In just the last two days, over 3900 people died from Coronavirus in the U.S.A. The total U.S. death toll now stands at 14,788 (and rising). [Note: day 10 is March 10, 2020.]
The number of confirmed cases stands over 400,000 — but only a fraction of actual cases are confirmed because so few people get tested.
We can plot both total cases, and total fatalities, on the same plot using a logarithmic scale:
Let’s take a look, not at the total death toll, but at the new deaths per day:
It too appears to be rising exponentially, but we see something interesting on a logarithmic plot, both for new cases per day and new deaths per day:
The good news — and it is amazingly good news — is that the rate of increase, in new cases and in new fatalities, has slowed. The difference is statistically significant. The slowdown in the spread of coronovirus, and subsequent deaths, is from social distancing. It’s a fact: it’s impossible for social distancing not to slow the spread of the disease.
It took this long for two reasons. First: there’s a delay between slowing the spread of the disease and slowing fatalities, simply because it takes people time to die. Second, we (as a nation) were so late adopting preventive measures.
The daily death toll is still on the rise, but it had been doubling about every 2.5 days (the “doubling time”). Now it’s taking over 5 days to double (on average, that is). That gives us twice as much time to prepare for that burden. We need it.
So thanks to all of you participating in social distancing. Yes it makes a difference. Anyone who tells you different …
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Open Mind 
A key milestone is when the doubling time gets to be longer than people stay in the ICU. That means the ICUs will begin to empty out. This could start around 6% (doubling time almost 12 days). When the daily new case rate gets below 3% (doubling time 23 days), ER beds should start to empty out. So a good thing to watch is how close we are to those milestones. Italy has already reached 3%, and Spain is right behind them.
I still think a big part of the change point in the cases corresponds to the plateauing/changepoint in the US testing capacity.
Looking at your final plot, the slopes are parallel and offset by a factor of 100x, but toward the end, the cases taper down faster to an offset of about 20x.
Take a look at the plot of tests run per day at https://twitter.com/COVID19Tracking/status/1247644470444584961 they do a good job of aggregating the state data.
I’ll try an image of the graph:
Thanks to Tamino for beautiful work on the numbers. drf5n says “I still think a big part of the change point in the cases corresponds to the plateauing/changepoint in the US testing capacity.”
Please say more. Spell it out for me please.
Thanks
Mike
First, look at the graph in https://twitter.com/COVID19Tracking/status/1247644470444584961 or the data behind https://covidtracking.com/ in the google spreadsheet
From differencing that data, the time seried of new cases, tests, and deaths per day is:
Date TodayCases Tests TodayDeaths
20200408 30,570 135,304 1,874
20200407 31,263 137,367 1,941
20200406 29,023 155,045 1,182
20200405 26,553 138,243 1,184
20200404 33,840 216,536 1,352
20200403 32,906 139,613 1,178
20200402 28,239 117,698 1,084
20200401 26,000 100,989 954
20200331 24,240 104,117 807
20200330 21,469 113,503 511
20200329 20,827 95,647 463
20200328 18,787 109,037 435
20200327 18,712 107,329 367
20200326 16,807 97,806 263
20200325 11,974 76,820 225
20200324 9,802 65,239 204
20200323 10,273 54,131 73
20200322 8,682 46,236 126
20200321 6,164 43,926 53
20200320 5,314 34,342 59
20200319 3,989 26,883 48
20200318 2,007 20,628 22
20200317 1,704 13,204 19
20200316 846 14,40211
20200315 723 6,169 11
20200314 528 4,017 10
20200313 607 6,179 3
20200312 262 2,233 9
20200311 275 2,538 27
20200310 194 634 0
20200309 167 1,199 0
20200308 76 602 0
20200307 118 356 0
20200306 47 665 0
20200305 263 0
20200304
My point is that if reported testing capacity has plateaued at around 140Ktests/day it similarly plateaus the new cases to about 30Ktests/day and makes the growth of # of confirmed cases additive rather than exponential.
If our testing capacity isn’t expanding as fast as the infections are spreading, we end up rationing our tests to the most infected folks on the way into the hospitals, the %positive increases. If testing is plateaued, then the exponential growth curves taper off smoothy toward additive growth.
