Follow the deaths

Yesterday’s numbers (from Worldometers, as of about 7 PM EDT March 30)

Total US confirmed cases: 164,435

Increase in cases since previous day: 21,689 (vs. 18,965 increase yesterday)

Percent increase in cases since yesterday: 15% (vs. 15% yesterday)

Percent increase in cases since 3 days previous: 33% (vs. 37% yesterday)

Total US deaths as of yesterday: 3,175

Increase in deaths since previous day: 686 (vs. 260 yesterday)

Percent increase in deaths since previous day: 28% (vs. 12% yesterday)

Expected* US deaths over course of pandemic:  85,749 (based on 4% case mortality rate)

*This number assumes a) Total cases grow by 33% into the future (= yesterday’s 3-day growth rate in cases); b) New cases drop to zero on April 28, because of the lockdown; and c) 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%.

Projected as of April 7 (7 days from today):

Total expected* cases: 335,830

Total deaths set in stone** over course of pandemic: 201,499

*Expected cases assumes a) Total cases grow by 33% into the future (= yesterday’s 3-day growth rate in cases); b) we wait until April 7 to impose a total lockdown; c) New cases drop to zero on May 5, because of the lockdown

** Deaths set in stone = expected cases X case mortality rate of 4%. To consider a 6% mortality rate, multiply the figure by 1.5. For 8%, double it. For comparison, Italy’s case mortality rate is currently 11%.

Projected*** number of actual deaths on 4/7 alone: 1,700

*** Projected deaths = previous day’s death number, grown by the 3-day percentage growth rate. Note this is calculated completely differently from the deaths set in stone.

Projected as of April 14 (14 days from today):

Total expected* cases: 503,157

Total deaths set in stone** over course of pandemic: 356,852

*Expected cases assumes a) Total cases grow by 33% into the future (= yesterday’s 3-day growth rate in cases); b) we wait until April 14 to impose a total lockdown; c) New cases drop to zero on May 12, because of the lockdown

** Deaths set in stone = expected cases X case mortality rate of 4%. To consider a 6% mortality rate, multiply the figure by 1.5. For 8%, double it. For comparison, Italy’s case mortality rate is currently 11%.

Projected*** number of deaths on 4/14 alone: 15,687 (equal to about five times total deaths on 9/11. And this is the reported deaths in a single day)

*** Projected deaths = previous day’s death number, grown by the 3-day percentage growth rate.

Reported death rate so far in the pandemic in the US:

Total Recoveries in US as of yesterday (3/29): 5,211

Total Deaths as of yesterday: 2,489

Deaths so far as percentage of closed cases (=deaths + recoveries): 38%

Date on which 100,000 deaths will be set in stone: April 1

Date on which 500,000 deaths will be set in stone: April 18

Date on which 1 million deaths will be set in stone: April 25

“Set in stone” means that on that date, a total lockdown will be put in place. It will be 100% effective (0 new cases) 28 days later.

I didn’t make any changes in how I’m doing calculations today, but I tried to make the results in the tables above a lot more understandable, and to provide the complete explanation of each number right below it. My goal, of course, isn’t to provide some dry statistics for scholars to review later on, but to try to project what will happen in a way that’s totally transparent. This compares with what you read in the newspapers, which is always what one expert or another says will happen. You don’t know how each expert projected their numbers (unless you’re prepared to read some lengthy paper somewhere, which almost nobody in the general public will do), and you don’t know why one expert’s numbers differ from another’s, or even what precisely the numbers mean.

I’m not developing estimates using anything but simple arithmetic: no modeling of the virus spread, etc. – I can’t do that, and frankly I don’t know how well the epidemiologists can either, since this is such a different situation from before. I’m just trying to explain how I project the numbers and what precisely my terms mean. If you don’t agree with the numbers (and I’m sure many if not most of you don’t), then please let me know your concern, so I can figure out if I’m doing something wrong. Unfortunately, the few people I’ve heard from with concerns have usually just said they’re tired of seeing my gloomy posts – they’re inundated with information and don’t know what to think (which sometimes – but not always - means they’ve made up their minds, so they don’t want to see any more information).

