Monday, 6 July 2020

Mr Lock's lockdown locks: and what happened to them

I'll let the pictures tell this story.


Mr Lock's lockdown locks


Amico, era peloso. Ma non pericoloso!
(Translated from the Italian: My friend, that was hairy. But not so dangerous...)


Doctor and patient enjoy reminiscences together


"The Cricketers" may be open, but where are the cricketers?

The decision to allow Premier League footballers to play, while ordinary cricketers were still denied their (far better socially distanced) game, may well come back to haunt Johnson.

 

Saturday, 4 July 2020

Music is infinite

By the Darn-Poor Rhymer

The Darn-Poor Rhymer has been silent for almost six months. But yesterday, I was contemplating a phrase of a melody I had composed a few months before; which my brass band and our young cornet soloist were about to start practising, when the COVID lockdown happened. We haven’t met since; and no-one seems to have any idea when we’ll be allowed to practise together again. Let alone hold a concert. Anyone that tries to make out that the lockdown is over, is both deluding themselves and bullshitting us all. (By the way, I have a barber appointment for Monday).

I realized that this melodic line was about as simple as you can possibly write in the Western tradition. An upward scale of C, down and back up again in the scale of A flat to a top C, then a downward scale to a pause on E (the first time) or G (the second). The rhythm, though, is a complex one (7/8), and the effect when the Sibelius program plays it back is magical. It’s a pity I can’t post the .mp3 on Blogger (sigh).

That realization set the Darn-Poor Rhymer going. This is what he wrote:

Music is infinite

Eight billion monkeys
Each with a keyboard,
Writing songs at the speed of light
For the duration of the Universe.
Will they find all the melodies?

Eight bells in the church tower,
Eight monkeys each with a rope
Pulling now faster, now slower,
For ever and ever; so be it.
Can they play all the melodies?

As Kurt Gödel showed us
Some truths are not provable inside a system.
And as I’m showing you here
Music is greater than your imagination;
Music is infinite.

If there’s a god, is he in our finite Universe?
If not, why bother about him?
But if he’s in our Universe, he too is finite;
So, he can’t conduct all the melodies.
Or maybe he exists (or not), but we can’t prove it?

Now, I hope, you’ll understand why I’m agnostic.

Wednesday, 1 July 2020

Is the UK government misleading the public on COVID tests?


So, that’s over 9 million COVID tests done in the UK up to June 27th a.m. Sounds pretty impressive, doesn’t it? As of today (July 1st), that count has moved on to 9,426,631 – fourth in the world in total tests! (The UK is also fourth in the world in COVID deaths per million population, and closing in on Andorra for third place; but that’s another story). Now… is that figure believable?

I recently wrote a paper about understanding the published statistics – deaths, cases, tests – on the effects of this virus around the world. It is very long, and a little bit technical – although it does include lots of pretty (and not so pretty) pictures! Those interested in the detail can find it here: https://wattsupwiththat.com/2020/06/20/covid-19-understanding-the-numbers-coronavirus/. I had a bit of a laugh when one commenter at “the world’s most viewed site on global warming and climate change” mentioned me (though, I must say, not totally approvingly) in the same breath as Judith Curry, who is a true climate-science expert!

In the course of writing it, I compared the two primary sources of world-wide statistics on this virus. One is worldometers.info, https://www.worldometers.info/coronavirus/. This is kept updated daily with data provided by the national health systems. The other, far more comprehensive because it includes historical daily data from the beginning of the epidemic, is Our World in Data, https://ourworldindata.org/coronavirus. I used Our World in Data.

I found some interesting discrepancies between the two. One was with the Swedish cases numbers – a political hot potato, because of the lack of lockdown in Sweden. With the help of a Swedish commenter at WattsUpWithThat, I found that the issue seems to arise because the Swedes allocate each positive test to the date the test was done, whereas Our World in Data (whose data, if I understand right, comes via the World Health Organization) allocates each positive test to the date the test was reported, which is often days or even weeks later.

More concerning, though, was the UK’s data on numbers of tests carried out. Now for the UK, new cases and deaths reported by Worldometers and Our World in Data are in sync, with Worldometers always one day ahead. That’s consistent with the idea that Our World in Data gets its feed via a third party. The UK does report tests on a daily basis, but there’s often a gap of three or four days before a particular day’s tests appear at Our World in Data.

So… the daily Twitter update, shown at the head, gives the numbers of new cases and deaths on the day in question as 890 and 100 respectively. I’d expect those two numbers to appear in Our World in Data against the following day, June 28th. And indeed, they do:

But what about those numbers of tests? 4,852,547 is the cumulative total recorded here, against the 9,067,577 stated in the Twitter feed. This means the total reported on the Twitter feed was 87% greater than – i.e. almost twice – the “official” figure which, if I understand right, must have been reported to the WHO. That’s an awful lot of missing test kits!

Is such a discrepancy normal? To answer that question, I compared the UK with other countries. I took the cumulative total numbers of tests per million population reported at Worldometers up to June 23rd, and compared these with the numbers reported at Our World in Data up to June 26th. I had no expectation that the numbers would match anywhere near exactly. Indeed, what I found is that the Worldometers numbers were consistently above the Our World in Data ones, in most cases by between 1% and 18%. This seems reasonable to me, given that testing is still ramping up in many countries, and the Worldometers count will probably include situations such as test kits sent out but not yet returned.

I then plotted the numbers of tests per million from the two data sources on a scatterplot:

The plot thickens! The UK shows by far the biggest discrepancy in absolute terms among all the countries, and as a ratio it is only surpassed by Peru and France (and the French are not providing any meaningful data on tests at all). Of the three other “bad boys,” two, Belgium and Spain, are also among the countries hardest hit by the virus. Exactly the places, where you would expect there to be most political pressure to make the numbers look good!

Even the BBC seem to think all is not well on the subject of COVID testing in the UK: https://www.bbc.co.uk/news/health-51943612. It looks as if one problem is that antibody tests are being counted along with the swab tests, thus making the ratio of positives to tests lower than it ought to be. Also, they are counting test kits that have been sent out, many of which may never be returned. Moreover, the Chairman of the UK Statistics Authority, Sir David Norgrove, wrote to the government a month ago: https://www.statisticsauthority.gov.uk/correspondence/sir-david-norgrove-response-to-matt-hancock-regarding-the-governments-covid-19-testing-data/. He said, among much else: “The aim seems to be to show the largest possible number of tests, even at the expense of understanding.”

And one thing more. As I discovered while writing my article, the UK’s statistics collectors were recently required to move from their original basis of counting people tested to counting tests performed instead. This, obviously, resulted in increases in the headline numbers of tests right through the course of the epidemic. It also, unfortunately, meant that all the daily numbers of tests done in the UK prior to April 26th got wiped. And, while this move did bring the UK more into line with many other countries’ reporting procedures, countries such as Canada, Japan and the Netherlands are still reporting by people tested. So, my guess is that this move (likely both difficult and expensive), the over-reporting of test numbers, and the poor presentation of the data that Sir David criticizes, have all come about because of political pressure from those who want the numbers to look as good as possible. Sigh.

So, is the UK government misleading the public on COVID tests? Sir David Norgrove obviously thinks so; and I agree with him.


Saturday, 20 June 2020

COVID-19: Understanding the Numbers

As those acquainted with me will know, long ago I was trained as a mathematician. I’ve forgotten most of the specifics I learned. But I’ve retained the framework; even if it’s a bit rusty. For almost three months now, I’ve been looking at the numbers on the progress of the COVID-19 epidemic. I think I’ve now reached a point where I can put forward some tentative conclusions on how the many and various countries of the world have fared under the cosh of this virus, and why. You can learn a lot from data, if you look at it thoroughly enough!

This (very long) paper is about the data on the COVID epidemic world-wide. It will consist mostly of pictures – like the one at the head – which show the outcomes, to date, from this virus in different countries. It will show lots of pretty pictures on a most un-pretty subject; along with some deductions from those pictures. For those less familiar with the world outside their particular neck of the woods, it may also provide a geography lesson or two. And while I’ll allow myself an occasional acerbic remark about the politics, I won’t dwell on those aspects here; for they demand a whole other essay.

Our World in Data

For my analysis, I used the Excel spreadsheet from Our World in Data [https://ourworldindata.org/coronavirus-data]. It contains currently almost 25,000 records. Our World in Data is a project of the Oxford Martin School, part of Oxford University. Their data is free to use. I’ve used it before in other contexts, and I’ve found it extremely useful.

In essence, this data set gives two or three numbers each day for each country: cases, deaths and sometimes tests. These are also provided as cases, deaths and tests per million of population.

One big advantage of this data set over worldometers.info [https://www.worldometers.info/coronavirus/] is that it includes past history from the beginning of the epidemic. The version of the data, which I used for this exercise, came from June 18th. It includes, for most countries, data up to and including June 17th. This usually represents cases and deaths reported up to the previous day.

Reporting

There are several issues with how the numbers have been reported. First, the records are broken down by territory, meaning that off-shore dependencies like Gibraltar or Puerto Rico are expected to report separately from their mother country. But this has not always been followed. Most dependencies didn’t start reporting their own figures until March 20th or later.

Second, some countries only started reporting when they actually had their first confirmed case of the virus. Moreover, in the early stages of the epidemic, many countries have sporadic missing records. Only around the middle of March did all countries start to provide an explicit “no new cases or deaths” report for those days without a new case or a death.

