Sunday, 8 August 2021

COVID-19: The Fat Lady Approaches

How far have the various countries of Europe managed to get, in their attempts to conquer the COVID virus and restore some semblance of normality to our lives? There are some interesting signs, and even some moderately encouraging ones. The fat lady has not yet sung – indeed, she hasn’t even begun her gargling exercises yet. But there are signs that, absent a new and even more transmissible variant than the current “delta” variant, COVID may be on the way out in Europe fairly soon.

The data I used for this exercise comes from Our World in Data and the Blavatnik School of Government, both based at Oxford University. It covers 46 countries; 14 forming the core of Western Europe, 12 in Eastern Europe (North), 11 in Eastern Europe (South), and 9 mostly smaller countries, which I have labelled “Rest of Western Europe.” The data runs up to August 5th 2021.


I’ll start with vaccinations. Here are the lists of percentages of people fully vaccinated (two jabs) and vaccinated (one or two jabs):

I’ll also show the list of what I call “susceptibles.” This is an estimate of the percentage of the population in a country who are still susceptible to infection, with all that it brings in its wake. As I explained in an earlier paper, I calculate the susceptibles measure by, first, subtracting from 100% the percentage of the population who have been reported as cases. I then subtract from that figure the percentage of the population fully vaccinated, times an efficacy factor to allow for the possibility of a vaccination not working properly. I have used 95% as that efficacy factor, though for the delta variant that figure is probably too high. I also subtract from my figure half this percentage (47.5%) times the percentage of the population vaccinated but not fully vaccinated. Lastly, assuming the vaccination becomes effective two weeks after it is given, I move the figures forward so that the number of susceptibles is based on the vaccination figures as they were 14 days earlier. Here’s the result:

Other things being equal, you would expect the weekly growth in new cases at a given time (and so the reproduction rate or R-rate, that is, the average number of infections resulting from each case) to depend linearly on the proportion of susceptibles at that time. If the basic R-zero reproduction rate of the virus (in an uninfected population) is R0 and the susceptible fraction of the population is S, then you might expect the actual R-rate to be R0S. The point at which R0S becomes less than 1 among a population then becomes the point at which the virus (or, more accurately, the variant with that particular R0) is doomed to extinction in that population.


On to the numbers of daily new cases. Here are the spaghetti graphs over time for daily new cases per million population (weekly averaged) for each of the four groups into which I divided my 46 countries:

From this perspective, the “first wave” of spring 2020 looks like just a little blip; albeit a deadly one. The big surge in cases began in October, throughout most of Europe. As countries’ daily new cases have risen, governments have locked down, with the aim of bringing down the daily new case counts. This, in turn, was intended to avoid hospital and (particularly) Intensive Care Unit beds overfilling with COVID patients.

As vaccines have come on stream since the New Year, though, the peaks in daily new case counts have tended to get lower with time. Some of the most recent peaks, however, have been of a different kind from the earlier ones. The earlier peaks always happened shortly after new lockdown actions were taken to reduce transmission of the virus. With the latest ones, though, this is not necessarily so. As I’ll show a bit later, at least two of the sudden downturns on the right-hand ends of the graphs seem to have been a result of a spontaneous drop in the number of daily new cases, without a significant change in lockdown policy.

Later in the paper, I’ll look in more detail at six countries with such downturns:

1.     The UK (pink peak on the first graph, which has just levelled out).

2.     Spain (dark blue peak on the first graph).

3.     The Netherlands (narrow dark green peak on the first graph).

4.     Portugal (dark brown peak on the first graph in early July).

5.     Cyprus (big light blue peak on the third graph).

6.     Malta (wide light blue peak on the fourth graph).

The ordered list of total (cumulative) cases per million follows:

And here is the ordered list of daily cases per million (weekly averaged), as at the time of writing:

Reproduction Rates

The virus reproduction rates (R-rate) are also worth showing. The R-rate is the average number of new infections resulting from one case. It correlates well with the percentage growth in daily new cases from one week to the next; but it is also considerably smoother, so easier to interpret on a graph.