I have developed a standard answer for these people: If you don’t want to read my posts on the pandemic, you have my permission to delete them from your inbox (as if you needed it). If you’re worried you then won’t know about new NERC CIP posts that I put up, you’ll have to check the blog every day to see if one of those has been posted (of course, this applies to Tom Alrich’s Blog, not The Pandemic Blog. I will only post pandemic posts on the latter). But I’m going to write about what I think is important each day. And frankly, I think any human being in the United States should be paying a lot of attention to what’s going on with the pandemic. Even if you’re not infected now, I’m sure it’s already affected your livelihood; those effects alone will continue to increase.

My projected numbers are based on three numbers that I get every day from a site called Worldometers (who gets their numbers from various sources, including the CDC, Johns Hopkins, etc. The numbers are a) total cases in the US, b) total Covid-19 deaths in the US, and c) recoveries in the US. I just project out the first two. However, even though I use the same calculation to project them out (a 3-day growth rate), they have very different significance for what’s most important in the pandemic – the number of deaths (and if this were a pandemic caused by a disease that is unlikely to kill many people, neither I nor most others who write about Covid-19 would be spending the time to do this).

I’m projecting future deaths in two very different ways. The first way I project deaths is to take the total cases and multiply that by an estimated case mortality rate. I project cases by growing the number three days ago by the most recent 3-day growth rate. Of course, that’s accurate when projecting out a day or two, but it loses accuracy rapidly as we go forward. Since there’s no clear trend to the case numbers (recently the rate of increase has been falling, but there’s no assurance that will continue – see below), the best one can do is update the growth rate daily, so it always includes yesterday’s number.

The mortality rate I’m using now is 4%. This compares with 11% for Italy, and 6-8% for France and Spain, as well as 1.4% for South Korea. I discussed the mortality rate in yesterday’s post. I frankly think that 4% might end up being low, once the pandemic is over and all of the counting is done.

However, there is a data point that can provide some evidence for the actual mortality rate. That is the ratio of total deaths to closed cases, which I report above as well. Closed cases equals total deaths so far plus total recoveries. At the end of the pandemic, when all cases are closed one way or the other, this will provide the final mortality rate, and there will be no need to project it anymore. That is, unless you think the US government is fudging one or the other number, or both. China now is being accused of under-reporting both cases and deaths, so I’m not trusting the numbers from them in the future, unless they can clean up the doubts.

So what is the ratio of deaths to closed cases today? It’s 38%. Of course, if this were to end up being the actual mortality rate, it would mean that many tens of millions of Americans would die in the pandemic. Fortunately, this ratio will certainly come down, as more recoveries are listed. But this is why I currently believe the mortality rate will end up being no less than 4%, and very possibly more.

But let’s focus on the case number. How accurate is that? It’s almost certainly way low. The Imperial College of London (whose study was used to justify the administration’s social distancing rules a few weeks ago) estimated the actual cases are between five and ten times that number. Why is this the case? Of course, it’s because of the woefully inadequate level of testing, which continues to be woefully inadequate.

Moreover, testing is likely to continue to be woefully inadequate, since the president said two days ago, on a call with the governors (who were pointing out that they need more test kits) that he hadn’t heard there weren’t enough kits. This is probably a true statement, since it’s likely that the limited set of news sources he listens to isn’t talking about this problem. However, those of us who have to live in the real world hear every day about a) people who clearly are sick, who can’t even be tested, or b) people who finally get tested, but have to wait up to two weeks to get their results, at which point the results are moot – either the person has gotten over the disease or they’ve died. And even though new kits are becoming rapidly available, the number of tests a hospital can do with each kit depends on their having adequate supplies of the cotton swabs required to get the sample, as well as the chemical reagents needed to conduct the tests – and these are in increasingly short supply.

