The Awful Arithmetic

Note from Tom 12/9/2023: For perspective on this, the rate of increase in coronavirus deaths (i.e. the second derivative) peaked at the end of March, when deaths were close to doubling daily. Had deaths continued to grow at that rate, the entire US population would have been dead about a month and a half later, around my birthday (May 10). Such is the power of exponential growth.

I love the people who now say we obviously didn't need the big lockdowns, since we never approached those extreme levels of death. That's like saying we didn't need penicillin, because the malaria went away in a few days. The lockdowns, inadequate as they were, at least held deaths to 1,184,575 as of tonight (this is the first time I've even looked at that number in maybe six months).

In 1862 and 1863, Abraham Lincoln was distraught: The generals of the Army of the Potomac (the Union’s main army in the Civil War) consistently kept allowing themselves to be beaten by much smaller Confederate forces – and then withdrew, even though they still far outnumbered the Confederates. And even when they won (as at Antietam and Gettysburg), they allowed the Confederates to slip away without pursuit. He could clearly see the way forward, and he said that he needed to find a general who could do the “awful arithmetic”.

Lincoln’s arithmetic was very simple: The Union army had hugely more human and material resources than the Confederate army, and they could definitely win the war. But his generals needed to be prepared to take big numbers of casualties in order to do that. He needed to find a general who understood that. Of course, Grant was the one he found. He did win the Civil War (with a lot of help, of course), but after taking huge casualties.

In the war on the coronavirus pandemic, the US[i] and the world are fighting death itself – not literally the fact that everyone will eventually die, but that there will be a huge number of near-term deaths from this virus. Since there have already been thousands of deaths worldwide (but not yet tens of thousands, hundreds of thousands, or millions), the battle is to keep that number as low as possible. Clearly, there will be at least in the hundreds of thousands of deaths worldwide, not tens of thousands – but will there be millions? That’s the only real question now.

For the US itself, there will ­without doubt be thousands of deaths, and likely tens of thousands (as I said, an epidemiologist over the weekend estimated there would be between 80,000 and 1.7 million deaths - another epidemiologist said he expected about 400,000 US deaths - although a British study said the total could be 2.2 million in the US. Remember, that’s deaths, not cases). Our goal at this point should be to keep total deaths from the pandemic – in the US – below 100,000, and of course as far below that figure as possible. And as a point of comparison, the total of all US combat deaths since World War II is below 100,000; we should be pleased – if that’s the word, which it’s not – if we can keep coronavirus deaths below that figure.

You might wonder how an epidemiologist could arrive at huge numbers like the above, given that we’re still at around 100 deaths today (I read two numbers this morning. The Times said the total was 97 - that was probably as of the end of day yesterday - while another site called Worldmeter says it’s 116). You have to understand the terrible power of exponential growth. At the moment, the number of cases seems to be doubling every three days. Since there were 3,100 cases on Monday, we’ll find out tomorrow morning if that continues to be true. However, I’ll point out that Worldmeter’s site says we’re now – 9:35 Central time on March 18 – at 7,300 cases. If that’s really true, then the number is more than doubling every two days! However, let’s see what the official numbers are tomorrow before we take that as true.

But keep in mind that the official numbers are a small fraction of the total cases, since testing has been so limited. Fortunately, testing is ramping up in the US now, and the reported cases will gradually approach the total cases – but I’m sure it will be weeks before all actual cases (that have showed symptoms, since we’ll probably never test the entire population, sick or not – although that may be necessary before long) are reported. The British study that prompted the White House’s announcements on Monday says there are between 5 and 10 times as many actual cases in the US as are being measured.

But let’s assume that the number of official cases tomorrow morning is the 7,300 that Worldmeter estimates for this hour today (i.e. the official numbers are the real ones). That leads to about two million cases in three weeks. And let’s apply a mortality rate of three percent to that (which assumes some areas –but not all - have hospital systems which are overwhelmed, as is happening in northern Italy now). That leads to an estimate of 60,000 deaths due to the cases that are identified in the next three weeks, but remember, that’s not total deaths to to the epidemic. If that's what you want, you need to additionally assume that a) all people infected have been identified by that time, and b) the number of new cases reached zero  two weeks previously (since the incubation time is a maximum of 14 days) – meaning that one week from today, we’ll have stopped all new cases.

