The bad news is my mortality rate estimate is too low by about half. The good news is it could be a lot worse.

Here’s a good illustration of what exponential growth means:

1. On March 30, the press noted that total US deaths from Covid-19 had surpassed the toll on 9/11.
2. 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.
3. 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.
4. 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 28^th 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 28^th 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 28^th 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.