Third, the national data providers quite often make adjustments to their figures. This can result in huge single-day peaks, or in days with negative new cases, or even negative deaths! And some countries’ figures have caused me to scratch my head. The French figures, for example, have been all over the place ever since I have been following the epidemic. The Ecuadorian figures make no sense at all. And there are many cases of sudden peaks in new confirmed cases over a few days. The most recent example was Sweden, which showed a huge surge in new cases starting on June 3rd. Presumably, due to a large batch of delayed test results?

Fourth, only some of the countries – usually the larger ones – are reporting numbers of tests done. And many of these are only reporting tests weekly, or on an ad-hoc basis.

Fifth, there have been cases of national data providers “re-writing history,” scrubbing out and replacing large chunks of past data. In early June, for example, the UK and the USA wiped out all their data on tests prior to April 26th and May 12th respectively. I suspect this may have been down to a change of units, for example from people tested to tests carried out (which would increase the number of tests recorded).

Sixth, the data has invisible biases. Different countries have been using different definitions of what constitutes a COVID death. A death from COVID is subtly different from a death with COVID, but caused by some other co-morbidity. Moreover, in many countries, cases have been severely underestimated due to limited availability of test kits.

Seventh, there is often, but not always, a weekly cycle in the data. There tend to be more cases reported on Fridays and Saturdays, and less on Sundays and Mondays. This weekly reporting cycle is quite distinct from the 5 to 6 day “wobble,” which is visible in many countries’ raw new cases data, and in which the troughs don’t always coincide with the week-end.

All that said, the numbers from Our World in Data are the best I have, so I’ll use them. But to try to work around some of the above problems, in most of my graphs I’ve used numbers of daily cases and deaths averaged over 7 days, from 3 days before the date shown to 3 days after.

The perfect Farr curve?

Time for some pretty pictures at last. Here’s the graph of (raw) cumulative cases for Iceland.

Isn’t that as pretty a “Farr curve” (symmetrical sigmoid curve) as you could wish for? In 1840, William Farr analyzed a then recent smallpox epidemic in England. He showed that a plot of deaths against time looked very much like the curve of a normal probability distribution, otherwise known as a bell curve. The Farr curve, in which the increasing and decreasing phases are symmetrical and of equal length, is the integral of a normal probability distribution. So, let’s look at Iceland’s (weekly averaged) daily cases (and deaths, too).

 

That looks fairly “normal” to me, if a bit jagged at the top. That, so I understand, is how you’d expect the daily cases graph of an epidemic to look, if it was allowed to run its course without any interference, either through public health measures or through importing new cases from outside. Note also how, in Iceland, the deaths have tended to follow some weeks after the cases.

Next, Switzerland.

 

 

That’s a less symmetrical example of a sigmoid curve. In Switzerland, the right tail of the cases graph is a little under twice as long as the left tail. A lot of countries’ cases graphs are similar to this, although in many cases the right tail is significantly longer than it is in Switzerland.

But now, I’ll throw you a curve-ball: Iran.

 

That looks more like the back of a camel than a mountain peak! There must be something else in play here. The most likely cause of the second peak seems to have been mass travel for the Eid Al-Fitr holiday towards the end of May, by which time most provinces were out of lockdown.

The worst of the worst

Here are the worst countries in the world in terms of deaths from the virus per million population, as at June 17th.

Notice that the top nine are all in Western Europe. The USA and Canada are in there too, and three South American countries: Ecuador, Peru and Brazil. South America seems to be fast becoming a “hot spot” for the virus. Apart from Ireland, the remainder are all small dependencies of countries higher up the list: Sint Maarten belongs to the Netherlands, and Jersey, Isle of Man, Montserrat and Guernsey to the UK.

In contrast, here are the countries with the most confirmed cases per million.

The two lists are quite different, apart from both having San Marino and Andorra near the top. Even Italy, the “poster child” for the epidemic, doesn’t make it into the top 20 in cases per million! As to why the lists are so different, one obvious possibility is that countries which do more tests tend to find more mild and asymptomatic cases, which don’t lead to more deaths. That seems to apply in Bahrain, for example, where they have done over 400,000 tests in a population of 1.7 million.

Western Europe

I’ll look at Western Europe first, since it’s the hardest hit area. Here are the deaths per million.

Some of the small countries listed here are off-shore dependencies of larger countries. For example, Guernsey is a dependency of the UK, and the Faeroe Islands are a dependency of Denmark. The close dependencies of the UK (Jersey, Guernsey and the Isle of Man) have generally done somewhat better than the UK itself. Dependencies further away from the mother countries have done better still, like Gibraltar and the Danish territory of the Faeroe Islands.

Among the remaining small countries, Andorra, sandwiched between France and Spain, has fared worse than either of them. And San Marino (landlocked inside Italy) has suffered worst of all. But these two disaster areas are outliers. Indeed, small countries which are bordered by bigger countries, such as Liechtenstein, Monaco and Luxembourg, have often done better than their neighbours. Even the Vatican falls into this category, despite its third place in cases per million! And small island countries like Iceland and Malta have done the best of all.

