Neil's Note: This was a follow-up to my earlier comment at Watts Up with That about the corona virus in the Netherlands.
Saturday, 11 April 2020
I found out something interesting in my researches today. I set out to answer the question: Why are the "hot spots" in the Netherlands, with the most (hospitalized) COVID cases per population, mostly in rural areas in the south-east part of the country, that I've never heard of? Even though I lived there for three years, albeit 40 years ago? I chose the Netherlands, partly because I know the country and can still read the language, and also because their data is both comprehensive and believable.
What I found was that the 10 municipalities which have been hardest hit in proportion to population (175 to 300+ hospital cases per 100,000 inhabitants) have something in common. They are in the Catholic areas of the country (except Oudewater, which has a long history of tolerance towards Catholics), and several of them are renowned for their Carnival festivities. Moreover, they're not so far away from Tilburg, where the first confirmed case of the virus in the Netherlands was reported on February 27th. The Carnival week-end was February 28th/29th. Confirmed cases of the virus multiplied by 8 or so between March 4th and 9th, by which time a third of those cases were in the Noord-Brabant province, which includes Tilburg.
In contrast, in the highly populated areas, the cases per population are far lower. I looked at the statistics for the 15 most densely populated municipalities in the country, including Amsterdam. They ranged from 20.3 per 100,000 in Krimpen aan den Ijssel (coincidentally, where I lived when I was there) to 43.2 in neighbouring Capelle aan den Ijssel. Odd! Two places on opposite sides of a river, connected by a short bridge, with such different infection rates? And in both cases, a lot of their working residents do their work in Rotterdam? Mmmm... Capelle, 40 years ago at least, was mostly blocks of high-rise flats, each surrounded by greenery. Krimpen, while closely packed, was low-rise; mainly conventional two-story houses.
What this suggests to me is that the virus spreads most rapidly when there are a lot of people in close proximity, as at Carnival and in high-rise blocks. It isn't how far you keep away from the next person that matters; it's how far you keep away from crowds. And that may provide a reason why the Austrians have done so well, relatively, in this epidemic. When they had a major problem with patients who had been to Ischgl, they quarantined the whole town. The Icelanders also took this approach, banning large public assemblies, but only putting individuals into lockdown in one small area.
Am I on right lines, or am I way off base?
Friday, 10 April 2020
Neil's Note: This is another comment I made at Watts Up with That. This one was in reply to "suffolkboy" who was looking to try to relate the coronovirus figures to "Farr's Law." That is a 19th-century law of epidemics, which postulates that new cases per period in time will often follow a normal distribution. That means that cumulative total cases will follow an S-shaped curve, beginning with an exponential increase, straightening out in the middle, then levelling out in a symmetrical way, in a similar shape to the first half of the epidemic.
Here's the comment:
Here's the comment:
suffolkboy, thank you for your very apt and lucid comment. I too am trying make as much sense out of all this as I can. The way I thought of to test whether Farr's Law (S shaped cumulative cases function, with symmetrical curves at the two ends) applies was to look at the countries which are nearest to over the epidemic.
South Korea seems to go for a while as if it is going to be symmetrical, but instead around March 10th settles into a fairly constant linear upward trend. Presumably this is due to increased roll-out of testing? Or could it be that the virus is expanding into parts of the country it hasn't reached before?
The Faeroe Islands gives something very close to a Farr's Law curve. It's such a small population that the virus seems to have gone straight through them all before anybody could do anything. They have tested 11% of their population now, so their figures are going to be as good as anyone's. Furthermore, they haven't had a single death yet! Iceland is on a similar path (9.5% of the population tested, 6 deaths), but the straightening-out of the cumulative cases curve isn't clear yet. Why the death toll in Iceland and the Faeroes is so low, in comparison to other small isolated places like San Marino and Andorra, which are among the very worst, is an interesting question.
Austria is showing a good attempt at a symmetrical curve, but if you look at the new daily cases it looks as if the right tail is going to be longer than the left. Maybe twice as long? But again, perhaps that's due to expanded testing finding cases which wouldn't have been found before.
What I have been trying to do is use an Excel spreadsheet to try to detect the peak in each country directly. What I do is average each day's reading with the 3 days prior and the 3 days after. This seems to smooth the data (which seems in most countries to have a persistent "wobble" in the new case count, with a period of 5-6 days) quite well. Here is what I've found so far:
Spain - peaked on 29th March, now down to 75% of peak.