In most of the countries, the R-rate was on a general downward trend until June 2021, when the delta variant took off. Looking more closely, though, some countries seem to have got this variant earlier. In the first graph, reproduction rates in the UK (pink), Portugal (dark brown) and Spain (dark blue) started rising earlier than in the other countries. As in the third graph did Cyprus (light blue), and in the fourth Malta (light blue) and Monaco (green).


In order to assess why a particular change in daily new cases, either up or down, took place, it is also necessary to know the history of lockdowns in the country in question. The Blavatnik School of Government defines a measure it calls “stringency.” It includes nine categories: public information campaign, schools lockdown, workplaces lockdown, public events lockdown, gatherings lockdown, public transport lockdown, stay at home lockdown, travel restrictions lockdown and international travel lockdown. Face covering mandates are not included.

Each category, as reported each day, is assessed on a points scale from zero up to a maximum of 2, 3 or 4, which is then converted to a percentage of the maximum value. Allowance is made for some countries at times implementing regional lockdowns rather than national; a regional lockdown in a particular category is assessed as half a point lower than the corresponding national lockdown. The nine category scores are then added together and divided by 9 to give an overall lockdown stringency percentage.

Here is the spaghetti graph of lockdown stringency for the Europe 14 group of countries:

And the ordered list of European lockdown stringencies at the time of writing:


Before I look at individual countries, I’ll show the spaghetti graphs of hospital bed occupancy by COVID patients. (Not all countries are reporting these figures):

These are not unlike the corresponding cases graphs, but displaced to the right by a couple of weeks. Prior to the arrival of the delta variant, though, they were almost all on a strong downward trend.

Intensive Care Unit Occupancy

Here are the corresponding graphs for ICU bed occupancy by COVID patients in the core of Western Europe:

This is very similar in shape to the hospitalizations graph. Although, curiously, the big peak in hospitalizations in Italy in late November isn’t reflected in the ICU numbers.

I won’t show the graphs for the other groups, as not enough countries are reporting ICU occupancies to make them interesting.

Individual Countries

I’ll now look in more detail at the data for the six countries I listed earlier as showing sudden downturns in the daily new case count. As controls, I’ll also show the data for Czechia and Hungary.

Czechia has the highest total cases per million of all countries in the world with populations over a million; 15.6% of the population. So, it is probably as close to herd immunity as anywhere. Czechia also currently has a fairly low daily cases per million, and a relatively low lockdown stringency. Suggesting that, if the fat lady is going to sing “It’s all over now” in the reasonably near future, Czech may be the language in which she sings it.

Hungary, on the other hand, has the worst record in Europe for deaths per million; more than 0.3% of its population have died of COVID, even though only about 8% of the population have been recorded as confirmed cases. It, too, now has low daily cases per million and lockdown stringency, as well as high vaccinations figures.

The UK

Here are the cases and deaths for the UK over the course of the epidemic:

Note the July 2021 downturn in daily new cases. Also note that in the last week or so, the daily cases averaged over the week have roughly stabilized. Modeller Neil Ferguson has talked of 100,000 or even 200,000 new cases per day over the next few weeks. But that now doesn’t look likely, after the slide of daily new cases from about 50,000 the Friday before the July 19th “freedom day” to only about 25,000 a week or so after.

Here is the weekly case growth, plotted against R-rate and lockdown stringency:

The orange line is my own measure of stringency, which I call “harshness.” In contrast to the Blavatnik stringency measure, it aims to assess the level of legal constriction faced by the individual under it. Thus, it does not take account of public information campaigns, but it does include face covering mandates. It ignores measures which are recommended only, so includes only those which are legally mandatory. And it weights those lockdowns which affect everyone (such as workplace closures, stay at home) more heavily than those which only affect some (such as school closures, international travel restrictions). The harshness value is generally a little lower than the Blavatnik stringency; when the two approach each other, as they did for most of January and February 2021 in the UK, this means that those in power have chosen the most unpleasant kinds of lockdown they could.

You can see the big drop in R-rate and weekly case growth, starting around the third week of June. But this was not associated with any increase in the lockdown stringency. This looks like good news!

From June 5th to July 18th, the measures in place were: Schools: Recommended closed, Workplaces: Some closed, Events: Recommended cancelled, Gatherings: Up to <=10 (Regional), Public transport: Recommended closed, Stay at home: No measures, Travel: No restrictions, International: Ban some arrivals, Face covering: Required when with others. On July 19th, the following changed (in England): Workplaces: Open, Events: Allowed, Gatherings: No restrictions, Public transport: Open, Face covering: Required in some places (Regional).

There’s more good news in the graph of hospitalizations and ICU occupancy:

Hospital bed occupancy by COVID patients is now at only 15% of the level it was at the peak of the epidemic back in January. And it has stabilized over the last week or so, as people recover who caught the virus during its last peak. ICU occupancy, too, is under 22% of its peak value back in January. So, there’s enough “slack in the system” to support a considerable rise in daily new cases – if it were to happen – without any further lockdown. It seems that the vaccines, while they don’t limit transmission of the virus nearly as well as was hoped, do lead to a big reduction in the proportion of cases needing hospitalization.

To complete the picture, here is the graph of deaths per case, with the cases shifted back by 21 days (which is the mean time between case confirmation and death if it eventuates):

If you do get the virus in the UK now, your chance of dying from it is only 0.22%. A far cry from the bad old days of a year or even six months ago!


The recent downturn in Spain isn’t as precipitous as the one in the UK.

Spain, like the UK, has experienced a falling R-rate and weekly case growth since late June. For most of July, this was under a régime of falling lockdown stringency. The recent increase in harshness was caused by a stay-at-home mandate in one region.

The Netherlands

This one doesn’t look like such a success story. On June 26th, the Dutch did a huge unlock; the stringency level was almost halved “at a stroke.” The measures at that point were: Schools: Recommended closed, Workplaces: Recommended closed, Events: Recommended cancelled, Gatherings: No restrictions, Public transport: Open, Stay at home: No measures, Travel: No restrictions, International: Ban some arrivals, Face covering: Required in some places. The result was an immediate, almost run-away spurt of new cases. On July 10th, they re-closed some workplaces (this seems to be a favourite lockdown for the Dutch). Which seems to have produced an immediate downturn in the daily new case count.

It looks as if the Dutch went too far, too fast with their June unlock; then had to renege on it. The people whose workplaces have been closed (and their customers) must be furious.


It doesn’t look, from these graphs, as if the Portuguese are anywhere near an end-game with COVID. They haven’t even really started doing any serious unlocking. Right now, they are second, behind only Germany, in the list of hardest locked down countries in Europe. And that last little fall from a peak isn’t a spontaneous drop; it’s just the effect of yet another lockdown.


The Cypriots are at a relatively low level of lockdown, compared with many other countries. The current level is: Schools: Recommended closed, Workplaces: Recommended closed, Events: Recommended cancelled, Gatherings: Up to 11-100, Public transport: Recommended closed, Stay at home: No measures, Travel: No restrictions, International: Quarantine high-risk, Face covering: Required when with others.

In some ways, their story looks similar to the Dutch. A large unlock on June 8th opened all workplaces, and allowed gatherings in the hundreds. This produced a spurt in cases, so it was mostly reversed on the 22nd. But I’ll give the Cypriots a plaudit for trying out different unlocks, to see what works and what doesn’t.


Malta is the most vaccinated country in Europe. So, I would expect them to have been quite gung-ho about unlocking. And they were, indeed. By July 5th, their measures were: Schools: Recommended closed, Workplaces: Recommended closed, Events: Recommended cancelled, Gatherings: Up to <=10, Public transport: Open, Stay at home: No measures, Travel: No restrictions, International: Ban some arrivals, Face covering: Required when with others. The result was a big, sudden spurt in cases. On the 14th, they closed some workplaces again. We now know, both from Malta and from the Netherlands, that closing “some” workplaces (whatever those workplaces may specifically be) does have a strong effect against spread of the virus. But at what cost, economically and psychologically, for the affected workers and their customers?


Czechia (also known as the Czech Republic) has been unlocking steadily since March. Since July 6th, their lockdown measures have been: Schools: Recommended closed, Workplaces: Recommended closed, Events: Recommended cancelled, Gatherings: Up to >1000, Public transport: Open, Stay at home: No measures, Travel: No restrictions, International: Ban some arrivals, Face covering: Required in some places.

During July, the Czechs managed to overcome a period of R-rate above 100%, without the daily new case count going above the low hundreds – in contrast to over 12,000 at the third peak of the epidemic in early March. Reported cases so far are 15.6% of the population. Their vaccination statistics are somewhere in the middle of the European league table. So, it looks as though the sluggishness of the virus’s spread might well be down to approaching herd immunity. At least, this may give other countries an idea of where the finishing line may be.


Since June 29th, the lockdown measures have been: Schools: Open, Workplaces: Open, Events: Allowed, Gatherings: Up to 11-100, Public transport: Open, Stay at home: No measures, Travel: No restrictions, International: Ban some arrivals, Face covering: Required in some places. For the last several weeks in Hungary, new daily cases have been fairly stable, averaging out at about 50-60 cases per day, against more than 9,000 at the peak in March. So, they may well be approaching herd immunity, helped by the high level of vaccinations.

Excess Mortality

Lastly, here are the graphs of excess mortality (from all causes, not just COVID) for these countries. The calculation divides deaths for each time of year (week) by the average deaths for the same week over a reference period of five years, in this case 2015-2019; then makes it into a percentage, and subtracts 100%.

Clearly, the overall trends have been downwards since April 2020 in Western Europe, and since about November in Eastern Europe. So, in excess deaths terms, we’re on course to get back down there soon! Which lends weight to the argument that we just have to learn to live with this virus, and we must never allow politicians to use COVID as a stick with which to destroy our rights and freedoms.

Here are the current excess mortality values:

The 14 countries at the bottom of the list are now doing better, even allowing for COVID, than they did in the same week in the reference period. And the geographical spread is clear, with most of the countries with high current excess mortality being in South Eastern Europe.

To sum up

Czechia and Hungary lead the way. If I only knew how many unreported infections there have been for each reported case, I could estimate how close they are to herd immunity given a particular R-zero and a particular level of vaccination success. That snippet of information, however, I have not been able to find, even for the UK. I found some estimates, but they came from different periods of the epidemic, and they varied so much that they give me no confidence at all. That said, my feeling for the numbers tells me that, absent a more transmissible variant even than the delta variant, Czechia and Hungary have all but got COVID under control; at least, until they open their borders again.

The UK seems to be in a surprisingly good position. Despite the post-“freedom day” splurge of cases anticipated by Neil Ferguson and the media, daily new case counts in the 25,000 to 30,000 range don’t seem that bad. This kind of loading should be supportable for a couple of months at least, without overfilling the hospitals or ICUs with COVID patients. That's assuming Sajid Javid holds his nerve, and doesn't let SAGE steamroller him into another lockdown.

But even Neil Ferguson seems to think the worst should be over by the end of September. So, I’d guess there’s quite a decent chance of the UK reaching herd immunity without any further lockdowns. The overall lockdown stringency figure, of 44%, is still quite high compared to many other European countries. But this is misleading, because England, which has 84% of the UK population, now has a stringency level of only 23%.

Other countries, such as the Netherlands, Cyprus and Malta, have been a tad over-eager in unlocking, and have had to backtrack somewhat. They will try again. One country which does concern me is Portugal. They still don’t seem able to control the spread of the virus without extensive lockdowns; and their hospital and ICU facilities have been among the most stretched in all of Europe. I am also concerned for the people in those countries, notably Ireland, Germany and Greece, which have chosen to control cases by means of long-term, relatively harsh lockdowns; meaning that they now have further to go than others in order to reach herd immunity.

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