Among the larger countries, Germany is an odd man out. It has far less deaths per million than you’d expect, based on the numbers from other European countries of comparable size. Germany seems to have been doing a better job of tracing the travel histories and contacts of infected people than many other European countries. Indeed, the Germans were among those who alerted the Austrians to the infection hot-spot they had in the Tyrolean resort town of Ischgl.

To show the progress of the epidemic in each country, I plotted total cases per million population (up to June 17th) for each of four groups of countries, from south to north, while including the UK dependencies in the same group as the UK. Spot the Farr curves! It looks as if, the shorter the duration of the epidemic in a country, the more symmetrical the curve is.

 

 
 

 

In the last graph, you can see Iceland’s Farr curve in light blue, also the second half of a Farr curve (grey) in the Faeroe Islands. (The first half of the curve is missing, because reporting from the Faeroes didn’t start until 24th March).

Most of the countries have either all but flatlined in terms of cases per million, or reached a state where the new case count is much reduced from its peak, and has become roughly constant. As to the others, Portugal needs a closer look. The UK has clearly “turned the corner,” but is as yet nowhere near flatlining. Gibraltar, too, may repay a closer look. And Sweden… Ah, Sweden.

As an aside, the numbers of new cases for Sweden shown on worldometers.info for the first few days of June don’t match the spreadsheet from Our World in Data; even the latest version. For example, a peak of 2,214 new cases on June 4th appears in the latter, but not in the former, which only shows 1,042 new cases on that day. What’s going on?

A typical example – Italy

Here are two graphs I prepared for Italy, the first European country to be seriously hit by the virus. First, daily new cases and deaths, averaged over the 7-day period. This is much like the Swiss graph in shape, but with a far longer right tail.

 

Second, I thought I would look at the ratios between deaths and cases, and cases and tests, over the course of the epidemic. I thought that deaths per case as a percentage would be a useful metric, for two reasons. First, a high deaths per case ratio over a long period is a symptom of a poor health care system, if not also of an unhealthy populace. And second, underestimating the number of cases through a lack of testing is also a sign of a poor health care system. And such an underestimate will result in increased deaths per case.

I also thought that the ratio of positive tests to total tests (“cases per test”) might be instructive, and happily the Italians have provided daily numbers of tests all the way through. In both cases, I’m calculating the ratios of the cumulative counts over the whole period, all the way from the very beginning of the epidemic. That should provide a natural “smoothing,” and allow comparisons to be made between countries, even if some test results are being significantly delayed.

This pattern is typical of many countries. From the beginning of the epidemic, confirmed cases per test rise fairly steadily to a peak. As the virus takes hold, it becomes increasingly easy to find people who have it. The peak occurs at about the same time as the peak of new cases per day. The percentage of cases per test then starts to fall, even if the number of tests is still increasing or even increasing rapidly, as tests are rolled out to successively less susceptible groups of people.

As to deaths per case, this ratio may initially be high, because many of the very first patients diagnosed were already dying. But afterwards, it rises slowly. In many countries, including Italy, it eventually flatlines. In some, it falls again; but that’s another story.

The sick man of Europe – the UK

In the 19th century, Turkey was labelled by many as “the sick man of Europe.” Since then, this title has been awarded to different countries at different times. But in the context of COVID-19, I think the UK deserves that moniker right now. Here are the weekly averaged cases and deaths.

 

The path down the mountainside is long and winding, but at least it’s downward. Note that, unlike Italy where the deaths peak came a few days after the new cases peak, here they were all but simultaneous. That may, perhaps, be because a higher proportion of those who got the virus in March ended up dying quickly, than of those who got it later. And the surge of cases in late May might perhaps be explained by the Bank Holiday week-end.

Now, let’s look at deaths per case and cases per test.

Hey, where did all that data go? In the version of the spreadsheet from June 1st, there were figures on tests in the UK all the way back to January. By June 17th, they’re gone!

But more interesting is the deaths per case ratio. Whereas in Italy, and in most other countries in Western Europe, this number seems to converge towards a constant from below, in the UK it overshot, going to 16% before dropping back to 14%. This suggests, perhaps, that the virus may have found more “low hanging fruit” – older people, and those with serious co-morbidities – in the UK than in other places. Or, maybe, that the unusually warm weather for much of the UK during the period had an effect of slightly lowering the lethality of the virus.

In the daily cases graph above, there’s a detail at the left of the graph, far too small to see on that scale; namely, the beginning of the epidemic. So, I devised a third graph to show this. It shows the ratio of (weekly averaged, to avoid enormous early spikes) daily cases each day to the previous day, as a percentage. The Excel formula gets quite complicated, because you have to deal with days with new cases next to days without new cases. I decided to give +100% to a day with cases which follows a day without, and -100% to the reverse. Here’s the result for the UK.