Italy - peaked on 23rd March, now 72% of peak.
Germany - peaked on 30th March, now 82% of peak.
Switzerland - peaked on 22nd March, now 67% of peak.
Austria - peaked on 25th March, now 40% of peak. They seem to be the country to follow.
Portugal - peaked on 31st March, now 88% of peak.
Norway - peaked on 26th March, now 56% of peak. Second best after the Austrians.
Belgium and the Netherlands are currently wobbling around what seems likely to be their peak. The UK, Sweden, Ireland and Denmark are still trending upwards, but increasingly slowly. France, I haven't even looked at, because all their data prior to 3rd April is in essence rubbish.
As to whether it is the lockdowns that are having an effect, or the virus starting to peter out naturally (which would require an earlier entry of the virus to each country, and a much higher proportion of unreported asymptomatic and mild cases, than we're being led to expect), I'm firmly in the agnostic camp at the moment. Evidence for the lockdowns doing it is that the time lapse from lockdown to peak seems to be varying between about 6 and 15 days. But this could simply be a result of each government deciding to impose a lockdown at much the same point in the epidemic. Hopefully, Sweden will give us some conclusive data one way or another.
On the other hand, there's evidence from the geographical distribution of cases in the Netherlands for a much higher level of immunity in the general population than many think. Most of the "hot spots" there are in rural areas, many of them way out in the south-east of the country. The densely populated Randstad is little affected. In particular, Amsterdam and Rotterdam are showing lower cases per population even than some of the more suburban areas around them. That will need some explaining.
Tuesday, 7 April 2020
I’ve been doing some more playing with the new-cases figures for coronavirus. I took the raw figures since March 17th from worldometers.info for the following countries: Spain, Italy, Germany, UK, Switzerland, Belgium, Netherlands, Austria, Portugal, Sweden, Norway, Ireland, Denmark. I left out France, because of their recent data issues. I used Excel to smooth the figures over 7-day periods (so e.g. for March 20th I averaged the figures from March 17th to 23rd inclusive). I chose 7 days, because that is roughly the period of the “wobble” I saw in many countries’ data when I first looked into the detail a few days ago.
I came up with some interesting results. The countries divided clearly into three groups:
(1) Eight in which the smoothed new cases have already peaked and are on a downward trend: Spain, Italy, Germany, Switzerland, Belgium, Austria, Portugal, Norway.
(2) One (Netherlands) where smoothed new cases have only very recently peaked, and it’s not clear whether or not that will be the final peak.
(3) Four in which the smoothed new cases have not yet peaked: UK, Sweden, Ireland, Denmark.
For the first two groups, I worked out by how many per cent per day the numbers have been falling since the peak. I took the latest smoothed number of cases (dated 3rd April, because that’s the last day for which I have a full 3 days of following data), divided by the peak number of cases, then took the Nth root, where N is the number of days between the peak and 3rd April, and converted the result to a percentage decay per day. My Excel formula was:
=ROUND((1-EXP(LN(<latest count>/< count at peak>)/<number of days since peak>))*100,2)
Obviously, the Netherlands was an outlier on the low side. Of the remainder, six all showed a decay rate between 1.8% and 2.8% per day: Germany 2.79%, Switzerland 2.52%, Spain and Italy both 2.25%, Belgium 2.03%, Portugal 1.8%. If I take the Spanish and Italian figure as representative, that corresponds to a half-life of 30 days for new cases of the virus.
But in some places, it’s better than we thought. Norway is showing a decay rate of 3.55% per day, and Austria a whopping 7.25% per day. Indeed, the smoothed new Austrian cases per day are already down very nearly to half of what they were at their peak on 25th March.
Whatever the Austrians have been doing to combat this virus, seems to be working. They did quarantine one particular town which was a big source of infection, which as far as I know no-one else has done. And apparently, they have mandated that face-masks are worn in stores; but that only started yesterday, so can’t have had any effect on these figures. So why, I wonder, has the Austrian experience been so much less bad than anyone else’s? Inquiring minds want to know, and to apply that knowledge.
Indeed, the Austrians, and the Danes too, have very recently announced that the restrictions are to be relaxed over the next few weeks. For Europeans it looks as if, as Winston Churchill famously said after the battle of El Alamein: “Now this is not the end. It is not even the beginning of the end. But it is, perhaps, the end of the beginning.”
