# Lockdown WORKS

Over 2400 Americans died yesterday from Coronavirus. Here are the new deaths per day (“daily mortality”) in the USA since March 10, 2020 (note: this is an exponential plot)

As bad as that news is, there is good news too. Notice that the daily mortality has levelled off. It might still be rising, but then again it might not. But it’s definitley not increasing at the same rate it was before.

There was a time, from about the 10th to the 25th of March, when daily mortality was rising at a rate of about 30% per day. At that rate, it was doubling about every 2½ days. Now, it might have stopped rising altogether.

The reason is: social distancing and the lockdown. That’s the reason the death toll isn’t WAY higher than it is. That’s the reason the death toll isn’t still rising fast.

Here’s a mathematical approximation of the daily mortality (a “piecewise linear fit”)

It shows visually, and more to the point it can confirm statistically, that yes the rate of increase dropped, and that for the past week or so, there’s no evidence of continued increase. It might be — and then again, it might not.

And that is superb news, because without social distancing and the lockdown, there is no doubt that the daily death rate would still be rising.

The reason the lockdown is working: you.

Thanks to all for kind donations to support the blog. If you want to help, please visit the donation link below.

This blog is made possible by readers like you; join others by donating at My Wee Dragon.

### 37 responses to “Lockdown WORKS”

1. kinimod

Wow. Very good. A death has been a new infection about 10 to 12 days before, so the curve of new infections should look even better.

2. chrisd

Prediction: If the death toll fails to reach the 100,000-200,000 range that was modeled, a new class of deniers will say, “See? It was all overblown, garbage models, alarmist scientists at it again!”

Never mind that we failed to reach that level of mortality BECAUSE we listened to the scientists and took appropriate actions.

This scenario can be seen over and over. Think acid rain, Y2K, and the ozone hole for starters.

• Michael Sweet

There are widespread reports of people dying in their homes in the USA. The bodies are taken straight to the morgue and they are not tested for corona virus. People avoid going to the hospital because they cannot afford the costs. It will take a long time to sort how many excess deaths there really are. In many locations the morgues do not have tests to confirm corona virus. New York added about 3500 deaths yesterday to their count for some of the missed deaths.

• That must be the main driver of the spike to ~6000 new deaths that Worldometers records for April 14th.

That statistical anomaly is about the only shred of evidence giving color to the so-called president’s assertion that we’ve reached some sort of peak in the US. We’re still running an exponential increase in cumulative confirmed cases, at 5% per day, which is a trajectory that would, if sustained, take us to 1.3 million cases or so by the end of the month.

3. Mark

Surely that’s a piecewise exponential fit.

4. Here in New Zealand, we went into lockdown quite early. We’re a small nation, so it’s hard to compare to other countries without doing the maths. However, as soon as it was perceived that community transmission was occurring, we went into lock down (with a couple of days warning, with those couple of days being at a partial lockdown). It does appear to be working, with new cases being in the teens for the last few days and most of those being connected to existing cases. If the improvement continues, we might relax some restrictions towards the end of next week, though there will still be many restrictions similar to lock down.

Fingers crossed, there is a chance that we could eliminate the virus from our country, but keeping out would take a continuation of very strict border controls – difficult for a country with a (formerly) large tourism industry.

• John Brookes

There is something weird about the way Australia and New Zealand have done so well. Australia’s death rate is 3 per million, and New Zealand’s is 2 per million. Of the US states, only Wyoming is comparable.

I’m in Western Australia, and our lockdown was not particularly early, or particularly severe. Most shops remain open, and you can still get a hair cut (not that many people are). Yet the instant we closed our borders, the rise in infections slowed dramatically. Indeed, the only way I can account for Australia’s numbers is to say that the period of roughly exponential growth (February 29 to March 22nd) was driven almost entirely by a constant influx of arrivals from overseas, and that as there was exponential growth in cases overseas (predominantly US and Europe), the fraction of infected arrivals grew exponentially.

It would seem that local transmission is very minor. And that doesn’t make sense to me unless the virus is strongly seasonal. We in Perth have been having our usual Indian summer, with only the last few days having maximum temperatures below 25C. Sydney too has enjoyed balmy weather, but Victoria and Tasmania have had their fair share of cool, wet weather.

So I can’t figure out what is happening here, compared to Europe and the US.

• @John Brooke’s,

I would suggest waiting a few weeks before doing a victory dance.

• Diaminedave

I would say that the quick easy statistic is population density.
Large open thoroughfares – easy social distancing
on top of a pretty quick response

5. Thomas P

This still leaves the more long term problem of how to restart society. You can’t keep a lockdown going forever.