As you see, the UK has had two separate phases of the epidemic. The first began in early February, shortly after the first case was reported on January 31st. There were 9 cases in total in this phase. There were then no new cases for a while; the raw data shows no new cases from February 14th to 23rd inclusive. At the end of February, a new rash of cases appeared, until on March 2nd the count of total cases jumped by over 50%, from 23 to 36, in a single day. This is the day which I assigned as the “onset date” for the UK; an idea I’ll discuss in the next section.

But right now, a few more interesting graphs from Western Europe. First, Sweden.

I'm tempted to say, in Hamlettian fashion, that Sweden’s case numbers have jumped from “To peak or not to peak,” to “Something is rotten in the state of Sweden.” That said, the Swedes have ramped up their testing considerably in the last few weeks, so some of the recent rise may just be down to finding a higher proportion of the mild or asymptomatic cases that were already there.

Next, Portugal.

The Portuguese were doing OK, until the beginning of May. Since the middle of May, the new cases have been increasing pretty much linearly. Now, Portugal began to ease its lockdown restrictions on May 4th, with small shops re-opening. And on the 18th there was a further easing of restrictions, including re-opening restaurants, cafés and some schools. It seems reasonable that these may have caused the subsequent slow rise in new cases.

In Gibraltar, the epidemic has had two, or perhaps three, phases; the first being close to a bell curve. It seems possible that the recent new outbreak was caused by relaxation of lockdown; and in particular by re-opening the border for those who live in Spain and work in Gibraltar.

Onset Dates

When the epidemic in a particular country has had only one phase, it’s quite easy to assign an onset date. This I define as the first day, after the very first day on which cases were recorded, on which the (raw) new case count increases by 50% or more over the previous day. In Italy, for example, the first three cases were reported on January 31st. Then on February 22nd there were 14 new cases, and on the 23rd a further 62. I therefore assigned February 22nd as the onset date for Italy. If the country has had multiple phases of the epidemic – like the UK and Singapore – then there’s an element of judgement in choosing which phase represents the onset.

After the onset, the case count climbs exponentially for a while, sometimes doubling in around 3 days. But this lasts no more than a week; one “wobble” cycle of the virus. After that, it settles into a state in which the day to day increase is still significant, but generally decreasing. You can see that in the graph above for the UK.

Here's my list of onset dates up to and including 14th March:

03 Jan: China (though there had been cases reported earlier)

17 Jan: Thailand

23 Jan: Japan

25 Jan: Taiwan

26 Jan: Australia, South Korea

31 Jan: Vietnam

21 Feb: Iran

22 Feb: Italy, United States

25 Feb: Bahrain, Kuwait

26 Feb: Iraq, Oman, Spain

27 Feb: Sweden

28 Feb: Austria, France, Germany, Norway, Switzerland

29 Feb: Georgia, Iceland, Israel, Netherlands, Romania, Singapore

01 Mar : Algeria, Azerbaijan, Pakistan

02 Mar : Belgium, Ecuador, Finland, Lebanon, Qatar, San Marino, United Kingdom

03 Mar : Czech Republic, India, Russia

04 Mar : Belarus, Denmark, Portugal

05 Mar: Chile, Ireland, Malaysia

06 Mar : Argentina, Botswana, Brazil, Canada, Estonia, Greece, Saudi Arabia, Slovenia

07 Mar : Egypt, Hungary, Indonesia, Luxembourg, Macedonia, Palestine, Philippines, Poland

08 Mar : Afghanistan, Latvia, Malta, Slovakia, South Africa, United Arab Emirates

09 Mar : Bulgaria, Costa Rica, Maldives, Peru

10 Mar : Albania, Dominican Republic, Somalia, Tunisia

11 Mar : Lithuania, Moldova, Panama, Paraguay, Serbia

12 Mar : Armenia, Brunei, Cyprus, Liechtenstein, Mexico, Morocco, Sri Lanka

13 Mar : Cambodia, Congo, Croatia, Jamaica, Turkey, Ukraine

14 Mar : Andorra, Bolivia, Senegal, Trinidad and Tobago

Now that’s interesting. Seven countries, all in Asia except for Australia, had the virus in January. Then everything went quiet for 3 weeks or so, until on February 21st-22nd the epidemic went viral (no pun intended) in three countries: Iran, Italy and the USA. Then it was all over the Middle East and Western Europe inside 10 days, and all over the world inside three weeks.

There’s a school of thought, which posits that an “Italian strain” of the virus has spread more effectively and caused more deaths in the countries and US states it reached than the original “Chinese strain.” But the above suggests to me that the distinction, if there is one to be made, should perhaps be between the “February strain” and the “January strain.” The February strain could just as easily have come to the USA directly from China, as via Italy. Particularly given that it first appeared soon after the end of the (extended) Spring Festival holiday in China.

Deaths per million versus onset date

I thought that a scatterplot of deaths per million population against onset date might be instructive. In allusion to the well-known “Hockey Stick,” I call it the “Football Boot.”

