Monday, 10 May 2021

COVID-19: European Lockdowns Re-visited


It’s now two and a half months since I issued my “omnibus edition” report on the progress of the virus in Europe. Much has happened since then, particularly in Eastern Europe (and it isn’t good, as the above shows). I’ve also extended my spreadsheets, so I can look at the effects of individual kinds of lockdown, and try to assess which have “worked” and which haven’t.

The 46 countries in this analysis are the same as in the report in February. This time round, the data goes up to May 2nd. As before, it comes from Our World in Data and the Blavatnik School of Government, both at Oxford University.

My conclusions

I found out some very interesting things from this exercise. So, here is what I would have written at the end, if I had decided to put it there.

Given the knowledge I now have about the COVID virus and the effects against it of the various types of lockdown, what would I – in my alternate hat, as President Glock of the Free and Individualist Republic of Utopia, a medium sized country in Europe – have done to combat the virus and minimize deaths per million, with minimum disruption to the population? Of course, this list represents my personal views, as well as the knowledge I have gleaned.

1.     I would have closed the borders as soon as cases started to climb out of control.

2.     I would have divided the country into regions, in each of which the situation was to be assessed independently, in conjunction with its neighbour regions. In essence, I would have implemented a “tiered lockdown” system, somewhat like the one which the UK had (briefly) in October 2020.

3.     I would not have locked down schools at any point, or introduced any face covering mandates at all.

4.     I would have held back workplace closures as a “last resort” to be used only if all other measures have failed. But if I did have to close them, I’d close all of them, except those necessary for the continuation of life. Including government offices. No, particularly government offices.

5.     I would have cancelled all public events. This is the one lockdown I would have maintained right through until the virus is beaten.

6.     I would have brought in restrictions on gathering sizes quite early, but I would have started the limit somewhere between 10 and 100 – perhaps around 30.

7.     If cases were climbing out of control in a region, even with the national borders closed, I would have closed down all public transport in that region except taxis and school buses, and brought in appropriate restrictions on travel within the region. If I had felt I needed a slogan to reinforce the policy, it might have been: “Go by car! But not too far!”

8.     I would not have brought in any stay-at-home mandates unless the combination of travel restrictions and closing public transport was not enough.

But most importantly, I would have continually experimented with what worked and what didn’t. I would have tried relaxing this a tad in that region, and seeing what happened. If it didn’t work, I could always go back to the previous policy after a few weeks. I don’t think people would have objected to this, as long as they knew exactly how it was going to be done, and how long in advance they could make bookings for trips away with confidence.

And I would always have been receptive to the idea of re-opening flights and ferries to other countries, whose leaders were taking a similar attitude. Such agreements would be renewable, and travellers would always know the situation at least a month in advance.


OK, so to the detail! And the (not so) pretty pictures.

Here are the spaghetti graphs of total cases per million for each of the four groups:

As you can see, the spaghetti has become increasingly tangled as the epidemic has gone on. Somewhat reassuringly, the case counts for the highest countries in three of the four groups are rather similar, at 15% to 17% of the population. Although, not so reassuringly, all are still going up. In contrast, the highest case count among the core countries of the “Europe 14” group (Luxembourg) is only about 11% of the population. I suspect this may be because these were among the countries where the virus went epidemic earliest, and a lot of symptom-free and mild cases would have been missed in the first two months or so. In the UK, for example, it wasn’t until April 26th that the total tests done reached even 1% of the population.

Looking at the countries with the lowest case counts, Finland, Iceland and Norway stand out, with only about 2% of the population having become cases. The next group, with up to about 4% of the population having become confirmed cases, are Russia, Greece, the Vatican, Belarus and Germany. I assume that the Vatican’s success is due to washing their hands every 20 minutes in holy water (/sarc).

Here is the complete list of cases per million population, in order:

It’s notable that, of the top six countries in cases per million, only Czechia (the Czech Republic) has a population of more than a million. The rest are all small communities, in which, once the virus does get a foothold, transmission is likely to be quicker on a per-population basis than in larger communities.

Case Growth

Here are the spaghetti graphs of weekly case growth for the four groups of countries. I have started the plots only from September, because the data is too noisy prior to that time:

Beyond the sudden, large excursions as the virus discovers a new pocket of victims in one country or another, there is a common pattern. Growth rates tend to be decreasing towards a minimum around the new year; then they increase through January and February, then go down again. As at the beginning of May, the only countries with positive weekly case growth are Denmark, Ireland, Latvia, Lithuania and Russia (the last only just).

How much of the decrease since February is due to the vaccine roll-outs, is a question I plan to address in the future. But today, I’m going to concentrate on…


Lockdowns are supposed to control cases, and specifically case growth, by making transmission of the virus less likely. So here, I’m going to be plotting cases per million against various metrics of lockdown level.

The Blavatnik School of Government data provides for each country a “stringency” (percentage) which is intended to give an overview of how hard the country was locked down on any one day. There are also levels and national/regional markers for nine different individual kinds of lockdowns: Schools, Workplaces, Public Events, Gatherings, Public Transport, Stay at Home, Travel Restrictions (internal), International travel restrictions and Face Covering mandates. (The last is not counted when calculating the Blavatnik stringency).

Today, I am looking at lockdowns not during particular periods, but over the entire course of the epidemic. I have therefore devised two calculations for overall stringency metrics. The first is the average level of stringency over the entire epidemic to date; each day’s stringency figure, as a percentage from 0% to 100%, is simply added up, and the total divided by the number of days of data. The second is the full lockdown metric; that is, the number of days during which the lockdown level has been at its maximum possible value of 100%, divided by the total number of days of data. These metrics can be applied to individual kinds of lockdowns, or to the aggregate (though no country in this group has actually imposed 100% lockdowns of all the individual kinds simultaneously).

Here are the lists of average Blavatnik lockdown stringencies, and percentage time in full lockdowns (calculated by working out the percentage time in full lockdowns for all the nine kinds of lockdown, adding them up and dividing by 9):

The Irish are at the top of both stringency lists, by the proverbial country mile. That 32% bar represents an average, over the whole epidemic since late January 2020, of very nearly three out of nine kinds of lockdown being imposed at 100% stringency. The UK comes seventh out of 43 in average stringency, and fifth in time under full lockdowns. (The Vatican, North Macedonia and Montenegro do not report any Blavatnik data).

Here are the scatterplots of cases per million against average lockdown stringency and time spent under full lockdowns:

So, the more stringent the lockdowns, the higher the cases per million! That might seem counter-intuitive. But I think it’s probably because one of the things likely to trigger governments to lock down is a spurt in cases per million. So, it’s the high cases per million that leads to the lockdowns, not the other way round. The slope of this trendline, in the first plot, is +127 cases per million per % unit of stringency.

Note that the trend line for full lockdowns, in the second plot, is a lot steeper than that for average stringency; the higher the cases per million, the more likely governments are to wind lockdowns up to the max. The slope here is +1,039 cases per million per % of average time in full lockdown.

Also note the outlier (Belarus) at the left of the first plot, and the five outliers at the bottom left of the second (reading from the left: Belarus, Finland, Russia, Iceland, Norway). All these countries seem to have performed particularly well in controlling virus cases so far; they are five of the bottom seven in cases per million.

Individual Lockdowns

Next, I’m going to judge each kind of lockdown individually. I’ll explain here how I intend to do that.

It might at first sight seem a bit silly to put trend lines on the two cases per million graphs above. The data is so noisy, that most of the data points are miles away from the trend line. But there is some method in my (apparent) madness. What I’m going to do is plot the cases per million against the average percentage stringency for each of the individual kinds of lockdown. I’ll then compare the slopes of the trend lines with the slopes found above.

If the slope has decreased, or even gone negative, this suggests that the individual lockdown has had some efficacy in reducing cases per million, compared to the other kinds of lockdown. The further the trend line rotates in a clockwise direction, the more effective the individual lockdown is. If, on the other hand, the slope has increased and the trend line has rotated anti-clockwise, then probably the individual lockdown has been counter-productive in terms of controlling cases per million.

Thus, what I’m interested in is not so much the slope of the trend line, but the way in which it rotates when cases per million are plotted against individual lockdowns rather than against lockdown levels as a whole. It’s also worth noting that the cases per million values are the same in both graphs; they don’t change at all in the vertical direction. Each country’s data point can only move horizontally; to the right if the individual lockdown is more stringent than the average of all lockdowns, to the left if less stringent.

Where it’s appropriate for an individual kind of lockdown, I’ll also show the cases per million against the time in full lockdown for that kind of lockdown. These graphs exclude those countries which have not imposed a full lockdown of that particular type.


Here is the Blavatnik codebook’s definition of the schools lockdown figures:

The level on an individual day is converted to a percentage by first subtracting half a unit if the lockdown is regional (targeted), then dividing by 3 and multiplying by 100%.

Here are the average and full lockdown lists for school lockdowns:

Full lockdown, for schools, is “require closing all levels.” Sweden, Finland and Belarus haven’t mandated full school closure at any point in the epidemic; and Russia, Iceland and (strangely, considering its poor performance in deaths per million) Belgium have only required all schools to close for less than 5% of the time. The UK is twelfth in average stringency and sixteenth in full lockdowns.

And here’s the effect in terms of cases per million:

In the first plot, the line has rotated anti-clockwise; its slope is now +295 cases per million per % unit of stringency, as opposed to +127. This suggests that locking down schools is less effective overall at reducing cases per million than locking down something else instead.

In the second plot, though, the slope is now +378 cases per million per % of time spent in full lockdown, as opposed to +1,039. Thus actually “going the whole hog” and closing all schools does seem to have some effect of reducing cases per million.


Here are the lists of average and full workplace lockdowns:

Ouch! Economic freedom doesn’t matter to the Irish government, either. Nor, much, to the UK, which is in second position in both lists. Congratulations to all the countries with the blank bars at the top of the second list, which haven’t done any full workplace lockdowns; and even more so to Belarus, which hasn’t locked workplaces down at all.

The trend in the first plot is about +188 cases per million per % stringency. Again, the line has rotated anti-clockwise. Suggesting that locking down workplaces is less effective overall at reducing case growth than locking down something else would have been. In the second plot, though, the trend has gone all the way to -428 cases per million per % time spent in full lockdown.

This suggests that, while locking down workplaces mildly doesn’t do anything much useful, closing them altogether does bring down the cases per million. But given that, for ordinary people’s everyday lives, workplace lockdowns (including shops and services that some bureaucrat deems to be “non-essential”) are one of the harshest kinds of lockdown of all, I have to wonder whether all the pain has been worth it.

Public Events

Here are the lists of average stringencies and full lockdowns:

In general, public events have been locked down harder and for far longer than schools or workplaces. This is understandable, since at an event there is inevitably a lot of mixing of people from a wide geographical area. Even Belarus has been recommending (but not requiring) event cancellations for a significant proportion of the time. But the UK is in fourth place in both lists; the three countries ahead of it in both cases are Albania, Italy and Germany.

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

The slope of the first trendline is +238 cases per million per % stringency unit; the second is +100 cases per million per % of time spent in full lockdown. So, locking down events seems to be more effective than locking down schools, but less so than locking down workplaces.


Again, the UK is in the same place in both lists – seventh; for most of the time, gatherings have been limited to 6, which is a full lockdown by the Blavatnik definition.

Here’s the effect of gatherings lockdowns on cases per million:

In the first plot, the trend is downwards as the lockdown level increases! It is -175 cases per million per % of stringency.  This suggests that gatherings lockdowns have had an effect on reducing cases per million. Not surprising to me, as the chance of virus transmission will be well more than linear with the number of people in the gathering.

In the second plot, on the other hand, there is still a positive trend, of +562 cases per million per % of time spent in full lockdown. This is an improvement on the +1,039; but not as much of an improvement as fully locking down workplaces, events or even schools. So, the question must be asked: is it worth it, to kill millions of people’s social lives for a year and more, in order (slightly) to reduce the number of COVID cases?

Public transport

Despite not actually having closed public transport, the UK still ends up sixth, because it has recommended closure of public transport for more than a year! Now, where I am, public transport is running perfectly normally – but it’s all but empty. Sensible people are taking the COVID safe option, and either walking or driving wherever they need to go. You can’t beat the convenience, comfort and COVID safety of “one man, one car!”

Here are the two plots of cases per million:

The trend in the first plot is small and negative, -66 cases per million per % of stringency. This suggests that locking down public transport may probably contribute something towards lowering cases per million. I find that not too surprising, as public transport in normal times has, from an epidemiological point of view, all the worst features of an event (many strangers around) and a gathering (everyone packed together).

The second plot shows a near flat trend, +96 cases per million per % of time in full lockdown. This is an improvement on the +1,039 shown by the average of all full lockdowns.

Stay at Home

Only two countries, Italy and Serbia, have ordered any period of full stay-at-home lockdown. These have been around 5% and 11% of the epidemic respectively. Therefore, there is only one list to show here, the list of average stringencies:

For once, the UK isn’t near the top! But this lockdown is similar to (but stricter than) the travel restrictions lockdown, which I’ll cover in the next section.

The trend is again negative at -211 cases per million per % of stringency; even more negative than for public transport. So, stay-at-home mandates do have an effect in helping to reduce cases per million. But at what cost?

Travel Restrictions

On average stringency, the UK is back to its usual fourth place. It is only in 10th place on full travel restrictions lockdowns. But note that many comparable countries – like Denmark, Germany, and the Netherlands – have at no point mandated any travel restrictions at all. Oh, and Ireland is up at or near the top yet again.

Again, negative trends of -188 cases per million per % stringency and -344 cases per million per % time in full lockdown. Suggesting that stay-at-home and travel restrictions lockdowns may have approximately equal effects on cases per million. But again, at what cost?

International Travel Restrictions

What I found when I looked at Australasia and Oceania was that early closure of borders at the beginning of the epidemic had led countries like Australia and New Zealand to much lower levels of cases than most of the rest of the world. I wonder if there has been a corresponding effect in Europe too?

Well, that’s a turn-up for the book. Hungary is way ahead of all the others on international lockdowns. The case counts aren’t out of the ordinary – 16th out of my 46 in cases per million. And yet, it has the worst rate in deaths per million in the whole world. But the UK is in the “hall of shame” yet again, at sixth from bottom in the very lockdown that has kept our friends Down Under so relatively trouble-free.

Here are the cases per million graphs:

Both trends are now negative: -734 cases per million per % stringency, and -426 cases per million per % of time in full lockdown. A bit odd that they should be that way round; but the outlier on the extreme right of the second plot, which is of course Hungary, may well be a large part of the cause.

Face Coverings

To face covering mandates; which the Blavatnik people did not see fit to include in their stringency calculation. And yet, to those of us concerned about human rights and dignity, face covering mandates are one of the worst COVID impositions. Not only are masks uncomfortable and demeaning. But the mandates also cause tensions in everyday life – for example, when supermarket checkout operators start to act like pocket Hitlers because you’re “not wearing your mask right.” So, it’s very important to ask, are these mandates objectively justified?

Here’s the Blavatnik definition:

Now, none of the countries in this particular region have gone beyond level 2 (50%) nationally, or in a few cases level 3 regionally. So, again, there’s only one list:

Here’s the graph of cases per million against face coverings lockdown:

What’s this? A big positive trend? +994 cases per million per % of stringency! Orders of magnitude above the +127 trend when cases per million are plotted against average lockdown stringency. So, does requiring the public to wear face masks actually increase the likelihood of virus transmission? That’s what this graph seems to be telling me.

Can anyone reading this find any good reason why my conclusion here is invalid?

To sum up

I’ll summarise the trends in cases per million against average lockdown levels and the levels of each of the individual kinds of lockdown in the form of a table:

Lockdown measure

Trend in cases per million per % of

Difference in trend from trend against average



Full Lockdown


Full Lockdown
















Public Events










Public Transport





Stay at Home





Travel Restrictions










Face Coverings





So, in terms of small increases in stringency, by a long way the most effective lockdown for controlling cases is the one on international travel. Stay at home mandates, travel restrictions and gatherings restrictions, and recommending public transport closures have a smaller effect on reducing cases per million. And workplaces, public events and schools measures have little or no marginal effect, unless and until a full lockdown is instituted (all schools closed, all “non-essential” workplaces closed, all public events cancelled).

The three most effective full lockdowns for controlling cases are closure of non-essential workplaces, mandatory travel restrictions and border closures. Full public events cancellations and public transport closures are less effective; and closing schools, and restricting gatherings to a maximum less than or equal to 10 people, are less effective still.


The metric, on which I expect politicians will be judged once it comes time for a post-mortem on the virus, is deaths per million. Here’s the list:

The Hungarians are not doing well. Indeed, Eastern European countries in general aren’t doing well. The UK is now down to 12th; better than it was a few months ago. But still bad.

Of course, the final result in a country may depend on the current level of cases per million, as well as on the deaths per million so far. If cases per million in a country are still low, they have further to go to reach herd immunity than those which have had more cases already. But hopefully, the vaccines will narrow these gaps.

Myself, I prefer to look at (cumulative) deaths per case over the course of the epidemic. This, I think, gives a better view than deaths per million of how bad or good a country’s health system is. Here’s the list according to this measure:

This shows why Hungary is doing so badly. Bosnia and Bulgaria may well be in trouble in the future, too. Notice that a lot of the countries near the top of the list are in south-eastern Europe, in or near the Balkans. And the UK is 8th out of 46, beaten only by Italy among Western European countries.

If you look down near the bottom, you will see some familiar names: Iceland, Norway, Belarus, Denmark, Finland. As well as some less expected ones, like Cyprus and Serbia.

Here are the scatterplots of cumulative deaths per case against average lockdown stringency and average percentage of time under full lockdowns:

Since both axes are percentages, I don’t need to worry about units for the trend line gradients. I can just express them as numbers. They are +0.0326 and +0.0387 respectively. Note also that, in the first plot, Belarus lies right bang on the trendline!

So, the more stringently locked down a country has been over the course of the epidemic, the higher the cumulative deaths per case rate tends to be! Again, this may be because the governments with the worst health care systems have felt a greater need to lock down in order to prevent utter disaster.

My curiosity inspired me to look through the plots of cumulative deaths per case against individual lockdown stringencies and percentages of time in full individual lockdown. I’ll show one of these plots, because it did rather gobsmack me:

The slope of this line is -0.0705, as compared with +0.0387 as the trend of cumulative deaths per case against average time spent in full lockdowns. Those relatively few countries, which have mandated the closure of public transport, seem to have got a big benefit from it in terms of deaths per case, as well as a benefit in cases per million. I presume this is because public transport not only exposes people to the virus, but can also expose them to potentially large doses of virus at relatively close quarters.

Here’s the table I constructed to show the results:

Lockdown measure

Trend in cumulative deaths per case against % of

Difference in trend from trend against average



Full Lockdown


Full Lockdown
















Public Events










Public Transport





Stay at Home





Travel Restrictions










Face Coverings





In terms of small increases in stringency, restricting gathering size is the most effective way of controlling deaths per case. Restrictions on public transport, workplaces and international travel are the next most effective. Locking down schools, and mandating face coverings, do no good at all.

By far the most effective full lockdown for controlling deaths per case is the complete closure of public transport. Closing workplaces, closing borders, restricting gatherings to a maximum size of less than 10, and cancelling public events can also be useful. Closing all schools does not appear to be a worthwhile thing to do.

Belarus and Hungary

I’ll conclude by following through two case studies from Eastern Europe. Belarus, which according to the figures has performed astonishingly well against the virus so far, while keeping lockdowns very low. And Hungary, the worst hit country in the world at this time in terms of deaths per million.

Both, fortunately, are in my Eastern Europe (North) group; so, I can show their cases and deaths data together on the same graphs. First, cases per million:

Hungary is that orange line, with two peaks in late November and in March. Belarus is the mid-blue one that has been bumbling along near the bottom for many months; though, from April to mid-June of last year, it was actually at the top of the group in daily cases per million.

Second, recent deaths per case:

Hungary’s orange rises above the rest like tongues of flame, while Belarus’s mid-blue has been bumbling along the bottom since November. The cumulative deaths per case, through the whole epidemic, are of interest too:

That big loop of orange string, and subsequent trajectory, suggest to me that there is something not right with the Hungarian health care system. I’ve read that, until recently, doctors and even hospital specialists were badly underpaid compared to other countries in the region. So, maybe they have a serious skills shortage, which could explain the consistently high deaths per case. And Hungarian isn’t a language commonly spoken by foreigners, so importing doctors from other places – as the UK has done from India and Sri Lanka, for example – isn’t going to be easy.

So, let’s look at lockdowns. Here is the stacked bar chart of average lockdown levels for the Eastern Europe (North) group:

Here are the lockdown timings for Belarus:

They got away with a (relatively) low case rate in the first wave of the epidemic, for most of which period they were quarantining arrivals from risky places, not banning them. In late October they escalated that to a full border closure, which has only recently been (slightly) released.

Belarus is not a country that gets many visitors at the best of times, so this may well have been sufficient to stop the second wave getting any traction at all. Beyond that, all they have done is to recommend that events be cancelled, and that face masks should be worn. Lukashenko being what he is (Belarus’s Freedom House rating is 19 out of 100), these may well be “recommendations” the people can’t refuse. But from a COVID point of view, they haven’t done much if any harm.

In contrast, here’s what the Hungarians have been doing:

Their international borders were closed through the first wave of the epidemic, and they didn’t get many cases. They were banning arrivals from risky places from May 2020 until late August. Then they closed the borders again. But the damage had already been done. If you look very closely at the graph of cases per million, you can see the Hungarian orange line starting to rise already at the beginning of September. The virus was already in the country before they closed the borders. And as they relaxed internal travel restrictions in September, it continued to spread. In November, they brought in stay-at-home mandates; which fixed the immediate rise in cases, but didn’t stop the further, third, wave that peaked in late March.

So, it looks as if the bad Hungarian situation is mainly the product of two things. The first is a health care system which, for reasons rooted in the communist past, didn’t have enough skilled doctors. That’s what socialism does to you; by suppressing the free market, it leads to imbalances between what people who do particular things are paid and what they are worth. And that can have disastrous consequences in the longer term. The second was a bad decision, in not imposing internal travel restrictions early in October, when cases had started to rise again even though the borders were closed.

To sum up (Or not)

If this was a musical piece, I’d write here: “D.S. al Fine.” So, please go back and re-read the “My conclusions” section near the beginning.

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