Here’s a good
illustration of what exponential growth means:
- On March 30, the press noted that total US deaths from Covid-19
had surpassed the toll on 9/11.
- It’s only 13 days later, yet the total of deaths just in the past
week (Sunday to Saturday) was
12,126 – i.e. four times the 9/11 toll. For the week just started, I’m
projecting 24,314 deaths, which of course is eight times the 9/11 toll.
But it looks like the 3-day rate of increase in daily deaths (which is
what I use for my projections) is probably again on a downward trend
(after pausing for about nine days). Let’s assume that yesterday’s 39%
rate miraculously drops to 25%, and continues the rest of this week. That
way, we’ll “only” have 20,000 deaths, which is about 6.5 times 9/11.
- On April 15 (usually a day that resonates with Americans for a
completely different reason than it will this year), we will likely pass
the 9/11 toll in deaths in a single day. And by the way, that’s two
days later than the date I projected yesterday – which was tomorrow.
- The worst part about passing this milestone is that it’s just that
– a milestone on the path to more and more deaths per day. Let’s look at
another disaster: the Vietnam War, which caused 57,000 American military
deaths (combat and non-combat). On what single day will we have 57,000
deaths for the first time? Using the current 3-day rate of increase in
daily deaths, that will be May 12, exactly one month from now. That’s more
than 2,000 deaths per hour. I suggest you turn off all
communications with the world that day, not that this will help anything.
Given the brutal
reality of exponential growth, it is inevitable – although I don’t have time to
try to quantify this – that soon the US will surpass the rest of the world in
total cases. And soon after that, in total deaths. The only question remaining
in my mind is whether we’ll end up leading the world in deaths per capita, as
well as total deaths. Of course, that’s something that could only be calculated
after the pandemic is over worldwide, and also after allowances are made for
the inevitable underreporting of deaths (for example, Kevin Perry emailed me
yesterday “I listened to an EMT from NYC the other day. He had five cardiac arrest fatalities on his
shift and while all of them had apparently displayed symptoms of COVID-19, none
were tested nor hospitalized. Therefore,
they were not counted in the official statistics.” Of course, this means that
both reported cases and reported deaths are too low).
But here’s the really bad news
The biggest assumption
that needs to be made in forecasting deaths from Covid-19, is the case
mortality rate – that is, what percent of total cases will result in death. I
started out this blog using a 3% estimate for this rate, and more recently
pushed that to 4%. I was thinking that there probably wouldn’t be any good way
to get a good estimate of the actual rate, until the epidemic was over in the
US.
Some people wrote
in to me to say they thought 4% was far too high an estimate, for various
reasons. All I could tell them was that I was sticking to that estimate, mainly
for one reason: We do currently know the actual case mortality rate for cases
that have been closed so far, meaning the person either recovered or died
(Worldometers only started publishing a recoveries number on March 26, so I
couldn’t calculate this rate before then). That rate is currently 40%.
So if we take that at face value, my 4% estimate is one tenth of the actual
mortality rate!
I’ve been assuming
that rate will soon come down, because there are many reasons to believe the
published number of recoveries is lower than the actual one (as I discussed in this
post). However, since March 26 there has been no downward trend at all. In
fact, the rate on March 26 was 41%, vs. 40% today. So when people have said my
4% case mortality rate estimate is too high, I’ve essentially asked “Would you
like me to use the only real number we have, which is 40%?” Of course, that
would mean I have to multiply all my deaths estimates by ten.
I continue to believe
that number will come down, even though Italy’s is still around 40% (Spain’s is
around 20%, but even that’s five times my current estimate of 4%). And until
about an hour ago, I thought there wouldn’t be a good way to estimate the
mortality rate until the pandemic is over.
However, I just
performed a simple analysis with my spreadsheet. I looked at the ratio of total
deaths on day X and the total reported cases on day X-7, X-14 and X-21. In
other words, I compared each day’s total deaths number with the reported cases
1, 2 and 3 weeks previous. The assumption is that there is some average number
of days between the date a person tests positive for the virus and the date
that person dies, if they do die. I didn’t really expect to get any clear
information out of this, but I was surprised that I did. The story that information
told is appalling, although as the title of this post says, it could have been
much worse.