This does, indeed, show that almost all the worst affected countries first “went viral” in a short period from February 21st to about March 7th. Superficially, there appears also to have been a second wave around the third week of March. But the “tongue” of the boot – those countries that have both high death rates, and onset dates around that time – are all dependencies. So, this is an artefact of those countries not starting to report their numbers separately until that time.

Interestingly, all the countries which first reported cases before 21st February have very low deaths per million. Moreover, up to 19th February, there had been only three deaths reported from the virus outside China: in France, Japan and the Philippines. Two were Chinese citizens; the third had just returned from Wuhan. The hypotheses that the February strain of the virus was able to transmit from human to human more easily than the January strain, or that the February strain was more lethal than the January strain, cannot, I think, be ruled out on this evidence.

World cases and deaths

Before I look at regions and countries of the world beyond Western Europe, I’ll show the cases and deaths graph for the world as a whole.

You can see the first phase of the epidemic on the left, separated from the second by a couple of weeks of relative calm, in which only China was finding significant new cases. The resemblance of the cases curve through March and early April to a Farr curve is also striking. Even though it's in the daily cases, not the cumulative totals as the Icelandic Farr curve was!

All that said, the Farr curve starts to go off base in April. After having all but levelled off, it starts to wobble, then to rise again. I wonder why? A third phase, perhaps, on a longer timescale than the first two? As we’ll see a bit later, yes, that’s what it is. And the countries it’s impacting include some very large and populous ones, like India, Pakistan, Bangladesh and Indonesia. That’s potentially worrisome. How long it will last, and how far up it will go, I have no idea.

But something interesting pops out of the graph of world-wide deaths per case.

 

That significant decline since late April in the ratio of (cumulative) deaths to cases might mean that the virus has taken most of the available “low hanging fruit” from aging Western polities. Or that it is weakening. Or that it is reaching places like tropical Africa, where the conditions – heat and humidity – are not so conducive to its survival and spread. Or that roll-out of testing is finding more and more mild cases, that don’t end in death. Which? I don’t know.

Since I earlier suggested “deaths per case over a long period” as a potentially useful metric with which to judge individual countries’ health systems, I’ll also list the worst deaths per case ratios. Remember, if your country is high up in this table, that’s a black mark against its health system.

North America

Time to set off on a tour of the rest of the world. I arbitrarily divided the world into nine regions: Western Europe, Eastern Europe, North America (mainland), West Indies, South America, Middle East and North Africa, Asia, and Australasia and Oceania. I’ll start in North America.

That doesn’t look too good for my American friends. Here are the cases per day for the USA.

It looks as if it may be a long, slow path down from the high plains! Though that would be easier to judge, if the figures were broken down by state. After all, the USA is in some ways 50 separate countries. American friends might care to do a similar exercise to this one on a state by state basis, if the data is available. But the deaths per case ratio is far lower than in Western Europe, about 6%; which is good.

Canada, in contrast, looks to be on the mend.

And here are the daily cases and deaths from Mexico. Not good, I fear.

The West Indies

I grouped together all the, mostly small, countries on islands in and around the Caribbean Sea under the heading “West Indies.” Here’s the league table.

I won’t follow up on any individual countries in this region. But what is very notable is that six of the top seven countries in the region in deaths per million (the Dominican Republic being the exception) are dependencies. One belongs to the Netherlands, three to the UK and two to the USA. It seems plausible to me that the cases in these countries were sparked by travellers from the mother countries. Support for this idea comes from the onset dates for each of these six countries, which were all between 23rd and 28th March.

South America

We’ve heard lots of bad news coming out of Ecuador. And I’m not sure I believe any of their figures at all. Here are their raw cumulative case counts.

 

Yes, that’s right, the total cases go down at least twice during the second week of May. The Ecuadorians can’t even work out how much trouble they’re in! So, let’s try Peru.

Inconclusive; a couple more weeks will tell.

Brazil’s daily cases look as if they may just about have peaked, so the same applies to them. But they are currently running at about 90% positives per test (cumulative) – suggesting that their test kit resources are nowhere near up to scratch. Their deaths per case, though, show a strong decline. That’s probably good.

 

The Chileans are in trouble, with cases still going up. Not to mention deaths.

 

Eastern Europe

Back across the Atlantic, let’s take a look at Eastern Europe. I’ve included Russia here rather than in Asia, because most of the Russian cases have been around the Moscow area.

So far at least, Eastern Europe has been hit considerably less hard than Western Europe. In Moldova though, daily cases are on an oscillating but upward trend, and there was a recent spurt of new cases, a bit like Sweden on a smaller scale. So, there may be trouble brewing here; and, perhaps, in some other Eastern European countries.

Here’s the Russian data.

 

It looks as if the Muscovite daily new cases may have peaked. But Russia is a big country, so there’s still a long way to go.

