Thursday, April 9, 2020

The coronavirus teaches us what “exponential” means


I believe we’re heading for a fundamental political realignment, and very shortly. Why do I say that? Two words: exponential growth. Note the projections I’ve started doing below for total deaths by week for the next four weeks (including this one). These are projections of actual deaths during the week, not projections of deaths over the course of the pandemic (i.e. my set in stone estimates):

Date on which the number of new deaths on that day will probably exceed the toll of Sept. 11: April 12
Projected* number of actual deaths during week ending April 11 (Saturday): 14,316
Projected* number of actual deaths during week ending April 18 (Saturday): 38,627
Projected* number of actual deaths during week ending April 25 (Saturday): 109,697
Projected* number of actual deaths during week ending May 2 (Saturday): 295,998
Number of new deaths on May 1 alone: 60,549
* Projected deaths for each day = previous day’s deaths grown by yesterday’s 3-day percentage growth rate in new deaths – equal to 54%. The weekly number is the sum of the projected deaths for the 7-day period.

The Surgeon General (yes, the same guy who said just eight days ago that “We don’t recommend you wear a face mask in regular life.”) said early this week that this would be “Pearl Harbor moment” for the American people. He implied that deaths this week would mark the peak of the pandemic – although of course they will fall slowly from now on.

He was right about two things:

  1. This week will be a peak so far. But next week will be an exponentially higher peak. The following week will also be exponentially higher…and on and on until we get the coronavirus totally under control.
  2. This week will include a Pearl Harbor moment. In fact, I expect total deaths tomorrow alone will surpass the 2400 US deaths at Pearl Harbor.

Folks, this is exponential growth. Cases have been growing exponentially all along (remember, the US had 100 reported cases at the beginning of March. Today we have 435,000), but cases aren’t deaths, and the fact that they’re growing so rapidly doesn’t in itself mean anything to most people. They – very naturally – continue to hope actual deaths per case (the case mortality rate) will be much lower than all the experts are projecting now.

But deaths have been growing exponentially, too, and at a much higher rate than cases, especially in the last couple of weeks. Now they’re up to numbers that people are really paying attention to. And guess what? As we pass the total number of 9/11 deaths in a single day (which I currently show to be Easter Sunday, but could easily be next Monday), people will notice. They’ll notice even more when, in two weeks, we start having more than 10,000 deaths every day. Of course, it keeps getting worse and worse from then on.

On March 19, I wrote a post entitled “April will be hell on earth. May will be worse.” I certainly agree with both of those statements, although I’ll add that June will probably not be much better. But it’s almost laughable what I was basing these statements on: I was expecting 30,000 deaths in April (i.e. 1,000 a day) and 60,000 in May (2,000 a day). Those are certainly hellish numbers, but total deaths for April now look like 340,000 (vs. 4,000 for March). This means average daily deaths in April will be over 10,000. And you don’t want to know what they will be in May.

You might ask, “Surely this growth will be slowed soon by the social distancing measures we’re taking, right?” But remember, most of the social distancing that’s in place now was put in place 2-4 weeks ago. That’s had a huge effect: On March 19, the daily change in reported new cases peaked at 49%; yesterday, it was 9%. But the problem is, that rate of change has stopped declining, at least for the past few days. It might drop some more but it won’t do much more, absent much stronger social distancing measures than are in place now (i.e. a nationwide lockdown, combined with prohibition of all non-essential interstate – and hopefully also intrastate – travel).

As the deaths keep piling up, people are going to start to ask more and more questions about why the US is now guaranteed to end up with a big multiple of total pandemic deaths, compared to the rest of the world combined – and more importantly, what measures need to be taken right away to change the course of the national government. Even though they will mean some important people – including the two at the top – will have to be pushed aside to make way for competent managers who actually pay attention to facts, a prospect that still seems almost inconceivable this week. But it will be anything but inconceivable next week, and it will be widely seen as inevitable in two weeks, if it hasn’t happened already by then.

