaths, and later higher Death Rates were used.

Furthermore, it has become clear that “Flattening the Curve” will not be enough, and Isolation is likely required to stop the spread of The Coronavirus.

If you’d like to see the analysis updated with the most recent information then please consider making a donation to the FastMath Institute to support independent quantitive research.

Now let’s discuss potential Deaths. Estimating the potential deaths is very complex, and we’ll simplify our analysis to make make estimates relatively quickly.

We can also use different values for different rates involved (like the Severe Infection rate).

A high estimate is to use a 5% Death Rate for the entire US Population of 330 Million which will give us 16.5 Million deaths.

A low estimate for number of Deaths given a wide outbreak in the United States to use a 0.5% Death Rate and estimate that half the US population becomes infected. This will give a total of 825,000 Deaths, or almost a Million Deaths.

$330 \text{ Million} \times 50\% \times 0.5\%=165 \text{ Million}\times 0.5\%=825,000$

I want to put the number 1 Million in context.

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Let’s say you want to deliver medicine via injection to 1 Million people. If you can treat to one person every minute, and you work 10 hours a day, 5 days a week, how long will it take you to treat (deliver the medicine to) 1 Million people?

Try to do it without using a calculator.

Here’s the Math
If you can treat 1 person per minute, that is 60 people per hour.
Working 10 hours a day is 600 people per day
Working 5 days a week is 3,000 people per week.
If you work 50 weeks a year (and take two weeks off), you can treat 150,000 per year.
You would therefore need to work over 6 years (close to 7 years) to treat 1 Million people, as . Working another year (beyond 6 years) would allow you to treat 1 Million and 50 Thousand people.

For comparison, 6 Million people is about the population of the State of Colorado.

## Estimation Approach

In order to simplify the analysis, I am are going to use the following approach for estimating deaths. We can adjust the specific values later to see what the numbers look like.

I am going to estimate that a 10% of Infections require ventilators. We will call this proportion the Ventilator Rate, and call these Infections/Patients “Patients Requiring Ventilators.” Keep in mind that there is a limited supply of ventilators. This rate could be considered analogous to the to the Severe Infection Rate discussed earlier.

For Infected patients who require ventilators, they will need ventilators for 15 days, what we will call the Treatment Period. If they have ventilators for this amount of time, they have a Death Rate of 10% (of the patients Requiring Ventilators). We will call this Rate the Treated Death Rate. If they do not have ventilators for 15 days, they have Death Rate of 50%. We will call this the Un-treated Death Rate. Note that these Rates only apply to Patients Requiring Ventilators which is 10% of overall Infections.

This approach is consistent with a 1% Overall Death Rate when Infected Patients receive adequate treatment and a 5% Overall Death Rate when Infected Patents do not receive adequate treatment.

We’ll ignore deaths form patients who do not require ventilators.

We will use Doubling Time for number of Infections of 3 days to calculate how many new infections occur at any given time to see when ventilators are in use.

The Number of Ventilators is also relevant and is about 62,000, as is the number of existing Coronavirus Infections in the Untied States, which we’ll estimate at 1,000

Lastly, the percentage of the US population we believe will eventually be infected is an important metric as well. I will call this the Total Infection Rate, and use a value of 60%.

We don’t know for certain what these values are, but we can do the calculations with different values and adjust over time.

We could also do a similar calculation that defines Severe Infections as those needing treatment in Intensive Care Units and applying Death Rates for Severe Infections that do and do not get treated in Intensive Care Units. You would need a value for the number of patients that can be treated in Intensive Care Units at any given time.

## Estimation Numbers

If you use these values, pretty quickly you see that since ventilators are very limited they are all used up by the time we reach 620,000 total Infections, if the Ventilation Rate is 10%

Thus, half of all further Patients Requiring Ventilators die.

If 60% of the US Population is infected, that is 198 Million (we’ll round it to 200 Million):

$60\%\times 330 \text{ Million}=198\text{ Million}$

This puts the total number of deaths at over 9 Million:

The Ventilation Rate is 10%, there are 20 Million Ventilator Patients:

10% of 200 Million

This is likely to occur within the next two months (3 Day Doubling Period).

However, we only have 62,000 Ventilators and each Ventilator Patient needs one for 15 Days, so we can only treat 124,000 Ventilator Patients each month. That is, we can treat two batches of 62,000 Ventilator patients every month and $(2\times 62,000=124,000)$.

If this happens over a 2 month period, which corresponds to a 3-Day Doubling period, we can only treat less than 250,000 Ventilator Patients as $(2\times 124,000 = 248,000)$.

If it happens over a 4 month period (6-day Doubling Period), we can treat under 500,000 Ventilator Patients as $(4\times 124,000=498,000)$.

Remember that with a 6-Day Doubling Period, within 4 months the disease could infect the entire US population — but we assume it the maximum percentage infected is 60% of the Population (this is the Total Infection Rate).