The bottom line is that the number of actual Covid-19 cases in the US is likely to be many times the reported cases for a long time, even if it ever catches up. And since there’s no good way to determine where in the range of 5-10 times the multiplier is now, and more importantly since it’s very likely that the multiplier itself is going up, as the people with unreported cases infect others, I’m just going to stick with projecting out the reported number. And I’ll continue to estimate total deaths over the course of the pandemic based on the reported numbers, as described at the beginning of this post.

But this means that the reported case number is a good representation of one thing only: the availability of tests. If the number of tests available were to double tomorrow, the reported cases would almost certainly double – on top of the normal rate of increase due to an increasing number of total cases. So the projections I’m making are almost certainly going to continue to increase for a long time.  The 3-day growth rate that I’m using to project out has varied between 115% and 33%. 33% is the most recent rate, so I’m using that in my projections, but as I said there’s no trend to that rate – it’s already gone over 100% twice during March.

But you have to remember that the number of cases is more than doubling every three days, even at the 33% rate. This is why the 100 cases reported at the beginning of March had grown to 164,000 yesterday, which in case you have the courage to look at it, means cases have increased 1,639 percent in 30 days. If we project that out over the next month, that means total cases will be 2.7 million at the end of April. And not surprisingly, that’s very close to the 2.8 million I’m projecting, since both numbers are based on the same three-day growth rate. This is why I’m projecting 1.7 million deaths over the whole pandemic, if the current 33% 3-day growth rate continues through April (at which point a total lockdown is put in place). And since the number of actual cases is some multiple of reported cases, if anything both of these April 30 numbers will be too low, not too high.

Of course, all of this comes from projecting out total cases. What about projecting total deaths, which I’m projecting independently? Those are calculated by growing the reported increase in deaths 3 days ago by the most recent 3-day growth rate, which as of today is 87% - and by the way, this rate has been going down since March 17, when it was 117% (where’s the luck of the Irish, anyway? Now that we need it most!).

Projecting the 87% rate through April 30 yields 2,183,000 total reported deaths as of that day – this isn’t an estimate of total deaths over the pandemic, as the other number is. So this is in effect hugely bigger than the 1.7 million figure estimated above, since there will be a lot more deaths coming, certainly in the millions.

Yet I’m sure many of you won’t believe the 1.7 million figure (which I also find unbelievable). Great, where did I go wrong? I think many of you will point out that there’s a lot more social distancing going on now, and that has to affect it. It certainly will, but remember that’s been going on for about 3 weeks already, and the case growth rate has already fallen significantly; it almost certainly has somewhat  further to fall. I certainly hope that continues – but then you have the opposite consideration, which is that the reported case rate is a fraction of the actual rate, and as testing ramps up, the number of new reported cases will ramp up as well. Which will win out? I don’t know, of course.

But there is one thing I do know: At the end of the pandemic, the two numbers will end up at the same point. Whether it will be closer to the number estimated based on cases or the number based on reported deaths so far isn’t clear, of course. However, the fact that the actual cases is a multiple of the reported ones only affects the reported case number. The actual deaths depend on the actual cases – people don’t die only if their case has been reported earlier. So at the moment, I have to say the final toll for the pandemic will be well above 1.7 million (perhaps the 2.2 million high estimate of the Imperial College).

Unless, of course, a total lockdown is imposed very soon – certainly before April 30 (of course, my 1.7 million projection for the total pandemic, based on cases, assumes there will be a total lockdown on that day). And it will be, too – although some dead wood will almost certainly need to be cleared out before this can happen. Why am I optimistic about this? Two words: exponential growth. On April 15, there will probably be more than 100,000 reported deaths. If that doesn’t get somebody’s attention, God help us. Probably nothing will.

Comments and questions are welcome. You can reach me at tom@tomalrich.com.