The main
observation is that people are dying on average between one and two weeks after
their positive test. I say this because the mortality rate with a 3-week lag
between test and death as of March 21 (the last day I can calculate it, since
that was three weeks ago) is 97%. The series starts at 555% on March 2. Since
neither of these two numbers is believable, people must be dying on average at
a time other than three weeks after testing. And since the numbers are even
more unbelievable if we assume a longer-than-3-week lag, this probably means
the average interval between test and death is around one or two weeks (and
remember, since people don’t get tested until they feel bad – if then – they
have probably been infected for at least a week before they are tested).
So what do the
one- and two-week numbers look like? I’ll start with the 1-week numbers. They
start at 26% on March 2 (meaning 26% of the people who tested positive on March
2 died by one week later), and decline to 7% on March 22. From there until
April 4 (the last day I can measure the one-week rate), the rate stays at 7%.
How about the
two-week rate? It starts at 87% on March 2 and declines to 18% on March 28 (two
weeks ago), and it declines up to that date. This means it will probably
continue to decline as we go forward – and maybe it will end up leveling off at
the 7% rate, as the one-week rate has.
I hate to say
this, but it really looks like 7% is a much better estimate of the actual case
mortality rate than 4%, meaning all of my deaths projections should be
increased by 75%. I’m not going to immediately change those estimates,
though, although tomorrow I will probably start including estimates at both a
4% and a 7% mortality rate.
Of course, if
there were some number published that could show definitively what the average
time to death (after testing) is, then we could decide whether to use the 7-day
number, the 10-day number, 14-day number, etc. But I’m sure there’s no way you
could do that now. I think the fact that the seven-day rate has been at 7% for
so long is a very good indication that this is close to the true mortality
rate, although of course it could go up if hospitals start experiencing severe
shortages of ventilators, etc. That doesn’t seemed to have happened yet even in
New York, but it could all change in a week. Remember, the number of deaths per
day won’t go down for a long time, and even the rate of increase in deaths per
day is still positive - although it has finally started declining again, after
stagnating for a week or so.
To be honest, I
was almost relieved to see the 7% figure emerge so clearly from the numbers. I
was really concerned that the rate might turn out to be something like the 40%
measured rate so far. But even 7% is appalling.
All numbers below
are based on yesterday’s reported figures of total confirmed cases, total
deaths and total recoveries, published on Worldometers.info. I’m happy to send
my spreadsheet that calculates all of these to anyone who wants to check the
calculations, although they follow the assumptions described below.
Date
on which the number of new deaths on that day will probably exceed the
toll of Sept. 11: April 15
Actual number of deaths during week ending April 11
(Saturday): 12,126
Projected*
number of deaths during week ending April 18 (Saturday): 24,314
Projected*
number of deaths during week ending April 25 (Saturday): 52,585
Projected*
number of deaths during week ending May 2 (Saturday): 109,126
Projected* number of deaths during month of April: 230,702
Number of new deaths on May 1 alone: 20,693 (was 29,186
yesterday)
* Projected deaths for each day equals the
previous day’s deaths, grown by yesterday’s 3-day percentage growth rate in new
deaths, which as of today is 39%. The weekly number is the sum of the
projected deaths for the 7-day period.
I. Numbers based on total cases, actual and
projected
Total US confirmed
cases: 533,115
Increase in cases
since previous day: 29,938 (vs. 34,282 increase yesterday)
Percent increase
in cases since yesterday: 6% (vs. 7% yesterday)
Percent increase
in cases since 3 days previous: 23% (vs. 26% yesterday)
“Set in stone” US deaths* over course of
pandemic: 148,657 (based on 4% case mortality rate)
*This number assumes a) Reported cases are a
fairly accurate estimate of total cases; b) Total cases grow by 26% into the
future (= yesterday’s 3-day growth rate in cases); c) We impose a massive
lockdown, with prohibition of all non-essential travel, today; d) New cases
drop to zero in 28 days, because of the lockdown, but they continue to grow at
the current projected rate up to the 28th day; e) testing is widely
available by the 28-day mark; and f) the case mortality rate = 4%.
To see what would happen with a 6% mortality
rate, multiply each set in stone deaths number by 1.5. For 8%, double it. For
comparison, Italy’s current case mortality rate (deaths so far divided by cases
so far) is currently over 12%, in spite of the fact that their daily growth
rate in cases is declining.