Middle East and North Africa

In this group, I’ve included the Arab and Muslim countries, from Pakistan, via Iran, Turkey and the Gulf, to Africa as far south as the Sahara Desert. I’ve excluded remnants of the former Soviet Union, except Armenia which has a close relationship with Iran.

 

We’ve already met the camel from Iran. Armenia’s graph looks a bit like Mexico’s, but more jagged. In contrast, here’s Kuwait.

 

The epidemic looks to be on the way to being contained in Kuwait, and the deaths per case ratio is low. It looks as if these guys know what they’re doing, even though cases per test are still going up. I’d guess they already have relevant experience, from dealing with MERS.

Turkey, on the other hand, shows a more European style profile, but cases have started to creep up again.

 

But there’s worse yet in the Muslim world. Pakistan has had a recent spurt of new cases.

So, too, has Saudi Arabia, after it had gone down for a while. I guess the drop may have been due to the fasting month Ramadan, which I’m told the Saudis take very seriously. And the second rise is probably due to Eid Al-Fitr again, the festival at the end of Ramadan.

Two more countries in this area are of interest. Yemen has the worst deaths per case ratio in the world, over 22%. And Qatar has the highest number of cases per million in the world.

That doesn’t say much for the Yemeni health care system, but at least the absolute numbers are still small for a country of 30 million.

 

Qatar is top of the “world league” in terms of confirmed cases per million population. Like several other countries, it has had a two-phase epidemic. One began in early March, at the same time as the outbreaks in Europe. The second, bigger outbreak started about three weeks later. At the other end of the epidemic, they seem to have turned a corner, although the proportion of tests proving positive is still going up. Moreover, the deaths per case are minuscule compared with Western Europe or the USA. I’m told they’ve had quite an aggressive program of contact tracing since early in the epidemic; so perhaps this may be how they achieved these results.

Bahrain has one of the most aggressive virus testing programs, per million, in the world. Worldometers puts it second only to the United Arab Emirates in countries with populations over a million. But Our World in Data doesn’t have any data on tests in the UAE; sigh. So, here’s Bahrain.


 

They may or may not have reached their peak of daily cases. But if they really are “over the hump,” they’ve done well.

Sub-Saharan Africa

Where is (or are) Sao Tome and Principe? I hear you ask. It’s a small group of islands off the western coast of Africa, near the Equator. Now, their cases and daily deaths data, when weekly averaged, make it look like they have had a series of epidemics, each lasting a week or so. However, if you look at the raw data, you see a number of large single-day bursts.

 

If we can believe the data, and those really are three big clusters, all quickly snuffed out after a single day, then maybe the virus doesn’t survive easily in the conditions there – high heat and humidity? But how did the virus get there in the first place?  Perhaps the outbreaks might have been started by visitors; it’s an oil-rich area, so there may be Westerners jetting in.

Djibouti, on the other side of Africa, seems to have much more reliable data collection. And it does show a multi-outbreak pattern, including an almost perfect bell curve on the first outbreak. It’s a big port, with lots of international traffic, and regularly has Western soldiers passing through. I think this supports the idea of the virus dying out, and later being re-introduced.

 

But South Africa, unfortunately, still has a near exponential new case count.

Asia

 

All these death rates are minuscule, compared with the hardest hit regions of the world. But, even within such an exclusive club, you can see immediately that some of the countries closest to China – Thailand, Taiwan, Vietnam – have unexpectedly low death rates.

Here are the Maldives. Again, a multi-peak epidemic, with fast-dropping tails, suggesting that the virus doesn’t enjoy monsoon conditions too much.

So, we come at last to the source of our woes, China.

Nothing to see here, perhaps? Apart from one huge adjustment on February 13th, it’s not unlike a bell curve. But what about those blue bits further to the right? They look like several small clusters, each of which is relatively quickly snuffed out. That’s very clear in the daily growth chart.

Maybe the Chinese now have a high degree of immunity to this virus? In which case… their recent case figures may even be truthful. Pity about the human transmission bit.

Now, why not compare China with its neighbours, as I did for Western Europe? Here’s the data for China and the six other countries, whose onset dates were in January.

Vietnam seems to have shrugged off the virus as if it didn’t even exist. China and Taiwan have it under control, and Thailand very nearly so. But I wouldn’t be surprised if people in these countries already had some level of immunity to this virus. Perhaps via SARS? Or might there have been some small “pre-releases” of the new virus from China even before January?

The other three countries are all well past their peaks of daily cases, with cases increasing roughly linearly. Let’s take a closer look at one, South Korea.


You can clearly see the two phases of the epidemic, January and February. And the February strain of the virus was more harmful than the January strain; indeed, most (60%) of the South Korean cases are said to have come from the same cluster. It’s also noticeable that, for a month or so starting in the middle of March, the daily case count stubbornly refused to go down.

The South Koreans have been assiduous throughout on contact tracing and isolation, and on testing. But they still haven’t completely beaten the virus. As shown by the continuing new cases in May; caused, we are told, by a single new cluster.

