Friday, 10 April 2020

Coronavirus and Farr's Law

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: 

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.

No comments: