Tuesday, 25 May 2021

COVID-19: World Report, Omnibus Edition (Lockdowns)

This paper is the companion to my recent report on the medical aspects of COVID-19: cases, deaths, tests and vaccinations. Today, I’ll look at lockdowns from a world-wide perspective, following on from my report on lockdowns in Europe a few weeks ago.

As for the previous report, the data I am using, from Our World in Data and the Blavatnik School of Government (both at Oxford University), runs up to May 15th 2021.

Average Lockdown

I decided to change slightly the way in which I average lockdowns to give overall measures of lockdown. Rather than using the Blavatnik stringency figure directly, I decided to calculate separately the average level over all days of the epidemic for each kind of lockdown (schools, workplaces, public events, gatherings, public transport, stay at home, internal travel restrictions, international travel restrictions), then average these eight to give an “Average Lockdown %.” This has the effect of reducing the result compared with the Blavatnik stringency. I also revised the way I calculated the percentage of time spent in full lockdowns, so that it used the same list of eight kinds of lockdown as the Average Lockdown % measure.

The first reason for these changes was to exclude Public Information Campaign, which is not a policy measure but is included in the Blavatnik stringency (and almost always, almost everywhere, contributes 11.11% to it). The second rationale was to exclude any consideration of Face Coverings, which is not counted in the Blavatnik stringency, in either averaging process. It is, however, still possible to assess the stringency of Face Coverings lockdown against the average of the rest.

I’ll start with the top 20 and bottom 20 countries in Average Lockdown percentage over all eight kinds of lockdown and over the entire course of the epidemic. 18 out of the 190 countries which have reported cases have not provided stringency data; so, there are 172 countries in the list from which these selections are chosen:

Ouch! People in Honduras, Libya, Venezuela, Argentina and Eritrea have been locked down, on average, at over 72% on every single day of the epidemic since January 24th, 2020! Their Freedom House ratings out of 100 are respectively 45, 9, 16, 85 (!) and 2 (equal lowest in the world – worse even than North Korea). India is in the top 20, too; but it doesn’t seem to have helped them much recently.

At the other end of the scale, though, Nicaragua, Burundi, Belarus and Tanzania are not much noted for freedom either – with scores of 31, 13, 19 and 40. But Belarus has done well against the epidemic so far; as have Tanzania and Burundi. And Nicaragua too, if I can believe their figures. Moreover, there are three countries in that bottom 20 with Freedom House ratings over 90 – Taiwan, New Zealand and Japan. And, as my previous report shows, Taiwan and New Zealand are in the bottom 20 in both cases and deaths per million population. So, this gives the lie to the notion that stringent lockdowns and success against the virus necessarily go together.

Here’s a plot of average lockdown percentage against Freedom House rating world-wide:

Not much “trend” there at all! I suspect that the places where a government’s general nastiness leads them to lock people down as hard as they think they can get away with, and the places where they are more worried about the economic and psychological consequences of locking down heavily, tend to balance each other out.

And here are world-wide plots of cases and deaths per million against average lockdown percentage:

What those trend lines show is that world-wide, each percent of increase in lockdown (averaged over the eight kinds of lockdown listed earlier) is associated with an increase of 612 in total cases per million and an increase of 13.3 in total deaths per million. The likely reason for the two positive trends is that significant spurts in either cases per million or deaths per million are likely to trigger politicians into locking down harder.

Time in Full Lockdowns

The other metric that I used in the European report was the percentage of days during the epidemic that a country is in full lockdown (100% stringency for that particular measure). This can be applied to individual types of lockdown (schools, workplaces, public events, gatherings, public transport, stay at home, travel restrictions, international). Or it can be applied to lockdown as a whole, by averaging the number of days in full lockdown for all eight of the lockdown types above.

In contrast to the earlier European calculation, I did not try to include face coverings in this averaging, since no government has yet imposed a 100% face mask wearing mandate (everywhere outside the home). But I can still assess the effectiveness of face covering mandates against the average of the rest.

Here are the top and bottom 20 in time spent under full lockdowns:

Ouch again! Hondurans, Venezuelans and Libyans have been, on average since January 24th 2020, under four or more full lockdowns out of eight. The Irish are the worst hit in Europe, having been under an average of three full lockdowns out of eight since the epidemic began.

At the other end, China is right down there, third from bottom. I suppose this may be because, in such a large country, full national lockdowns would not be appropriate while the virus is only active in certain provinces. Russia, Indonesia and Brazil are probably down in this group for similar reasons. But India, for some reason, is not.

Here are the plots of cases and deaths per million against average time spent in full lockdowns:

The respective gradients are +702 cases per million and +13.2 deaths per million, both per 1% of time spent under full lockdowns.

Effectiveness of Lockdowns World-wide

When I addressed the effectiveness of lockdowns in Europe, I was using slightly different measures of what constituted a percentage point of average lockdown, and of what constituted a percentage point of full lockdown. I have also switched to using deaths per million rather than cumulative deaths per case, since this is the metric on which the politicians will be judged. Towards the end of the paper, I will, therefore, need to re-work those figures in order to compare the European situation with the world-wide one I will present below.

But I decided to continue with my methodology of plotting cases and deaths per million against stringency for each of the individual kinds of lockdown, then comparing the slopes of the trend lines with the plots above, which give the trends of cases and deaths per million against the average over all eight kinds of lockdown. The method is seat-of-the-pants and lacking in statistical rigour, surely; but it does let me get a feel for the effectiveness of different lockdowns when compared with the average.

I put the results into four graphs, the first of which looks like this:

The blue bars represent the actual trend line gradients, in this chart in cases per million per percentage of average lockdown stringency (averaged over all eight kinds of lockdown, and over the course of the epidemic). The grey bars are the result of subtracting the gradient (+612 cases per million) of the trend line on the graph of cases per million against my new “average lockdown %.” Where a grey bar stretches to the right, this means that a mild lockdown of this kind is less effective in controlling cases per million than other kinds of lockdown. Where a grey bar stretches to the left, this means it is more effective.

In contrast to what I found in Europe, world-wide it seems that face coverings are more effective than any of the other measures in controlling cases per million. These are closely followed by international travel restrictions, internal travel restrictions and public transport closures. Stay at home mandates and school closures are less effective, and restrictions on gatherings, cancellations of public events, and workplace closures, are less effective still.

Here’s the corresponding graph for trends in cases per million against % of full lockdowns:

On a world-wide scale, it seems that even restricting gatherings to the full lockdown level of 10 or less has little effect, and cancelling public events does little more. The most effective full lockdown is stay at home, followed by border closure, followed by the four others in quick succession.

Here are the corresponding graphs for deaths per million:

For controlling deaths per million world-wide, the most effective full lockdown measures are international travel restrictions and public transport closures. These, along with face coverings and internal travel restrictions, have the most effect when the lockdowns are relatively mild. Locking down workplaces is of little utility unless it is a full lockdown; and restrictions on public events and gatherings are surprisingly ineffective.

Specific Lockdowns

Next, a look at which countries have favoured which particular kinds of lockdowns. In most cases, I’ll show only the top 20 lists, as the bottom 20 often has many of the same countries.

It seems that Middle Easterners and Central and South Americans, in particular, tend to prefer to close schools rather than lock down something else.

Strict workplace closures, the worst kind of lockdown of all from the point of view of the general public, are strongly favoured by the usual suspects like Venezuela, Honduras, Eritrea and Libya. But also, by many European countries. Ireland in second place, the UK in sixth, and Italy in seventh fully deserve wooden spoons. Interestingly, China is up there, though it rarely uses full lockdowns.

A bit of a mixed bag; but Italy leads, and Honduras is up there again.

France has been hardest of all on gatherings, closely followed by Monaco and (I repeat myself) Honduras. But Belgium, Portugal, the UK and China are all in the top 20.

For public transport, I think it’s better to use the full lockdowns list, because anything below 100% lockdown is merely a recommended closure or a regional one, not a mandatory national closure.

It seems to be Middle Easterners who like to lock down public transport hardest, followed by Central and South Americans.

It’s the Central and South Americans – including Honduras – who like to force people to stay at home for long periods. China, India and Pakistan are in there, too.

For restrictions on internal travel, I’ll again show the list by full lockdowns, as any less-than-full lockdown here is only a recommendation or regional, not a nation-wide mandate:

Many of the usual suspects again; and Ireland gets a dis-honourable mention, too.

As to international travel restrictions, I’ll show both the top and bottom 20, as there’s shame in being in the bottom 20 if the country’s overall record against the virus is poor:

Australia, New Zealand, Canada – these guys got it right in the early stages. As did Vietnam. In the hall of shame on this one are: Bosnia, Andorra, Mexico, Brazil and the UK.

And, last but not least, face coverings:

It’s south-east Asia which leads on this one. It seems to have done Laos and Singapore no harm; though in Brazil and Peru, at least, it doesn’t seem to have done any good at all.

Comparison with Europe

I thought I would re-work the European numbers from my earlier paper under the new averaging conventions. So, here are the results per percentage of average lockdown, in the same format as above:

Which lockdowns work?

In Europe, face covering mandates and school closures have a negative effect on both cases and deaths per million, relative to the average! Whereas world-wide, they go the other way. Why such a big difference with face masks? Is it cultural – Western people don’t know how to wear face masks effectively? Or, perhaps, could it be that once the virus reaches a certain level of penetration in the population, face masks are a hindrance rather than a help?

Gatherings restrictions seem to work in Europe, but not world-wide.

There is much better agreement on the other lockdowns. To control cases per million, international and internal travel restrictions are the most effective – and closing public transport, if you actually go as far as doing it nationally. To control deaths per million, you need the same three; international and internal travel restrictions, and public transport closures. And when it comes to 100% lockdowns, full workplace lockdowns are effective – but expensive.

Saturday, 22 May 2021

COVID-19: World Report, Omnibus Edition (Medical)

It’s been a long haul, but I have finally been through the data for all 190 countries which have reported cases of COVID-19, and assembled everything into a “master” workbook, from which I can produce spaghetti graphs, histograms, scatterplots and lots more. Here, then, is my first truly world-wide COVID status report; since last June, at any rate.

I shall confine myself today to medical data: cases, tests, deaths and vaccinations carried out. I plan to look at lockdowns world-wide in a separate report. I am also planning to address the efficacy of the vaccines a little later.

The data I am using, from Our World in Data and the Blavatnik School of Government (both at Oxford University), runs up to May 15th 2021.


Here’s the graph of cumulative cases per million world-wide:

Looking at the smoothness of the curve, I find myself thinking: First wave, second wave, third wave, what was all that about? To think of COVID-19 in those terms is to take a parochial attitude. When you look at the data for the world as a whole, you see a slight slowdown early this year; but otherwise, those numbers are still going up and up.

And 20,000 cases per million is just 2% of the population. Unless the number of recorded cases is a very serious undercount of the actual number of infections (which it certainly was in the early stages, but that’s less clear now), there are an awful lot of people still unexposed.

The daily cases (weekly averaged) are, up to scaling by population, the first derivative of the above:

The “first wave” in Europe, the Americas and the Middle East, up to May of last year, now seems like a bad dream. But it’s a bad dream that is still going on. The first sharp peak in the new year was the “second wave” in Europe, and the more recent one is India.

Now, let’s look at cases per million by country. I have a list of all 190, but it’s unwieldy. So, here are the top 20 and the bottom 20:

What do the top 20 have in common? Mostly, they’re in Europe; a lot of them in Eastern Europe. Many are relatively small countries: Andorra, Montenegro, San Marino, Luxembourg, and the Seychelles all have populations under a million. As to the bottom 20, please note the disparity of scales between the two graphs – a factor of around 150 between Georgia at the bottom of the top 20, and New Zealand at the top of the bottom 20. Here, the main factor seems to be isolation. Both in island countries, and in Africa where very few people travel internationally. And there’s something else: Chinese ethnicity. Brunei, Laos, Taiwan and Vietnam – not to mention China itself! – all have high proportions of ethnic Chinese, who might be already more familiar with this kind of virus than other races.

Lastly, a scatterplot of cases per million against the UN’s Human Development Index (HDI):

Well OK, I put in the trend line just for fun. But it’s positive. Probably because the higher the level of development, the more travel people can enjoy. If they’re allowed to.

Weekly case growth and reproduction rate

Here is the graph of the weekly case growth world-wide, and the corresponding reproduction rates (the latter are modelled data):

You can see there what happened at the beginning of the epidemic. In the middle of February 2020, both the R-rate and weekly case growth were way down. There had been a few cases outside China, but nothing much to worry about. Then all of a sudden, in the third week of February, both suddenly climbed to dizzy heights. In a paper last year, I looked at the “onset dates” – the first days when the case rates started to climb significantly – of the virus in various countries. I determined that the outbreak beyond China had begun in earnest in the period from February 19th to 21st, and started in three countries: Iran, Italy and the USA. This coincided with a wave of Chinese business people returning from China after the (prolonged by a week) Chinese New Year celebrations. In hindsight, it seems that they may have brought with them a new, and more virulent, strain than the earlier one.

All that said, it’s reassuring that R-rate and weekly case growth track each other so well; even though the weekly case growth tends to be jumpier. The virus seems to wax and wane in communicability over relatively short periods, often of one to two weeks. It’s also noticeable that the peaks and troughs in weekly case growth tend to come a few days before the peaks and troughs in R-rate. I suspect this may be because I am using centrally averaged weekly cases in my calculation, so if the R-rate is calculated over a week looking back from the day stated, this would produce an offset between the two of about half a week.


It’s so 2020 to talk about testing again! Back last spring and summer, tests were a big issue. Were they too sensitive, and over-reporting cases? And were the test numbers themselves being over-reported for political reasons?

But as I’ve said before, and say again, I’ll use the numbers I have. So, here are the top 20 countries in tests per hundred thousand:

In every one of these countries, each member of the population has had an average of more than one test. But there’s nothing much to see here. Yet.

Now, another of the metrics I look at is cumulative cases per test over the whole epidemic. Here are the worst and best performers:

Those top 20 are weird. 70% of tests in Brazil have been positive? Since the beginning of the epidemic? Now, most of the top countries in this particular hall of shame are in South and Central America. Perhaps because they were hit by the virus during the time when there was a world-wide shortage of testing kits? But there are also some Eastern Europeans there: Bosnia, Macedonia, Slovenia, to name but three.

But if you already know which countries have been doing better against the epidemic in terms of deaths per million, you will see some familiar names in the bottom 20. Norway, Finland, Iceland, Denmark. South Korea, Thailand, Singapore, Taiwan, Vietnam. Not to mention Fiji, Australia and New Zealand. And China, the source of the epidemic, at the very, very bottom.

Which countries are in both the top 20 in tests per 100,000 and the bottom 20 in cumulative cases per test? Cyprus, Slovakia, Denmark, UAE, Austria, Singapore. Having plenty of test kits available seems to lead to a lower proportion of tests giving positive results; as you’d expect. But the most successful countries of all in controlling the virus seem to have been those which have managed to hold cases per test down without doing a whole lot of testing: Norway, Finland, Iceland, South Korea, Thailand, Taiwan, Fiji, Australia, New Zealand, Vietnam, China. Add in Mongolia, Rwanda and Bhutan as unexpected wildcards, too.


Here are the daily deaths (weekly averaged) world-wide:

This time, you can see a lowering of death rates during April and May, after the “first wave” in Europe; during which, if the UK is any example to go by, the health “authorities” seem to have had almost no idea about how to treat serious cases.

After that, it follows much the same pattern as the daily cases per million, but displaced to the right by what looks like about 2 weeks. The deaths curve is also somewhat bumpier than the cases; suggesting that the lethality of the virus has a tendency to go up and down.

Here are the lists of shame and fame in terms of cumulative deaths per million, respectively:

The worst hit places according to this metric are all in Europe, and particularly in Eastern Europe. The count of shame is made up by Brazil, Peru, the USA and Mexico. And Bosnia, Macedonia and Slovenia were all in the top 20 on cases per test.

At the other end of the scale, seven countries which have reported cases have not suffered a single death. All island countries, except for the Vatican. Among those immediately above them, we see many of the same names that were in the bottom 20 in cases per test: New Zealand, Singapore, Fiji, China, Bhutan, Taiwan, Vietnam. It’s also worth noting the factor of 250 difference in cumulative deaths per million between Portugal at the bottom of the top 20 and Timor at the top of the bottom 20.

Singapore is unique in being high in tests done, low in cases per test, and low in deaths per million, all at the same time. I’ll put Singapore on my list for a specific case study a bit later.

Lastly, here’s the plot of deaths per million against UN HDI rating:

That doesn’t look so different from the corresponding plot of cases per million.

Deaths per case

Now for the deaths per case metric. Here are the graphs of cumulative deaths per case, and daily deaths per case with a 21-day offset. The first covers the whole course of the epidemic, the second from May onwards (the data for individual countries having been too noisy before that):

That suggests that there had been a “zeroth wave” in China at the end of 2019, which was on its way down in lethality by January 2020. By the end of January, it had led to a total of about 125 confirmed cases in: Australia, Cambodia, Canada, Finland, France, Germany, India, Italy, Japan, Malaysia, Nepal, the Philippines, Singapore, South Korea, Sri Lanka, Taiwan, Thailand, the UAE, the UK and the USA. Unfortunately, Our World in Data no longer includes any data on cases or deaths prior to January 22nd, meaning that I can’t analyze that zeroth wave – unless I go back and take a look at the original downloads. But the first download I took, on May 2nd 2020, had no data for China at all! There was data by May 10th, though.

The death rate began to ramp up with the arrival of the “first wave” of the virus in Iran, Italy and the USA on or about February 19th 2020; peaked in early May; and has been going gently downward ever since, apart from a small hump in March 2021. The bumps in the daily deaths per case graph suggest that the virus has actually been waxing and waning in lethality every few weeks all along; just as it does in communicability. It seems that it spawns a lot more variants than just the ones you hear about in the news! The recent drop-off may be partly an artefact of not all the data on recent deaths being in yet, or partly due to the effects of vaccines, or both.

Here are the top and bottom 20 countries on the cumulative deaths per case metric:

The people of Vanuatu have been unlucky; they have had only four cases, but one death. Yemen and Syria are war zones, Somalia is all but, and many of the other countries near the top of the deaths per case league have ongoing political problems. It’s a surprise to see Mexico right up there in third place; though their health care system does seem to have had some problems in the past. And Bosnia, Bulgaria and Hungary all have high deaths per million from relatively moderate cases per million, suggesting that they too may have health care system problems.

At the other end, though, Singapore is last of all among those that have had deaths. They surely must have been doing something right! And Mongolia, the UAE, Timor, Laos and Bhutan have all appeared at the right end of the table in some of the earlier lists.

Here’s the plot of cumulative deaths per case against UN HDI index:

The trend, such as it is, is downwards. So, the more developed countries have slightly less deaths per case; as you would expect from better health care systems.


Here’s the graph of world-wide vaccinations:

Those numbers look quite impressive. But 600,000,000 is only about 7.5% of the current world population. And many countries have not yet even started vaccinating. Here are the lists of the top 20 in people fully vaccinated (two jabs) and people vaccinated (one or two):

The Seychelles has the most vaccinated population in the world; but even they had new outbreaks early in May, resulting in the imposition of a new lockdown. But the Seychelles economy is almost entirely dependent on tourism, and some of the people infected have been visitors.

I’ll leave to another day the question of how well the vaccines are working. For today, I’ll simply identify a few countries, where we should already be able to see some significant effects of vaccinations. Israel and the UAE I think are good choices, particularly because they have similar populations of just under 10 million. And the only two large countries (bigger than 50 million) in the lists, the UK and the USA, need to be in there too.

To sum up

The seeming correlation between low cases per test and low deaths per million came as a bit of a surprise to me. But it seems to explain at least part of why some very different cultures, notably the Nordics and those of Chinese extraction, seem independently to be doing well against the virus, relative to other countries. They test early, and follow up quick.

Singapore seems to be an outstanding example of getting the virus response right. I’ll take a closer look at some time in the future. I’m not sure I believe the Chinese figures, particularly now the pre-January 22nd data has been disappeared; I’ll have to take a look at them, too. And Israel, the UAE, the UK and the USA will be on my list for looking at the effectiveness of vaccinations in a more quantitative way.