Half of all the other Ventilator Patients die.

Thus, even with a 6-Day Doubling Period, and Treating 500,000 Ventilator Patients, there are 19.5 Million Untreated Ventilator Patients, as 500,000 is 0.5 Million.

Half of 19.5 Million is 9.75 Million — so 9.75 Million people die

For comparison 9 Million is larger than many US states entire states, and the average population of a US State is 6.6 Million.

### Imagine all of Colorado gone!

If we can slow down the spread of the virus and reduce the number of people infected at any given time, and increase the number of Treated Ventilator Patients.

### Different Outcomes

The above analysis use one particular set of numbers. Things change pretty dramatically depending on rates at which people require ventilators and advanced medical care Ventilator Rate), and the availability of that equipment and care.

But it’s pretty clear that low estimates (lower than what we believe the values to actually be) for the Ventilator Rate quickly use up all the Ventilators and lead to Millions of Deaths.

If you do this, we still have about 500,000 Treated Ventilator Patients over a 4 month period (assuming a 6 Day Doubling Period).

We still have 200 Million people infected, but only 5% are Ventilator Patients.

$5\%\times 200\text{ Million}=10\text{ Million Ventilator Patients}$

We can treat 0.5 Million (500,000), the rest die!

So this is 9.5 Million deaths, compared to 9.75 Million deaths with the earlier scenario, which estimates a Ventilator Rate of 10% but that half of untreated Ventilator Patients survive.

As you can see the second variation reduces deaths by 0.25 Million or 250,000, but more than 9 Million people die.

It is unlikely that the Ventilation Rate (the percentage of Infected Patients who require a Ventilator and who will have an increased Death Rate if they don’t have access to it) is lower than 5% because we have observed overall Death Rates of 5% in overwhelmed areas.

## Nobody is Immune

Another thing to consider is that nobody is immune to the Corona-virus. With the regular flu, a lot of people are immune to different strains because of previous infections, or from using the vaccine. This is one reason why only about 40 Million people are infected with the regular flu in the United States every year.

With the Coronavirus, there is the very real possibility that 60% or more of the population of 330 Million becomes infected, which could be 200 Million or more total Infections.

## What do You Believe

If you believe that the Death Rates for the Coronavirus aren’t this high that’s understandable. I’m just trying to help people understand what the numbers could look like if certain things are true.

Just don’t tell me not to worry because more people die of the Common Flu every year.

… because that’s like at’s like saying it’s safe to jump into the Grand Canyon because only 1 person died from that last year.

We don’t know the Death Rates for if large numbers of people are infected, and we don’t know for certain how many people have the the Coronavirus and how easily it spreads. From my perspective, there is a certain amount of risk that it could be widespread, spread very easily, and have a Death Rate higher than the Common Flu, and have a large number of Severe Case that have higher Death Rates if left untreated.

Only time will tell, but I think it’s best to take steps to limit the rate at which the virus spreads.

# Flattening the Curve Is Not Enough

It’s also clear after we ran analysis with more recent information (using a Ventilator rate of 5% rather than a lower value that we used initially) that flattening the curve is not enough. We should update the earlier section of the article to reflect that. The reason is that:

We Don’t Have Enough Ventilators!!

While one could be led to believe that hospitals could accommodate more patients if doctors and medical staff work harder and we build emergency hospitals, we’re not going to get hundred of thousands of new ventilators because every country is going to be saving them for their own population.

If you believe the Ventilation Rate is at least 5%, this puts limits on the number of Infections that can occur per year before we have Untreated Ventilator Patients who will have very high Death Rates (likely close to 100%).

Also note that so far we have estimated that Ventilator Patients require use of a Ventilator for 15 days, when it might actually be up to 30 days, which would cut in half the number of Ventilator Patients we can treat each year.

Even using a 15-day Treatment Period, we can only treat 1.5 Million Ventilator Patients every year. At a 5% Ventilation Rate, this means that 30 Million people can become infected very year before we have Untreated Ventilator Patients:

$30 \text{ Million} \times 5\%=1.5\text{ Million}$

This means, that if that if the Coronavirus eventually infects 200 Million people, we have to spread this infection out over more than 6 years (6 years and 8 months) in order to not have Untreated Ventilator Patients. If this eventually infects 90% of the US population, we have to spread this over a 10 year period.

Neither of these are realistic. Unless measures are taken to limit the spread of the disease, this will go through most of the US Population within a few months:

### That’s Exponential Growth

Go ahead and use the calculator on your smart phone to run the numbers yourself!

These are some of the articles which I have read recently. Note that different articles use different terminology.

This is probably the best article for those interested in thoughtful analysis of how widespread  the Coronavirus is right now, and about medical capacity and estimated Death Rates:
https://medium.com/@tomaspueyo/coronavirus-act-today-or-people-will-die-f4d3d9cd99ca