Saturday, April 11, 2020

Will herd immunity save us? Depends on what you mean by “save”.

 
To summarize what’s changed from yesterday: First, total reported cases grew by a 3-day rate of 26%, vs. 28% reported yesterday. Is this cause for celebration? Well, it leads to a projection that, if we wait seven days and then do a total lockdown, the total pandemic deaths will be “only” 362,790, based on the very conservative assumptions below (which are frankly just about unattainable). Does that mean it’s time to break out the champagne? Only if we don’t remember that the Administration (plus Saint Anthony Fauci, Deborah “There is no shortage of ventilators” Birx, and virtually all of the media) still clings to the idea that 240,000 is the maximum number of pandemic deaths we’ll have.

362,000 is a wild underestimate of total pandemic deaths in the US, since epidemiologists say the true number of cases is 5-10 times the reported one. But even assuming total cases were only underreported by a factor of two, we would end up with twice as many (725,000) pandemic deaths if a total lockdown were imposed seven days from today. Also, I compute total pandemic deaths by multiplying reported cases by a 4% case mortality rate – and that rate will only be accurately known after the pandemic is over. However, it’s almost certain the 4% number is low, perhaps drastically so (see Section III below).

Second, total deaths grew by a 46% 3-day rate yesterday, vs. 53% based on the previous day’s numbers. Now this is a cause for celebration, right? Only if you ignore the fact that there’s been no trend in that number for the past six days (the rate was 48% several days ago). But let’s say the growth rate in daily new deaths stays at 46% (which of course still means the total deaths number will more than double every two days, given compounding). Then, we still end up with the weekly death numbers shown below, and the projection of total April deaths of 230,702 (vs. the actual number of 4,053 for March). This means that average daily deaths in April will be about 7,700 – and since we had 2,000 yesterday, this of course means the daily numbers will be much higher than 7,700 later in the month. In fact, I now show April 23 as the first day where daily deaths exceed 10,000. Compare this with the fact that Italy’s total deaths so far were around 19,000 yesterday, and their new cases are now declining each day.

And – grasping at straws here – now assume that the actual deaths number just grows at 23% (half the above rate) from today on. In that case, total deaths for April are “only” 107,764, which still works out to 3,600 deaths per day in April – i.e. more deaths than on 9/11, except happening every day. And we don’t get above 10,000 deaths per day (i.e. more than three 9/11’s) until May 2. Wow! We’ve gained a whole 9 days before we reach that dire milestone! Now there’s cause for celebration, right?

As I’ve pointed out repeatedly, once you have exponential growth (which means the addition to the number every period equals a positive percentage of the number itself), drops in the growth rate only push back the inevitable appalling numbers in time - they don’t eliminate them. You have to literally stop growth in new cases cold if you want to actually beat the virus.

And in this regard, I can’t believe that seemingly rational people (of all political stripes) are now waving the white flag and saying we can’t really expect to beat the virus completely until a) it infects enough of the population that the rest of us have “herd immunity”, or b) a vaccine is developed and produced in quantities large enough to vaccinate the entire US population – or at least all of them who don’t have immunity.

Let’s look at each of these ideas. Regarding herd immunity, epidemiologists estimate that will kick in when 40-70% of the population has been infected – let’s say it’s 50% for ease of calculation. The US population is about 320 million, which means 160 million would be infected. And let’s use a final case mortality rate estimate of two percent, which is almost certainly an underestimate – perhaps a huge underestimate (see Section III below) – of the final number. This means a minimum 3.2 million will die. So if we want to wait for herd immunity to save us, we have to be prepared for at least that number of deaths.

How about a vaccine? We really can’t assume one will be developed and tested for 18 months. But that’s not the end of it. Manufacturing it in the quantities required will take a lot of production capacity, which we certainly don’t have sitting around now. If we want to be ready to produce the vaccine within say a month of developing it, we need to at least have the facilities lined up, staffed, etc. And we need to start planning for that now. Anybody want to bet whether the current Administration is even thinking about this?....I didn’t think so.

This means that herd immunity is what will finally “save” us – and of course, I’m thinking there of the famous statement by some military officer during the Vietnam war: “We had to destroy the village in order to save it.” If “salvation” is losing 3.2 million people at a minimum, what’s the alternative?