How do we stop all new cases one week from now? By imposing a total lockdown on the country NOW (OK, tomorrow, since this will take some time to put into place), with a) total shutdown of transportation (except for food, and essential personnel and supplies for fighting the virus), and b) everyone not required for essential services – like keeping the lights on and medical care – staying at home except for essential trips for food and medical services.  The Bay Area has done that; it seems New York City may do that tomorrow; a few smaller cities have done that already. But this isn’t enough. We need a total lockdown of the entire country.

Will this happen tomorrow? Of course not, meaning that additional deaths due to this omission will ultimately be in the thousands, as I calculated roughly in yesterday’s post (i.e. when we get to the end of the pandemic, total deaths will be seen to have been made higher by 2,000 per day, due to this delay. And that is probably an underestimate). But I’m actually optimistic that total lockdown will happen next week – and if it doesn’t happen next week, it absolutely will happen the following week. Why do I say this? Because of exponential growth. Reported (not actual) cases will be over 40,000 by next Wednesday (and almost certainly higher), meaning that total deaths due to just those infections will ultimately be around 1300 (using the same 3% figure for mortality, which is in the high middle of the range estimated in the article that spurred Saturday’s post, which BTW has had 40 million views in the past week).

I expect that these numbers will finally spur the White House to order a nationwide lockdown (including lockdown of all travel except for emergency needs) next week. And if the lockdown is close to totally effective (obviously not a good assumption), there will be no new infections, meaning the reported cases in three weeks (remember, after the 14-day incubation period, when infected people will show symptoms – and assuming reported cases equal actual cases by that time, which by the way isn't a good assumption, given how far behind the US is in having adequate testing facilities available) will be the 2 million figure I said above. And that means 60,000 US deaths from the pandemic (vs. what looks like no more than 4,000 total deaths in China, and maybe 5,000 in Italy?). As I've mentioned repeatedly, this is 3,000 more than total US combat deaths in the Vietnam War.

And remember, the above numbers are all best case. They’re almost certain to be higher than that. Of course, the key will be the mortality rate. If we invest massively in the things needed to make sure our hospital systems don’t get overwhelmed (a very important one is massively ramping up output of ventilators and training for the people to use them – then pre-deploying them where they’re most likely to be needed), we could perhaps keep the mortality rate below 3 percent, meaning the number of deaths would be lower. Conversely, if we invest very little (and that is certainly the case so far), we’ll end up at probably many more than 60,000 total deaths.

And this is a word for policymakers: While we certainly need to support people who are out of work and who need medical care (for any reason), giving a massive tax cut or mailing $1,000 to every citizen isn’t going to do anything except slightly improve somebody’s currently dismal reelection prospects. Let’s make the massive investment needed to keep the death toll to close to 60,000, rather than be wondering in a few weeks how far above a million it will go. The economy is never going to recover if people have to keep worrying about catching the illness that will kill them the next day at the office.

And I have another prediction: in 4-8 weeks, there will be a big change at the top of the US government – if I’m anywhere close to correct in the numbers above (and of course, I’m far from the only person giving numbers like that, scientist or not). Nobody – Republican, Democrat or Independent – is going to accept numbers like this without demanding a big change.

Remember, two weeks and one day ago there were six reported coronavirus cases in the US and no deaths. Look at how much things have changed since then. And now consider how different they will be in two weeks, and especially in three or four weeks. The word of the day, week, month and year: exponential.

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[i] And Canada, of course. In fact, just about everything I say in these coronavirus posts should be interpreted as applying to both countries. Although my guess is they're in much better shape in terms of preparedness than we are. After all, Toronto got hit very hard by the SARS epidemic, and that was (and is) a coronavirus.