6. Diaminedave

In a lot of ways the urban landscape of America is better designed to prevent the movement of a virus. Driving to the shops is normal. Pavements (sidewalks) are massive. Lots of areas of the UK and Europe do not have that luxury. As a rough guide US pop density is roughly a third that of Spain and about an eighth of Uk or Germany.
It is difficult to envisage here in Europe how the health care system in the US actually works. Will large numbers of would be sufferers avoid going to medical facilities because they could not afford it?
Will those figures be reported, how is the data collected and how accurate is it?
Considering its own population density and its lack of cases Taiwan has got to be a shining example of how to deal with a pandemic. This is surely the best option for any and all countries to get out of this mess TEST, TEST,TEST and trace and isolate contacts.

I know that pop density is not the only variable I just think it is one of the more useful guides to how well a government is doing at mitigating effects of this pandemic.
In the UK it has bought to the fore the lack of planning and preparedness for such an event especially when compared to countries of a similar ‘type’ such as Taiwan or S Korea or Germany.

7. One caveat: one would also expect a flattening of the fataltiy curve if a major part of the population has already been infected and has become largely immune, and/or if most of the most at-risk population to die has been infected and has died.

Don’t get me wrong, this is very unlikely to be the case. Even if you really lowball the fatality rate down to flu-levels (0.1%), it would mean at most 26 million Americans have been infected, or at most 7-8% of the total population. That’s not nearly enough to bend the curve to this extent.

More realistically, infection fatality risks seems to be *at least* 0.3-0.4%, meaning likely less than 2% of the US population is infected at this moment.

8. Ralph Feltens

Just 2 days ago, the German Robert-Koch-Institut (RKI) which is the national Institution for tracking and surveying the Corona pandemic has pre-released a bulletin, summarized here (Article – as well as the original pre-publication – are in German only: https://www.heise.de/newsticker/meldung/Neue-RKI-Corona-Fall-Studie-Einfluss-der-Kontaktsperre-eher-maessig-4702096.html ). With missing data imputation and taking into account different types of delay for new infections to appear in the daily datasets, a “Nowcast” is calculated, that shows the “real” number of new infections for any given day and also the current reproduction times (the figures shown should be intelligible).
The Bulletin itself can be found here: https://www.rki.de/DE/Content/Infekt/EpidBull/Archiv/2020/Ausgaben/17_20_SARS-CoV2_vorab.pdf?__blob=publicationFile

Interestingly, the measures taken around the 9th and the 16th of March (increased Hygiene standards, stopping of events with more than 1000 people, closing of schools) showed a strong effekt. However, Lockdown measures (such as closing most shops and factories and enforcing social distancing) implemented around 23rd of March do not seem to have contributed to the further development of the pandemic.

• deconstruct

“Lockdown measures (such as closing most shops and factories and enforcing social distancing) implemented around 23rd of March do not seem to have contributed to the further development of the pandemic”
How would you know that? Do you know, how high the numbers would have been, without lockdown measures?

It would be very surprising, if it would not slow the spread of a very transmissive virus, when most people stay most of the time at home and do not meet other persons outside of their household.

What reasons would you think of, that this measures won’t have a very strong effect on transmission rates?

• Ralph Feltens

I do not have an explanation. But if youl look at the curve in Fig. 2 and, even more convincingly, at the reproduktion facor plotted in Fig. 4, you will seee that reproduction rate had already come down to the current plateau level of ~1.0 when these measures were implemented around 23rd of March.

One has to consider, however, that some of the larger companies such as car manufacturers had already told workers to stay at home (for home office or “Kurzarbeit”).

• deconstruct

@Ralph Feltens

I have looked at that figure (https://imgur.com/a/ZUZGzb5) but I still can’t follow your argument.Yes, the figure shows, that after 23rd March the reproduction rate does not drop further.

R is the quotient of the number of new cases in two consecutive periods of 4 days each.
This means, that if the number of new cases has increased in the second time period, R is above 1. If the number of new cases is the same in both time periods, the reproduction number is 1.

This is a very crude and unreliable estimate, because it only works on the assumption, that the number of cases detected is also the same in all those time-periods.
But testing in Germany was ramped up intensively, it is now roughly 4 times higher then at the begining of the measures. So, with testing still increasing you will now obviously find a higher number of cases in the second of those time-periods that are compared for calculating R and therefore the calculated value of R will go down slower, even if the real value of R would have declined more.