Of course, the alternative is doing as much of a total lockdown of the country as we can now, with grounding of all travel beyond a short range, except of course for various essential activities. We’ve come part way to doing that already, which is why the rates of increase in total reported cases and total deaths have slowed markedly since 2-3 weeks ago. But given the current stagnation in the rate of change in total deaths (and the total unreliability of the cases number – the only question is how huge an underestimate it is of the actual number), we certainly can’t count on much further drop in those two numbers, without more measures than we’re already taking.

So what could justify losing 3.2 million people? Of course, the argument made by many of both political persuasions is that “The cure is worse than the disease.” Meaning that not having to lock the economy down much longer than April 30 – vs. waiting until at least May 31, which is what Bill Gates is advocating – would be worth the price of 3.2 million deaths (or, more specifically, 3 million deaths, since even if we did a total lockdown today and left it in place through the end of May, we would still end up with close to 200,000 deaths. This is my “set in stone” figure for today).

Of course, the people who make this argument – including Holman Jenkins of the Wall Street Journal, in an op-ed today – aren’t even trying to estimate the total deaths. And they’re also leaving out one very crucial fact: Those 3 million deaths will be almost entirely of people who have to leave home to work. This certainly doesn’t include Holman Jenkins, and it doesn’t include me, either.

So what Mr. Jenkins and others are actually saying (including obviously one D.J. Trump, to the extent he understands the implications of anything he says) is: “Working people, you need to take a pretty bad gamble with your lives, in order that those of us who survive will have a better life in the long run. Hell, maybe we’ll even give you a few extra dollars per hour for your sacrifice. And give you a real nice funeral to boot!” Such a deal.

But the real question is: Will the workers take that deal? If the government decides to play hard ball, and leaves them with the choice between a) working and taking the chance of dying from Covid-19, and b) staying home but starving because all of the aid spigots will be cut off, maybe they will take it.

But I have a better idea: Let’s make sure people have enough to live on, even if the economy is totally shut down for three months. And don’t give me some c___ about the dangers of inflation ten years from now. Alternatively, maybe we can get Mr. Jenkins, and all who support this idea, to volunteer to man the factories and service counters, while everyone who cares more about their life sits at home. I’m sure we’ll get enough volunteers to staff one or two McDonald’s.


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 13
Projected* number of deaths during week ending April 11 (Saturday): 13,139
Projected* number of deaths during week ending April 18 (Saturday): 30,323
Projected* number of deaths during week ending April 25 (Saturday): 72,416
Projected* number of deaths during week ending May 2 (Saturday): 180,721
Projected* number of deaths during month of April: 230,702
Number of new deaths on May 1 alone: 29,186 (was 57,474 yesterday)
* Projected deaths for each day = previous day’s deaths grown by yesterday’s 3-day percentage growth rate in new deaths – equal to 46%. 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: 503,177
Increase in cases since previous day: 34,282 (vs. 33,735 increase yesterday)
Percent increase in cases since yesterday: 7% (vs. 8% yesterday)
Percent increase in cases since 3 days previous: 26% (vs. 28% yesterday)

“Set in stone” US deaths* over course of pandemic:  175,555 (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 of at least 60 days, 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 60-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.

Projected as of April 18 (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*: 937,966 (vs. 912,597 expected yesterday)
Total expected deaths set in stone** over course of pandemic:  322,276 (vs. 362,790 expected yesterday)
* The expected cases number assumes that total cases grow by 26% 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 26% into the future (= yesterday’s 3-day growth rate in cases); c) We impose a massive lockdown of at least 60 days, 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 60-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.

Projected as of April 25 (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*: 1,597,988 (vs. 1,611,111 projected yesterday)
Total deaths set in stone* over course of pandemic: 557,529 (vs.  649,928 projected yesterday)
* The expected cases number assumes that total cases grow by 26% 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 26% into the future (= yesterday’s 3-day growth rate in cases); c) We impose a massive lockdown of at least 60 days, 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 60-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 deaths will be set in stone: April 24  
Date on which 1 million total pandemic deaths will be set in stone: May 3
Number of deaths set in stone on April 30: 812,287  


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: 18,761
Increase in deaths since previous day: 2,064 (vs. 1,900 yesterday)
Percent increase in deaths since previous day: 12% (vs. 13% yesterday)
Yesterday’s 3-day rate of increase in total deaths: 46% (vs. 53% 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: 27,314
Total Deaths as of yesterday: 18,761
Deaths so far as percentage of closed cases (=deaths + recoveries): 41% (vs. 39% 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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