Sunday, 5 April 2020
(Neil’s Note: This was a blog comment I made in response to Christopher Monckton’s article “Are Lockdowns Working?” at https://wattsupwiththat.com/2020/04/04/are-lockdowns-working/#comment-2956309 about the efficacy of lockdowns at lowering the rate of spread of the currently raging coronavirus epidemic. I made some further comments in replies, too).
The former mathematician in me decided it was about time to use the data we have to make a direct assessment of Christopher Monckton’s hypothesis that the lockdowns are working.
What I did was look, not at comparisons between countries, but at the graphs of total cases and daily new cases which are readily available on worldometers.info. As long as the reporting of cases within a country is done in the same way each day, I should be able to make reasonably reliable comparisons between the numbers of cases in a country at different stages of the epidemic. I simply picked the top 12 European countries in terms of total number of cases, and looked at the graphs for each.
First up was Spain. Something interesting jumped right out of the paper at me when I looked at the total cases graph. The curve comes in two parts; an exponential part, followed by a pretty much linear part. The transition in Spain was quite sharp, around March 24th. The daily new cases graph shows it, too; new cases were increasing exponentially up to about that date, and since then have been increasing far less, or even static. The Spaniards seem to have brought in their lockdown very quickly on March 13th and 14th, so the change in the regime came about 10 days after lockdown. Not at all far from the incubation period of the virus, of which the best estimate I have heard is 6 to 14 days.
Next, Italy. Here, you see the same thing. An exponential phase, followed by a linear phase. The transition came somewhere around the peak of March 20th. When did the Italians go into full lockdown? March 8th, says Wikipedia. 12 days.
You can also see a wobble in the total cases line since 20th March. This shows up as an oscillation in the daily new cases, with a period which looks to be around 5 to 6 days. And the Italian daily cases now look as if they’re on a downward trend. Furthermore, you can see a similar wobble in the data before 20th March – there are often peaks 5 or 6 days apart. I don’t know what it is about the virus that causes this effect, but I’m not an epidemiologist.
Looking again more closely at the Spanish data, you can see the wobble there too, though it’s easier to see if you look at the minima rather than the maxima.
To Germany. Again, an exponential part followed by a linear part with a wobble. The wobble seems to have a bit longer period here, 6 to 7 days. The peak day so far was March 27th, only 5 days after Germany went into full lockdown. But equally, the effect may have come near the mid-point of the cycle. It’s not yet clear whether the overall trend in new cases in Germany now is up as in Spain, or down as in Italy. Time will tell.
The French problems with nursing home deaths data seem also to have applied to case data from those sources, so I’ll skip France.
UK data is inconclusive, but you surely can see that wobble between March 27th and April 1st! We’ll have to wait another week to see on this one. My best guess is a graph similar to Germany’s, with the transition to linear coming in the middle of the next cycle, since full lockdown began on March 24th.
Switzerland follows the Italian model of peaking, then starting to go down gradually. The wobble is a lot less obvious here. The peak on March 20th was only 4 days after the Swiss went into full lockdown, but they did start a partial lockdown on February 28th, and the Swiss are very law-abiding people.
Belgium started lockdown on March 18th, and the transition to linear may well have come around March 28th. Again, time will tell.
The Netherlands has a similar pattern to Spain, though with far less cases per million.
Austria looks to be the country which is ahead of the game – there is a clear flattening out of the total cases curve, and a very significant drop in daily new cases since that mighty peak on March 26th. I suspect the peak is higher than it ought to be because of late reporting of cases which actually happened on March 25th; but they went into lockdown on March 16th, which is... 10 days before the peak.
Portugal is another inconclusive one, like the UK. If that big bar on March 31st does turn out to have been the peak, it will have been 12 days after start of lockdown.
Sweden… ah, Sweden. This is the one which, I expect, will prove the matter one way or another. Looking at the total cases graph, what I see is not an exponential followed by a linear part with wobbles, but an exponential with wobbles. Yesterday’s low number notwithstanding, I don’t see anything in the daily cases yet to suggest any transition to linearity. And the Swedish semi-lockdown began on March 17th. If the Swedes are in big trouble at the top of the next wobble cycle, probably around April 8th, we’ll have some good evidence to support Christopher Monckton’s contention that the hard lockdowns are working.
Lastly, Norway is a really odd one. That March 27th figure looks suspicious to me; unless the wobble has a far longer period in Norway than anywhere else. Moreover, if there has been a transition to linear, it seems to have happened on March 12th – the precise day they locked down!