If you read the paper, this is also stated in the text (next to another reason, why the calculated value R might not be dropping anymore):

“One reason why the decline in new cases is relatively slow despite the serious measures taken is that the virus spreads more strongly among the elderly after 18 March and we are increasingly seeing outbreaks in nursing homes and hospitals. A further aspect is, however, that in Germany the testing capacities have been significantly increased and, through more intensive testing, an overall larger proportion of infections are becoming visible. This structural effect and the resulting increase in the number of reports can lead to the current R-value slightly overestimating the real situation. An adjustment for the higher test rates is not possible without further ado, since no sufficiently differentiated test data is available.”

So, no, I don’t think that is plausible, that R would not have dropped further, with those strong measures now in place. There is no medical, social or physical reason, of why those measures would not have a strong effect and I am sure, that the calculate value of R is simply not accurate, because of the reasons stated above.

• Al Rodger

deconstruct,
You say that the German testing rate “is now roughly 4 times higher then at the begining of the measures.” I would be interested to know if you have a source for that value.
There is numbers given for the German weekly testing rate on this OurWorldInData.org web page which shows a doubling of testing between the week beginning 8/3/20 and week beginning 15/3/20 with the rate of testing constant thereafter. This data is also given as test per case, this an accumulative number whch shows a 90% drop with the increasing rate of cases appearing, by week 147, 66, 28, 18, 15, 14. The peak R value falls into the first of these weeks and the leveling-out of R within the second week.

• @Ralph Feltens,

Yes, @deconstruct is right. While it is statistically possible to construct an inference against the counterfactual to establish causation (Imbens, Rubin, 2015), under the present circumstances, it is very difficult, both because of uncertain measurements and uncertain lags in reporting.

Moreover, the mechanism and premises of the distancing or “lockdown” are nothing new and have been modelled well. While the Washington Post made assumptions about there being a “herd immunity”, they did an excellent job of simulating how this works.

The most direct evidence comes from Asia, where lift and suppress is turning into an engineering art form. Simply put, without self-discipline in a populace, one resenting an initial lockdown, it is not likely that future attempts at reimposing released lockdowns in response to surges in deaths will work, something which I bet weighs heavily upon the minds of those responsible in the US and UK.

The net is going to be many more body bags than necessary, and a trashed economy due to sloppy controls.

The only upside is that some states and communities have exhibited more self-discipline, and are learning how to deal with the discomforts and economic dislocations of lockdowns, both in marshalling their own spirits, and in marshalling social supports and, so, when suppressions are needed again, they’ll respond, knowing these are likely to be shorter, and manageable. That upside is justice: The communities and states which are rebelling are showing no such self-discipline and they’ll suffer, both in outcomes and in economy, because the rules are being set primarily by Nature, not by government. The Northeast and parts of the West Coast will get through this and learn how to thrive among these new rules, while the rest of the country will be struggling and asking (once again) for handouts.

Of course, it may be no coincidence that the sections of the country which show the self-discipline, the Northeast and parts of the West Coast, are also some of the wealthiest, most economically productive, invested in high technology, and best educated.

And, speaking for myself, I think the Northeast will remember how it was treated by Republicans, the Gang of the Orange Mango, and some of these other states. You want separation from foreign countries: I say impose economic separation on states who were not there for us during a time of peril. The same goes for Northeast corporations and businesses who chafe under the rules: Care not for your neighbor here, documented or not, white or not, and we care not for you. Leave.

9. Looking at the new cases per day for various countries on the JHU site tells an interesting tale. A few countries appear to have gotten it right–NZ, Taiwan, S. Korea, Austria (the only country with a male leader to have gotten it right), etc. These countries are almost to the point where the economy could start to open again. Germany is a little behind Austria, but definitely getting there. Spain deserves credit for pulling the situation back from the brink and getting things mostly under control. Many countries have flattened the curve, but getting cases to decline has been a challenge–Italy definitely falls into this category. Russia is a basket case–the numbers are unreliable, but they still show catastrophe in the offing if measures are not taken immediately. Iran is an interesting case, as there is an initial rise, a leveling and then a much larger hump. It looks like what one would expect if they tried to open things back up too quickly.

I expect that the yahoos will cause the US curve to do something similar, since their only goal is to hold things together until November so the orange shit gibbon can get re-elected.

• Looks to me as though Canada may have managed to get to a decline in new cases as well, though due to the relatively small numbers of cases relative to some of the other nations you discuss, the data are naturally noisier. But on the Worldometers tracker, which graphs new cases, the worst day for Canada was on April 5. It’s been up and down since then, but more down than up. Time will of course tell whether what I think I see is signal or just noise.