What I would expect Tamino’s graph to show with a pure social distancing effect (under adequate testing) is that both graphs would change to reflect a slower (but similar) exponential growth. I would expect the lag, but I wouldn’t expect the expoenential growth of deaths to be be steeper than the expoential growth of cases. With inadequate/plateaued testing, the linear/additive growth in testing could explain the difference in the growths.
Or if you were asking me to spell out the 100x to the 20x narrowing, I was eyeballing the factor as offsets on the log plots.
Very interesting comment but I do not really understand the implications. Is it that we are not flattening the curve as much as we think and this will continue to grow for a longer period of time than most are speculating thus leading to many more infections?
Wild guessing, but I think it could well be possible that social distancing slowed the spread from +33%/day to maybe +15-20%/day, but our limited testing slowed the detection to an additive +30K/day, which looks like slowing exponential growth from 15%/day down to 8%/day. If we speed up on tests enough to sample at the same relative rates we were sampling at before, we could discover the cases we didn’t see before until we catch back up to 15%/day growth.
In terms of Tamino’s 5th plot, the new cases and deaths per day, the cases trace might bend back up and rise to approach a line parallel and 100x higher than the post-distancing deaths line. It still would be a far better slope than the pre-social-distancing slope, but it will be discouraging to see cases rise dramatically above the weak additive growth in cases we’ve seen the last week or so.
We’re doing a terrible job managing the testing, so I can’t be certain of these numbers, but it is clear from the covidtracking.com data that US testing capacity hasn’t expanded anywhere near the early +30-40%/day growth rate of deaths and early testing or even half rate that for the last week or so.
An alternate explanation of the convergence between cases and deaths on Graph #5 could be that the testing is accurate and consistent throughout, but the outcomes for folks with positive tests is getting 5-10x worse.
It is surprising that the breakpoint for the number of new deaths is so quickly after the breakpoint for the number of new infections. The time difference between being infected and dying is much longer.
The time between the infection being confirmed and dying could naturally be shorter, especially if mostly really ill people are tested. But wouldn’t the former be the relevant time scale for the break point if it is due to social distancing?
It could also be that (part of) the decline in the increase of new infections and deaths is due to the virus spreading faster than the testing capacity.
To VV: the confirmed case data is simply junk data because the way it has been collected doesn’t provide any controls. I figured that was certainly the case based on things I have read, but drf5n has really nailed this down.
to D5: this part! I understand this and this is the simple exposition I was seeking: Drf5n says “my point is that if reported testing capacity has plateaued at around 140Ktests/day it similarly plateaus the new cases to about 30Ktests/day and makes the growth of # of confirmed cases additive rather than exponential.
If our testing capacity isn’t expanding as fast as the infections are spreading, we end up rationing our tests to the most infected folks on the way into the hospitals, the %positive increases. If testing is plateaued, then the exponential growth curves taper off smoothy toward additive growth.”
Thanks
Mike
I noticed this yesterday. I haven’t done the analysis yet (just downloaded the data from COVIDtracker this morning).
It appears that the change in slope for the # cases is greater/more significant than that for the # of deaths–as would be expected given the delay between onset and mortality. Is that the case? Can you give the fits?
Extrapolate/estimate infected people from death data, but expect that relationship to change over time as social distancing, masks etc change the R0 of coronavirus. The other thing that is likely changing is progress with treatment protocols at ICU level that will likely start to drop the death rate for corona. Confirmed case data is simply guess work (for the US) because we botched the testing so badly. btw: the botched testing? Not a problem sent to us by the WHO, this problem likely originated in the west wing of WH where there is clearly a pandemic of stupid and infectious ideas. Another cluster issue at work in that location.
Overview of some of the Covid stats from BBC:
“… consider 100 people who have been infected with Covid-19. Ten of them have it so severely that they go into hospital, where they test positive for Covid-19. The other 90 are not tested at all. One of the hospital patients then dies from the virus. The other 99 people survive.