In contrast, elsewhere in Asia, Bangladesh’s new cases are still trending strongly upwards.

Japan’s graph is like Switzerland’s in overall shape, but with a sharper peak.

In recent decades, Singapore has taken over from New York as “the cross-roads of the world.” It’s very close to the Equator, so it’s hot and humid; and the Singaporeans are zealous about health matters. So, I expected to see a multiple-phase epidemic, perhaps a bit like Djibouti. And that’s what I got. A preliminary phase of the January strain; then the February strain brought a rise to a big peak; then two (or maybe three) further minor peaks.

 

Indonesia particularly interests me, because I worked in Bandung, Java for three months back in 1983, and I loved the place and the people. So, how are they doing? Not very well, I’m afraid.

 

Too early to tell, in my opinion. There may be a Ramadan effect here, too. But the deaths per case have dropped significantly since their peak.

Last, but very much not least, since it’s the second most populous country in the world: India.

 

In India, the new cases don’t look to be anywhere near peaking yet. That’s not good news. But the deaths per case have begun to decline, suggesting the heat and humidity effect may also be at work here, though not yet strongly. India (like the USA and Russia) is a big and very populous country, so there’s still a distance to go.

Australasia and Oceania

Only two things to say. One, the Northern Mariana Islands and Guam are both US dependencies. Two, I know how paranoid the Aussies and New Zealanders are about letting anything biological into their countries from outside; and it shows in the results here.

Who has done well, and who has done badly?

In Asia, several countries close to China (and China itself, if we can believe their numbers) have done well at containing the virus locally. They must have well used what they learned from SARS. Clearly, the key time for controlling a virus like this is the very beginning of the epidemic. Contact tracing and isolation seem to be the important factors in stopping the initial clusters of infection from spreading. If you lose that first battle, the war will be long and bloody.

On the other hand, at least two Asian countries, India and Bangladesh, still have substantially rising daily new cases. Indonesia has not yet peaked. And all three have big populations.

Some Middle Eastern countries, particularly in the Gulf area, have also done well; again, probably due to their experience with MERS. Pakistan, Saudi Arabia, and Iran and neighbouring Armenia are showing cause for concern. But North Africa seems relatively unaffected, perhaps due to a combination of heat and low population density.

Africa south of the Sahara seems to offer conditions that are not very favourable to the virus. Most African countries are, therefore, getting off relatively lightly so far, except for South Africa. I’d expect the same would apply to tropical Central and South America. That leaves, as the most vulnerable places: Europe (including Russia), North America north of the tropics, and South America south of them.

In the Americas, the countries currently causing concern are Mexico, Chile, Brazil, Ecuador and (a little bit) Peru. US new cases have peaked, but there’s still a long slog ahead.

In Eastern Europe, there are so far generally less cases and deaths than further west. But some countries, like Moldova, may suffer a rockier road than others. And Russia still has a long way to go.

In Western Europe, in every country except Sweden, new cases have now peaked. But the UK government Twitter feed (how amateurish!) reported 1,346 positive tests on June 18th. And the previous day’s count was 1,218; more than double Germany or Italy on the same day. There’s still lots of work to be done.

In Western Europe as a whole, the Nordic countries, except of course Sweden, have done best. The Germanic countries are next best. Germany in particular has done very well in light of its size; likely due to relatively good contact tracing in the early part of the epidemic. The Catholic countries in south and central Western Europe, the UK, and the Netherlands, have done worst.

Two small European countries have suffered disasters (San Marino, Andorra). But others (Liechtenstein, Monaco, perhaps even Luxembourg) have been more successful at keeping the virus at bay than their neighbours. Small, geographically close dependencies (like Jersey) have tended to do better than their mother countries, but not hugely. Small, remote dependencies (Faeroe Islands, Greenland, Gibraltar) and small island countries (Iceland, Malta) have done best of all.

The relative success of many small countries, and the disasters in others, suggest that for a virus like this, containment measures are best carried out on the scale of tens or at most hundreds of thousands of people. That means towns and cities, not large countries or even US states. The Austrians, I think, got it right when they quarantined the ski resort Ischgl.

Moreover, I don’t think it makes any sense to shut down normal daily life in areas which have few or no cases. Nor to close parks. If you want people to “social distance” from each other, why ban them from the very spaces in which they have a chance to get away from other people? Nor, indeed, does it make sense to force symptom-free people, with no known connection to anyone with the virus, and who have not recently returned from somewhere infected, into isolation.

To conclude. Who will win the “wooden spoon” for the country that dealt with the virus worst? In Western Europe at least, only three horses are left in that race: Belgium, Sweden and the UK.

The next question is, what will happen as the lockdowns are lifted? The example of Portugal suggests that new cases may start to rise again, but not catastrophically. I plan to wait a few weeks, and then to re-visit what has (will have) happened post-lockdown.