I’d say, though, that Canada ought to get some credit for holding their per capita caseload down relative to some of the others; currently it’s 793/million, as compared with the US’s 2,040 per million. A low bar? Sure, but it’s also lower than any of the others mentioned–except, ironically, Russia, which despite its rapid ascending trend in caseload, still is only at 191 cases per million. I read that a lot of that country isn’t very much affected yet; the hot spot is Moscow.

https://www.worldometers.info/coronavirus/#countries

• Sadly, the apparent decline in new Canadian cases turned out to be noise; consecutive new caseload records were set on the 16th and 17th.

• Al Rodger

Doc Snow,
The national daily data is often very lumpy with a daily figure often composed of data spread over half a week or more. So I wouldn’t put too much store by data as it arrives.

With that in mind, I think it is now safe to say that, as well as Lockdown working, South Korea shows test-&-trace can turn a Covid-19 outbreak aroind, with peak infection rates dropped to 3% over a seven week period. Given the world may only have test-&-trace as a workable alternative to Lockdown for some months, it is very reassuring to see test-&-trace working.
The one worry is that, if South Korea has tested-&-traced its way out of this infection, it presumably has been finding he vast majority of the infection. That makes its 2% mortality rate look a bit worrying – miles higher than the sub-1% figures I see being suggested elsewhere. One thought was that, with massive mortality rates amongst the old, a more-elderly age profile could have boosted the death rate significantl. But comparing overall mortality calculated using the age distribution of infection with that calculated using the Korean national age profile, there is no impact on mortaility rates. The Korean situation also shows a long tail for the mortality. The peak infection was reported seven weeks ago and the rate of mortality is still not showing a convincing level of tailing off. So that 2% figure keeps creeping upward.

• @Al Rodger,

The other disturbing thing that came from Korea yesterday was that a portion of those recovered seem susceptible to the virus again.

• Al Rodger

ecoquant,
The instances of people testing positive having previously recovered from Covid-19 have been reported from Korea (& elsewhere) a lot earlier than “yesterday” and the jury is still out on why this is happening. Generally folk do not seem to be blaming a loss of immunity or that the recovered patient is “suseptable” to external re-infection.
Saying that, the long-term immunity to a coronavirus infection has always been considered doubtful and a matter of concern and becoming worthy of study ((eg here) since the arrival of SARS.

• Thanks. While experience with SARS-CoV may be instructive, that it only has 80% commonality in its genome with SARS-CoV-2 is of some concern. The bat SARS virus is much closer, 98%. Fortunately, there are recently experimental results with a rhesus monkey model to indicate immunity is conferred.

It’s becoming clearer now that the only way out of the economy vs pandemic mess is to use privacy-invading tracking. Not sure that will sit well with the anti-quarantine Gangs of the Orange Mango.

10. Diaminedave

I hate to say it but Australia seems to have very similar numbers to New Zealand.

• deconstruct

Australia is indeed doing good.

But Japan? They see at the moment a strong rise in their cases and they have done only very limited testing. Australia tests 20 (!) times as much as Japan. For all of Japan they have done only around 100.000 tests so far. That is the amount of tests a country like Germany (with much less population) is doing on a single day now. And yesterday Japan declared a nationwide state of emergency…

And I would strongly suspect, that if Japan would have done the same testing rates as Germany or Australia, they would have reported a lot more cases. But my other suspicion is, that Japans premier Abe didn’t want that (“waste of resources”), because he didn’t want to see to many cases to be reported, because he had hoped till the end, that they might be able to carry out the Olympic Summer Games (which was completely unrealistic already weeks before the games got canceled).

What I want to say in general:
The reported number of cases of any country can’t just be compared easily, because you have to take into account that countries do test at *very* different rates, report deaths/cases by *very* different standards, are in different phases of the pandemic, etc.