Projected as of April 19 (7 days from today):
These numbers answer the question: What would
happen if we wait seven days to totally lock down the US, based on the
assumptions below (which frankly are themselves wildly optimistic).
Total expected cases*: 936,345 (vs. 937,966 expected yesterday)
Total expected deaths set in stone** over
course of pandemic: 255,707 (vs. 322,276 expected yesterday)
* The expected cases number assumes that
total cases grow by 23% every three days, for the next 7 days (= yesterday’s
3-day growth rate in cases).
**This number assumes a) Reported cases are a
fairly accurate estimate of total cases; b) Total cases grow by 23% into the
future (= yesterday’s 3-day growth rate in cases); c) We impose a massive
lockdown, with prohibition of all non-essential travel, on April 19; d) New
cases drop to zero in 28 days because of the lockdown, but they continue to
grow at the current projected rate up to the 28th day; e) testing is
widely available by the 28-day mark; and f) the case mortality rate = 4%.
To see what would happen with a 6% mortality
rate, multiply each set in stone deaths number by 1.5. For 8%, double it. For
comparison, Italy’s current case mortality rate (deaths so far divided by cases
so far) is currently over 12%, and their daily case growth rate is declining.
Projected as of April 26 (14 days from today):
These numbers answer the question: What would
happen if we wait 14 days to totally lock down the US, based on the assumptions
below (which frankly are themselves very optimistic)?
Total expected cases*: 1,500,882 (vs. 1,597,988 projected yesterday)
Total deaths set in stone* over course of pandemic:
418,516 (vs. 557,529 projected
yesterday)
* The expected cases number assumes that
total cases grow by 23% for the next 7 days (= yesterday’s 3-day growth rate in
cases).
*This number assumes a) Reported cases are a
fairly accurate estimate of total cases; b) Total cases grow by 23% into the
future (= yesterday’s 3-day growth rate in cases); c) We impose a massive
lockdown, with prohibition of all non-essential travel, on April 18; d) New
cases drop to zero in 28 days, because of the lockdown, but they continue to
grow at the current projected rate up to the 28th day; e) testing is
widely available by the 28-day mark; and f) the case mortality rate = 4%.
To see what would happen with a 6% mortality
rate, multiply each set in stone deaths number by 1.5. For 8%, double it. For
comparison, Italy’s current case mortality rate (deaths so far divided by cases
so far) is currently 12.77%, and their daily case growth rate is declining.
Date on which 500,000 total pandemic deaths
will be set in stone: April 29
Date on which 1 million total pandemic
deaths will be set in stone: May 9
Number of deaths set in stone on April
30: 552,411
II. Numbers based on total deaths, reported
and projected
(All of the numbers below are based on
reported deaths, not reported cases and an assumed case mortality rate of 4% -
which itself is probably low. The case number is some fraction of the actual
cases. So the projections below are going to be much more accurate estimates
than the ones above)
Total US deaths as of yesterday: 20,580
Increase in deaths since previous day: 1,819
(vs. 2,064 yesterday)
Percent increase in deaths since previous
day: 10% (vs. 12% yesterday)
Yesterday’s 3-day rate of increase in total
deaths: 39% (vs. 46% reported yesterday)
III.
Reported case mortality rate so far in the pandemic in the US:
These
numbers are also unaffected by the error I made.
Total
Recoveries in US as of yesterday: 30,502
Total
Deaths as of yesterday: 20,580
Deaths
so far as percentage of closed cases (=deaths + recoveries): 40% (vs. 41% yesterday) Let’s be
clear. This means that, of all the coronavirus cases that have been closed so
far in the US, 40% of them have resulted in death (compare that to the 4%
mortality rate I’ve been using to calculate total pandemic deaths, based on total
cases). Of course, this number will come down as time goes on and more cases
are closed in which the victim recovered. But it’s only come down by about 4
percentage points since Worldometers started publishing the recovery rate on
March 26, and on about half the days, it’s gone up; there is still no sign of a
downward trend. I’d say it’s much more likely my 4% mortality rate will turn
out to be too low, after the pandemic’s over and all of the bodies have been
counted, than it will be too high.
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