That would give a case fatality rate of one in 10, or 10%. But the infection fatality rate would be just one in 100, or 1%.”
https://www.bbc.com/future/article/20200401-coronavirus-why-death-and-mortality-rates-differ?xtor=ES-213-%5BBBC%20Features%20Newsletter%5D-2020April10-%5BFuture%7c+Button%5D
@smallbluemike — there’s a good article on medium that bounds the measurable case fatality rates (CFR) between the deaths/cases and deaths/(deaths+recovered), since the deaths/cases underestimates it by including folks whose fates have yet to be decided in the denominator, and the deaths/(deaths+recovered) overestimates it since the ‘recovered’ excludes people who have not yet been proven recovered.
When all is said and done, the two do converge. But there is a big difference in outcomes when the hospital systems get overloaded or not. A non-overloaded medical system can reach Infection Fatality Rates (IFRs) of 0.5-1%, but if you exceed the capacity of the medical system to adequately treat people, you can get IFRs more like 4%.
View at Medium.com
Don’t forget that deaths due to the virus also are woefully underrreported. Home deaths in NYC are reported to be ~20-25 on average before COVID-19 but ten times that amount currently. AFAIK none of them enter the statistics.
… and that “ten times” thing was a week ago …
“. Home deaths in NYC are reported to be ~20-25 on average before COVID-19 but ten times that amount currently. AFAIK none of them enter the statistics.”
Incredible how many people question the mortality rate, as if any other way of measuring it is valid.And always accompanied by absurdly optimistic claims that 99% of undiagnosed positives will survive.
Sorry, but there are normally healthy people getting this virus, passing it to others because they feel fine, and then dying overnight. According to a New Orleans respiratory therapist, many of these rapid decliners are expiring with bloody froth coming from their mouths and nose.
Way too much we do not know about this disease, including whether there are now distinct strains, and what the antibody response is like. Just last week Dr Fauci was chuckling at the preposterous idea that one could survive Covid-19 and not have a robust antibody response. Chuckling at the notion that some people could recover from Covid and then get it again.
Don’t think anyone is laughing about such matters now.
The Covid-19 virus will undoubtedly be mutating. Indeed, there is mention (eg here is talk of an original “S-type” mutating into an “L-type” although some do not see these as different strains).
But proper mutation could be a good thing or a bad thing. Mutation of bugs usually involves them becoming more easily transmitted but it also usually involves them becoming less deadly; the balance will be critical and data on the mutation of deadly coronavirus (SARS & MERS) is absent as they never spread greatly and coronavirus mortality/death data in other species is presently restricted to knowing of its percentage existence within a population from antibody data. (So if 84% of living Chinese horshoe bats have antibodies, how many would have died from it and how many of those 16% withuot antibodies were infected but lost their immunity?)
The immune response in coronaviruses is well-known to be transcient and could be so transcient in some patients to be effectively non-existant.
Gingerbaker,
What Fauci actually said was that if you get COVID, you will likely be immune through at least September. That is based on his past experience with other Corona viruses–that is, on expert opinion. In the absence of data driven answers, an expert-opinion Bayesian prior may be about as good as we can do. People also laugh when placed in a stressful position.
This looks likes a reputable source to me
https://nextstrain.org/ncov/global
Anyone know any different please say. From Bedford lab research part of Fred Hutch in Seattle US.
I’m from UK and have no idea about it
Of course, the mortality of viruses in theory can only be computed at the end of the epidemic: most cases lead to death some time after having been detected.
But should not, over time, the average increase due to this delay keep nearly constant, and hence the mortality rate, i.e. the average death toll / case ratio?
The mortality rate does not, at least for the five countries considered (Germany, USA, France, Spain, Italy). Here is e.g. the US plot:
https://drive.google.com/file/d/1tHlwt33kgfLzJBRRKjBQ66N9a1ITr9yw/view
Not only it doesn’t; it doesn’t even increase linearly, as show the quadratic fits in purple resp. blue, starting with 1.26 % on March 23, till 3.56 on April 9.
Can anyone explain the reason for this permanent increase to me layperson?
N.B. : it was interesting to see how good the ratio prediction, computed on March 31 for April 9, has been using the purple quadratic fit (pred: 3.61 % vs. actual: 3.56 %).
Rgds
J.-P. D.