Anyone who thinks our government and our society are going to emerge from the pandemic anything like they were beforehand is literally whistling past the graveyard.


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.

I. Numbers based on total cases, actual and projected
Total US confirmed cases: 435,160
Increase in cases since previous day: 34,611 (vs. 32,890 increase yesterday)
Percent increase in cases since yesterday: 9% (vs. 9% yesterday)
Percent increase in cases since 3 days previous: 29% (vs. 29% yesterday)

“Set in stone” US deaths* over course of pandemic:  204,462 (based on 4% case mortality rate)
*This number assumes a) Total cases grow by 29% into the future (= yesterday’s 3-day growth rate in cases); b) We impose a massive lockdown, with prohibition of all non-essential travel, today; c) 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; d) testing is widely available by the 28-day mark; and e) case mortality rate = 4%. To consider a 6% mortality rate, multiply each projection by 1.5. For 8%, double it. For comparison, Italy’s case mortality rate is currently 11.75%.

Projected as of April 16 (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*: 859,854 (vs. 789,250 expected yesterday)
Total expected deaths set in stone** over course of pandemic: 369,646 (vs. 340,245 expected yesterday)
* The expected cases number assumes that total cases grow 29% for the next 7 days (= yesterday’s 3-day growth rate in cases).
** The expected deaths set in stone number assumes that a) Total cases grow by 29% into the future; b) We impose a massive lockdown, with prohibition of all non-essential travel, on April 16; c) New cases drop to zero 28 days later, because of the lockdown, but they continue to grow at the current projected rate up to the 28th day; d) Testing is widely available by the 28-day mark; and e) case mortality rate = 4%. To consider a 6% mortality rate, multiply each projection by 1.5. For 8%, double it. For comparison, Italy’s case mortality rate is currently

Projected as of April 23 (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*: 1,554,524 (vs. 1,430,883 projected yesterday)
Total deaths set in stone* over course of pandemic: 670,426 (vs.  614,248 projected yesterday)
* The expected cases number assumes that total cases grow 29% for the next 7 days (= yesterday’s 3-day growth rate in cases).
** The expected deaths set in stone number assumes that a) Total cases grow by 29% into the future; b) We impose a massive lockdown, with prohibition of all non-essential travel, on April 23; c) New cases drop to zero 28 days later, because of the lockdown, but they continue to grow at the current projected rate up to the 28th day; d) Testing is widely available by the 28-day mark; and e) case mortality rate = 4%. To consider a 6% mortality rate, multiply each projection by 1.5. For 8%, double it.
However, if you assume the final mortality rate will equal even half of the current actual case mortality rate (i.e.

Date on which 500,000 deaths will be set in stone: April 20  
Date on which 1 million total pandemic deaths will be set in stone: April 28
Number of deaths set in stone on April 30: 1,215,460  


II. Numbers based on total deaths, reported and projected
Total US deaths as of yesterday: 14,797
Increase in deaths since previous day: 1,940 (vs. 1,949 yesterday)
Percent increase in deaths since previous day: 15% (vs. 17% yesterday)
Yesterday’s 3-day rate of increase in total deaths: 54% (vs. 52% reported yesterday)

Date on which the number of new deaths on that day will probably exceed the toll of Sept. 11: April 12
Projected* number of actual deaths during week ending April 11 (Saturday): 14,316
Projected* number of actual deaths during week ending April 18 (Saturday): 38,627
Projected* number of actual deaths during week ending April 25 (Saturday): 109,697
Projected* number of actual deaths during week ending May 2 (Saturday): 295,998
* Projected deaths for each day = previous day’s deaths grown by yesterday’s 3-day percentage growth rate – equal to 54%. The weekly number is the sum of the projected deaths for the 7-day period.


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: 22,891
Total Deaths as of yesterday: 14,797
Deaths so far as percentage of closed cases (=deaths + recoveries): 39% (vs. 37% yesterday) Let’s be clear. This means that, of all the coronavirus cases that have been closed so far in the US, 39% 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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