Typically if you fail to contain the cases and you see a larger outbreak, containment does not work anymore (because you have to many cases a day to be able to trace and quarantine all contacts) and cases spike. The only country that did manage to go from a substantial outbreak back to containment is South Korea. Many other countries did manage to hold containment for a while, but then failed eventually. Look at Singapore for example, that was also louded for their containment in the first weeks/months, but now sees an enourmous outbreak with exponential growth.Or Russia also did manage to contain it a long time (and did a lot of testing, if you believe their official numbers), but is now also having a massive spike in cases…

And others like the US didn’t even really try doing containment and just letting things happen until it was to late anyway…

• Diaminedave

Mea Culpa,
I did not look at the testing data, I did not realise they had done so few tests per head of population. I expected them too! Again look at the data, me that is!
Singapore is weird. They seem to have done all the right things but then housed the people doing the work for them with little space and therefore no social distancing! (according to report I saw in the guardian). It is almost as though those workers are a separate species

11. Reblogged this on hypergeometric and commented:
Tamino favors LASSO and piecewise linear models. I favor splines, especially penalized smoothing splines via the R package pspline, using generalized cross validation to set the smoothing parameter. Tamino looks for breaks in the piecewise linear case to check for and test for significant changes. I use the first and higher derivatives of the spline.

Both methods are sound and good.

I don’t know how you might use a random forest regression for this purpose, but I bet there is a way. I doubt it is as good, though.

• Sorry, change LASSO in above to LOESS.

12. As I noted in a comment at the Financial Times, overestimating an actual outcome in a matter this dire is probably what an informed observer wants to see. When errors are made in this case, the losses incurred underestimating deaths and suffering or overestimating deaths and suffering are not symmetric about the estimate. High levels of death and suffering are to be avoided, and, since there is less of an underestimate and so less death and suffering if the estimate trends high, that’s where you would expect it to go.

Whether or not people bother to assign losses to errors, they actually do. But these should be paid attention to when they matter.

13. tamino,

Having trouble logging into WordPress, so I don’t know if this will post.

How do I test cointegration for two variables that are not integrated to the same level? E.g. if temperature anomalies are I(1) and CO2 is I(2), could I use an Engel-Granger test? Please let me know.

14. P.S. climatefreak = Barton Paul Levenson. I tried to set up a blog recently and this resulted, giving me all kinds of trouble whenever I try to comment on a WordPress blog. God, I hate those people.

15. Very pleased to note that, for the first time, active cases dropped in Italy and Spain! True, the Italian number was only -20, so really it’s statistically more like a flatlining than a decline, but still. The proverbial curve has been flattening in both nations, but this is the first really substantial indicator that a meaningful peak has actually been reached.

“Really substantial” is deliberately subjective; some might view the daily new cases peak as “really substantial,” and I couldn’t really fault them. For example, in Spain the ‘new cases’ peak occurred on March 26, when 8,271 new cases were reported, with a secondary peak of 8,195 on April 1. But I’d tend to use the non-exclusive term “promising.” YMMV.

16. I learned a rule-of-thumb from an epidemiologist friend yesterday. To assess whether or not enough testing is being done in a populace, test with a good lab test (high specificity and sensitivity) and crank up until see 9 negative results for each positive.

I’m going to spend some time today or tomorrow trying to understand where that ratio comes from but apparently it is based upon broad averages of viral presence across the globe.

• Al Rodger

ecoquant,
Michael Ryan, executive director of the WHO Health Emergencies Program, is quoted putting the ratio as 10:1 in this NPR article. The ratio is for tests used in Test-&-Trace and presumably will not include either testing of health workers & carers or surveys of the general public being used to identify national levels of infection.

A good example of how to Test-&-Trace your way out of Covid-19 is South Korea. They suffered an outbreak reaching 900 cases/day which they have brought under control with Test-&-Trace. Through the height of the outbreak they managed a Test/Positive Ratio above 20 on all but 9 days and it never fell below 10 through the height of the outbreak. The Ratio averaged 90 through the ‘fat tail’ of the outbreak and has been running at 250 in recent days with the cases/day falling from a few dozen to about ten. (Numbers from data at OurWorldInData.org.)

A good example of how not to Test-&-Trace your way out of Covid-19 is my place of residence – the UK. I’ve been monitoring the UK’s Test/PositiveTest Ratio for a while now, ever since the government started giving all the symptoms of that deadly disease Terminal Arse-Coveritis.
The government stopped all Test-&-Trace when they couldn’t keep ahead of the infection rate and while always talking of increasing testing, their bold statements of being in control tend not to be matched by any reality. The Test/PositiveTest Ratio was up at 200 back when the outbreak arrived (so much better positioned than South Korea) but the Ratio rapidly declined as increased testing has not kept pace with the increased infection. The Ratio is running at 3 today and involves zero Test-&-Trace. It will soon bottom out as the Lockdown works its business and as the hapless government slowly works out how to turn testing capacity into actual real tests, and then hopefully actual real useful tests.

17. barry

woodfortrees, a handy online app for simple plots of climate related data, has now added in some simple COVID19 data to plot.

http://www.woodfortrees.org/plot/