An interesting question. I have been graphing that ratio for USA, Spain, Italy and Canada, and I’m pretty sure the increase isn’t actually permanent. On the traces I have (starting 2/29) there’s initially a *decrease* in the ratio, which makes sense since cases lead. Then there is a slow increase.
On my graph, the rate of that increase has been slowing for both Italy and Spain, though not for the US or Canada. I’m looking for a sharp increase for the two former nations, because as they pass the peak caseload should nearly flatline, while deaths will keep on climbing for a couple of weeks.
Doc Snow
” … and I’m pretty sure the increase isn’t actually permanent. ”
You are right concerning SP and IT of course, I had only a superficial look at the spreadsheet data. Plots reveal more. My bad.
1. Spain
https://drive.google.com/file/d/10ywu7bocaIhTUWt5ILPdu7Gg0pumf1bK/view
2. Italy
https://drive.google.com/file/d/1UysSwvHvU-x0EmVIC7sCGaJ5MruIq8U3/view
Both show a slowdown in the death toll / case increase.
For France, the data follows the linear fit. I did not collect data for UK but think it will look like for the US.
For Italy and Spain, I think it’s now safe to say that death and caseload have now converged, with both currently running at ~3%/day. Not the North American nations, though. It’s interesting that the ratios for Italy and Spain are consistent over the trace, with the lines running in parallel for the whole duration monitored, barring a little noise here and there.
There are many questions of interpretation just in my little graph, but more of that another time.
The data so far available to identify a countries mortality rates and their timings relative to time-of-infectiond is probably not possible for most countries. Either the numbers reported are incomplete or reported late or the few weeks of data is inadequate to see the full picture.
South Korea which has done a lot of testing provides some interesting numbers. They suffered an 18-day spike in infections (the crazy Shincheonji cult was responsible for two-thirds of it) producing an average of 400 cases a day. The 24 days since have seen roughly a flat tail of 100 cases per day. So 75% of the infections were in the 18-day spike and 25% in the 24-day tail.
The resulting mortality rose quickly through the 18-day spike to 4 deaths per day, a rate that continued through the 24-following days with an added bulge bringinh mortality up to 6 per day half way through those 24 follow-on days. In terms of percentages of mortality, 25% have ocurred in the last 10 days. They possible still include some of the 75% of ‘spike’ infections.
Thus the mortality resulting from infection is played out over the 3+ weeks (or so) after infection.
Germany has also done a lot of testing. They have suffered a near constant rate of infection, roughly 4500 per day) over the past 24 days while mortality has risen steeply with no real sign of it leveling off. Again this sort-of suggests a 3-week post-infection mortality spread.
So then we have Italy whose data shows a peak in mortality 2 weeks after the peak in recorded infections (and with death/infection rates far in excess of S Korea or German levels), or Spain where the infection and mortality peaks were almost simultaneous. How to interpret such reported data will probably need some appreciation of the data actually provided.
And trying to use the UK or US numbers where both infection rates and death rates are still on the climb – that is surely far too soon.
My theory (see above) is that the sampling process for testing isn’t scaling consistently as the virus spreads, Since testing has plateaued to testing ~140K/day, it is limiting the new cases to an additive growth of ~30K/day. Dividing an exponentially increasing metric like deaths by an additive growth metric to would give a non-constant and increasing ratio.
Additive US testing growth graph and refs to data: https://twitter.com/COVID19Tracking/status/1249083172169469953
Also, since it takes some time between diagnosis and death, some folks model the lag and find a better relation between cases some number of days ahead of deaths.
Since you often analyze global surface temperature trends, Dr. Foster, I thought you might be interested in the following:
HadOST is a recent instrumental global surface temperature trend analysis. It uses land air data from Cowtan+Way, with sea surface temperature data from the Hadley Centre Sea Ice and Sea Surface Temperature analysis (HadISST2) and the Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA). It is used in the following sources:
1 : https://journals.ametsoc.org/doi/pdf/10.1175/JCLI-D-18-0555.1
2 : https://www.carbonbrief.org/guest-post-why-natural-cycles-only-play-small-role-in-rate-of-global-warming
I’m interested in HadOST in part because it seems to show accelerating global warming, as per link 2 above. Dr. Haustein, the lead author of link 1 above, has posted a link to the data for HadOST: