COVID-19: the “second wave” in Europe

By Neil Lock

Preface

Charles has asked me to clarify the Blavatnik stringency index I use in this paper. Here’s where you can find its definition: in Chapter 4 of https://www.bsg.ox.ac.uk/sites/default/files/2020-11/BSG-WP-2020-032-v9.pdf. I share Charles’s concerns about the way the index is put together. My own criticisms are: One, they weight their 9 factors equally, without justification. My main objective in this paper is to try to put together some evidence to test that equal weighting! Two, they do not rightly weight regional lockdowns in comparison with national ones. In my view, any regional lockdown should be weighted according to the population affected by it. A lockdown measure in England (84% of the UK population), for example, ought to carry almost 17 times as much weight in the index as the same measure in Wales (5% of the population). All that said, if the Blavatnik data has been put together honestly (and I don’t have any evidence to lead me to doubt that), my inclination is to use it to get the best picture I can.

A month ago, I compared the histories of the COVID-19 epidemic in fourteen Western European countries. At that point, the “second wave” of the virus, which had been building throughout the region for three or four months, was giving governments an excuse to start re-introducing lockdowns. So, I said that I would review the situation in a month or so. That month has now elapsed, so here’s the review. Maybe, just maybe, I’ll now have enough data to form some idea of which lockdown measures have been effective, and which haven’t.

Once again, here is the list of countries:

Austria

Belgium

Denmark

France

Germany

Ireland

Italy

Luxembourg

Netherlands

Portugal

Spain

Sweden

Switzerland

UK

The data sources are the same as before: Our World in Data and the Blavatnik School of Government, both at Oxford University. The data I used was taken on December 3^rd, and it included figures up to and including December 2^nd.

In the last week or so, the Our World in Data feed has changed quite substantially. Most data before the third week of January has been deleted. Some countries – France, Germany and Sweden at least – have taken the opportunity to wipe and re-write a lot of their data, some of it right back to the beginning of the epidemic. And the data for UK dependencies (Jersey, Guernsey, Isle of Man, Gibraltar) and Danish dependencies (Faeroe Islands, Greenland) has disappeared entirely. I would have expected that this data might have been consolidated into the parent country’s; but for the UK at least, I don’t see any evidence of this.

Every so often, the Our World in Data feed adds new data columns. One of these recently added is the reproduction rate (Rt). This is the average number of new infections passed on (as at a given day) by a single infected person. It is usually expressed as a fraction. Rt bigger than 1 means the infection numbers are generally rising, and less than 1 means they are generally falling. In the UK at least, this is modelled data rather than measured data. And, as we’ll see, some countries’ figures are smoother than others, so it looks as if different countries are calculating it differently. But it’s still of interest to compare even a modelled Rt with the observed rate of growth of new cases.

Also, in November the Swedes have also completely re-written their lockdown stringency data, and it now looks as if for months their lockdown hasn’t been nearly as light as we had been led to believe. All this said, I’ll repeat what I’ve said many times before: It’s the best data I have, so I’ll use it.

Cases

I’ll begin with cases. Here are the total (cumulative) cases per million population over the whole period of the epidemic, up to December 2^nd.

Here is a daily cases per million population comparison. The data shown are centrally averaged over a 7-day period. That is, the date against which a count is plotted is the 4^th (central) day of the period.

In the great majority of the 14 countries, the new case counts have peaked since late October, and in many have since fallen significantly. So, the recent lockdowns must have had an effect. Which measures have had the most effect, is a moot point at this stage.

Here is the list of daily cases per million as at the end of the month:

To put this in perspective, only Spain, Ireland and France are currently below the 200 new cases per million population per day, at which the WHO considers the virus to be endemic, and no unlocks should be considered. However, four more countries, including the UK, are now only slightly above it.

Another way to look at the cases figures is in terms of weekly new case growth. This is the percentage growth in the (weekly averaged) new cases from a particular day to the same day of the week a week later. This requires the weekly averaged new cases up to 3 days after the current date, meaning there must be at least 6 days of case data after the current date. That is why the graph stops before the end of November.

It’s obvious that, over the last four weeks, the trends in weekly case growth have almost all been downward. So much so, that only three of the countries are now showing positive growth in new cases:

Another way to look at infection rates is to plot the reproduction rate, Rt. This is based on numbers of infections, not cases, so it may show a slightly different picture to the weekly case growth. Later, when I come to plot the two on the same axis, it will become plain that while the two are clearly related, they don’t always move together in perfect sync.

Here are the Rt values supplied by each country over the course of the epidemic. With the exception of Sweden, the Rt rates have been trending down throughout November:

The UK is one of only four of the countries with an Rt rate below 1 at the end of November.

In contrast, the trends in lockdown stringency have almost all been upward since late October:

The UK (pink line) appears to be bucking this trend; but, like most things political, that is a deceit. The apparent drop around November 10^th was caused by the release of “circuit-breaker” lockdowns in Wales and Northern Ireland. Yet people in England are (were?) far harder locked down at the end of November than at the end of October. At the moment at least, the figure pulled through to Our World in Data only reports measures which are in place UK wide; it seems to miss additional measures in the individual constituent countries. On top of the currently reported figure of about 64%, these additional measures account as of November 30^th for around 5% extra stringency in England, 3% in Northern Ireland and Wales, and around 1% in Scotland.

Tests

The number of cases which get found depends, in part at least, on the testing capacity available. Here are the cumulative tests carried out per 100,000 population in each country (except Sweden and France, which do not report cumulative test counts):

Luxembourg and Denmark are well ahead of the rest. In fact, the number of tests done in Luxembourg since the start of the epidemic is more than twice the population!

Another interesting statistic is the cumulative percentage of positives among the tests done since the very beginning of the epidemic:

In many of the countries, the cases per test percentage has climbed significantly in the second wave of the epidemic. I’d guess this is simply because infections have been climbing faster than any increase in the number of tests available. This is consistent with the observation that, in most of the countries, this ratio now seems to be nearing a second peak.

Deaths

Here are four spaghetti graphs of deaths from the virus. The first is total deaths per million population. The second shows the daily deaths per million, over the course of the epidemic; and I have appended to it a histogram of the deaths per million rates as at November 30^th. You can see here which countries have started to “get on top” of the second wave, and which haven’t. The third shows deaths per case, with the cases offset 21 days back from the deaths (21 days being the mean length of the course of the disease, in the UK at least). The fourth and final graph shows the cumulative totals of deaths per case over the whole course of the epidemic.

The UK (pink line) is not doing well in the deaths-per-case stakes. It is second only to Italy in current daily deaths per case. And the UK is now top of the list in terms of deaths per case over the whole epidemic, at about 3.6%. Deaths per case is, I think, a fair indicator of lack of quality in a country’s health care system; for lack of testing capacity, and less effective treatment of those who need hospitalization, will both tend to increase it.

Lockdowns

I come now to the meat of this review. For each country, I have plotted weekly case growth percentage (blue line), lockdown stringency percentage (brown line) and Rt rate multiplied by 100 to express it as a percentage (grey line), all on the same graph. Both the weekly case growth and Rt are capped at a maximum of 200%. If a particular lockdown measure is effectual, then I would expect the grey and blue lines to move in the opposite direction to the brown, at or shortly after the day the measure comes into effect. A newly introduced lockdown measure, if successful, ought to visibly slow Rt rate, or weekly case growth, or both, within the incubation period of the virus (maximum 12 days).

This is complicated by the fact that, as you will see from the graphs, the virus has a rhythm of its own. Under conditions of constant stringency, the weekly case growth tends to oscillate periodically. The period can be different in different countries, and sometimes varies from time to time within a country; but 2 to 6 weeks from peak to peak or trough to trough is typical. Left to itself, over the course of many cycles, the weekly case growth will tend to rise. But if a lockdown measure is effective, it may change the overall trend between peaks or troughs from upwards to downwards, and may also start to smooth out the peaks and troughs.

As to the reproduction rate, it too tends to oscillate periodically, in the same direction as the weekly case growth. Peaks and troughs in weekly case growth often show a few days ahead of peaks and troughs in the Rt rate. However, as some of the examples below will show, it is now quite common to have Rt above 1 and case growth negative at the same time.

The other component of my review is the detailed data, which the Blavatnik School of Government provide on the status of 12 lockdown indicators (9 of which contribute to the stringency index) for each country for each day. I have converted these to a list of measures which have been imposed (or unlocked) in each country, with dates, since August 1^st. I have also included a summary of the currently active lockdown measures in each country.

Austria

Date	Stringency	Measures
20200906	36.11	Schools: Recommended closed (Regional) International: Ban some arrivals
20200914	36.11	Face covering: Required when with others
20200917	37.04	Workplaces: Recommended closed (Regional) Gatherings: Up to 11-100
20200929	40.74	Stay at home: Recommended
20201013	44.91	Events: Mandatory cancelled (Regional) Gatherings: Up to <=10 (Regional)
20201017	58.8	Workplaces: Some closed (Regional) Stay at home: Required with exceptions (Regional) Travel: Mandatory restrictions (Regional)
20201023	60.19	Gatherings: Up to <=10
20201027	64.81	Schools: Recommended closed Events: Mandatory cancelled
20201102	75	Schools: Some closed Workplaces: Some closed Public transport: Recommended closed Stay at home: Required with exceptions Travel: Recommended not to travel
20201117	82.41	Schools: Mandatory closed Workplaces: Mandatory closed

Current (20201127): Schools: Mandatory closed, Workplaces: Mandatory closed, Events: Mandatory cancelled, Gatherings: Up to <=10, Public transport: Recommended closed, Stay at home: Required with exceptions, Travel: Recommended not to travel, International: Ban some arrivals, Public info: Co-ordinated, Testing: Open, Contact tracing: Comprehensive, Face covering: Required when with others.

Notes: Given the high peaks in both Rt and case growth near the end of October, I don’t think the lockdown measures introduced during September and early October had a whole lot of effect. However, the September 29^th “Stay at home: Recommended” did appear to produce an all but immediate downturn in weekly case growth and in reproduction rate. The October 23^rd reduced limit on the size of gatherings also seems to have had an immediate beneficial effect. The November 2^nd measures also had some positive effect, though it’s not possible to tell which of them were responsible for it. The November 17^th measures have continued the drop in weekly case growth, but I don’t yet have the Rt figures to cross-check with.

There’s something else curious about this graph. Look at the peaks in Rt and in the weekly case growth. They seem to be getting vertically further apart from each other. As time goes on, it looks as if it takes a higher Rt to produce a given growth in cases. I wonder, perhaps, if the proportion of infections which do not lead to confirmed cases (for example, because they are asymptomatic) is rising? If so, that’s good news.

Belgium

Date	Stringency	Measures
20200729	62.96	Workplaces: Mandatory closed (Regional) Gatherings: Up to <=10 Stay at home: Required with exceptions (Regional)
20200807	59.26	Stay at home: Recommended (Regional)
20200809	64.81	Travel: Mandatory restrictions (Regional)
20200812	58.33	Workplaces: Some closed Stay at home: Required with exceptions (Regional) Travel: No restrictions
20200827	52.78	Stay at home: No measures
20200930	47.22	Events: Recommended cancelled Face covering: Required in some places
20201001	47.22	Face covering: Required when with others
20201009	45.37	Workplaces: Some closed (Regional)
20201019	54.63	Workplaces: Some closed Stay at home: Required with exceptions
20201029	56.48	Schools: Some closed (Regional)
20201102	65.74	Workplaces: Mandatory closed Events: Mandatory cancelled
20201116	63.89	Schools: Recommended closed

Current (20201123): Schools: Recommended closed, Workplaces: Mandatory closed, Events: Mandatory cancelled, Gatherings: Up to <=10, Stay at home: Required with exceptions, International: Ban some arrivals, Public info: Co-ordinated, Testing: If symptoms, Contact tracing: Comprehensive, Face covering: Required when with others.

Notes: I added the July 29^th measures to the list above, because they do seem to have had an immediate and significant effect. The only national measure in that group was the restriction of gathering size to 10 or below, so that may have been what “did the trick” at that stage. The precipitate fall in weekly case growth around October 22^nd, and in the reproduction rate a little later, looks likely to be due to the October 19^th “Stay at home: Required with exceptions.” The November 2^nd mandatory closure of workplaces and cancellation of events have in fact been followed by an increase in weekly case growth, though it is still (just) negative. Rt has continued to drop, but there is no “knee” to suggest that these measures on their own made a significant difference.

I will, however, note that the stringent October 1^st “Face covering: Required when with others” mandate seems to have done nothing at all to prevent the huge peak in new cases in mid to late October. And it seems to have sent the reproduction rate up, not down! I think that gives us some evidence that mandating face coverings brings little or no benefits.

Denmark

Date	Stringency	Measures
20200801	50.93	Schools: Recommended closed
20200822	50.93	Face covering: Required in some places
20200909	47.69	Workplaces: Some closed (Regional) Gatherings: Up to 11-100 (Regional) Public info: Co-ordinated (Regional)
20200919	50.93	Workplaces: Some closed Gatherings: Up to 11-100
20201010	41.67	Workplaces: Recommended closed Gatherings: Up to 101-1000 Public transport: Open Public info: Co-ordinated Contact tracing: Limited
20201021	37.04	Schools: Open Gatherings: Up to 11-100 Stay at home: No measures Contact tracing: Comprehensive
20201026	39.81	Gatherings: Up to <=10
20201109	54.63	Schools: Some closed (Regional) Stay at home: Recommended Travel: Recommended not to travel
20201116	50	Stay at home: Recommended (Regional) Travel: Recommended not to travel (Regional)
20201119	43.52	Schools: Recommended closed Stay at home: No measures Travel: No restrictions
20201123	45.37	Stay at home: Recommended (Regional)

Current (20201130): Schools: Recommended closed, Workplaces: Recommended closed, Events: Recommended cancelled, Gatherings: Up to <=10, Stay at home: Recommended (Regional), International: Ban some arrivals, Public info: Co-ordinated, Testing: Open, Contact tracing: Comprehensive, Face covering: Required in some places.

Notes: Denmark’s Rt rate looks smoother than either Austria’s or Belgium’s, and it doesn’t show all the peaks and troughs in weekly case growth. It looks as if they may be calculating it a different way from the others.

The last three troughs in Rt (the final one is only just visible) look to have all bottomed out at similar values around 120%, and all at stringency levels near 50%, too. The October 26^th reduction of maximum group size, combined with the stay at home and not-to-travel recommendations in force from November 9^th to 19^th, have brought the Rt down somewhat, but not as much as I would have expected. They may also have contributed to the small size of the following case growth peak; but I can’t be sure. We’ll have to wait a bit longer to draw any conclusions from Denmark.

France

Date	Stringency	Measures
20200803	46.3	Face covering: Required outside the home (Regional)
20200814	48.15	Workplaces: Some closed (Regional)
20200901	46.76	Gatherings: Up to <=10 (Regional)
20200903	48.61	Schools: Some closed (Regional)
20200922	46.76	Schools: Recommended closed
20200926	49.54	Events: Mandatory cancelled (Regional)
20201010	43.98	Events: Recommended cancelled Travel: No restrictions
20201017	49.54	Stay at home: Required with exceptions (Regional)
20201030	78.7	Schools: Some closed Workplaces: Mandatory closed Events: Mandatory cancelled Gatherings: Up to <=10 Stay at home: Required with exceptions Travel: Mandatory restrictions
20201128	75	Workplaces: Some closed

Current (20201128): Schools: Some closed, Workplaces: Some closed, Events: Mandatory cancelled, Gatherings: Up to <=10, Stay at home: Required with exceptions, Travel: Mandatory restrictions, International: Ban some arrivals, Public info: Co-ordinated. Testing: Open. Contact tracing: Comprehensive, Face covering: Required when with others.

Notes: To help make sense of the French data, I’ll also show the daily cases graph:

What seems to have happened is that the French waited until the last possible moment, then on October 30^th threw in just about every lockdown idea they could think of, all at the same time. It seems to have “worked,” after a fashion; but it’s been almost as harsh as the first lockdown. Moreover, the French have had “Face covering: Required when with others” nationally since July 20^th. So, that rush up to the peak from July to October, I think, is fairly good evidence that face mask wearing by the public doesn’t hamper the spread of the virus.

Note also that, as of mid-November and under stringent lockdown, Rt was still above 100%, and yet new cases were dropping.

Germany

Date	Stringency	Measures
20200807	59.72	Schools: Some closed (Regional)
20200808	56.94	Gatherings: Up to 11-100 (Regional)
20200824	59.72	Gatherings: Up to <=10 (Regional)
20200903	57.87	Schools: Recommended closed
20200904	49.54	Travel: No restrictions
20201001	46.76	International: Quarantine high-risk
20201015	56.02	Stay at home: Recommended Travel: Recommended not to travel
20201022	57.87	Stay at home: Required with exceptions (Regional)
20201102	59.26	Workplaces: Some closed Gatherings: Up to <=10 Stay at home: Recommended
20201110	62.04	International: Ban some arrivals

Current (20201129): Schools: Recommended closed, Workplaces: Some closed, Events: Mandatory cancelled, Gatherings: Up to <=10, Stay at home: Recommended, Travel: Recommended not to travel, International: Ban some arrivals, Public info: Co-ordinated, Testing: Open, Contact tracing: Comprehensive, Face covering: Required in some places.

Notes: German cases have recently all but stabilized. Here’s the new cases graph:

The most likely causes of this recent stabilization would seem to be the October 15^th “Stay at home: Recommended” and “Travel: Recommended not to travel.” Germans will usually do what they are told to! The November 2^nd restriction on group size, and the closure of some workplaces, have reduced Rt, but they don’t seem to have had much effect so far on case growth. And for much of November, Rt was well above 100%, but the new case counts weren’t consistently growing.

Ireland

Date	Stringency	Measures
20200808	59.72	Workplaces: Mandatory closed (Regional) Gatherings: Up to 11-100 (Regional) Stay at home: Required with exceptions (Regional) Travel: Mandatory restrictions (Regional)
20200818	63.43	Events: Mandatory cancelled
20200921	52.31	Schools: Recommended closed Workplaces: Some closed Events: Mandatory cancelled (Regional) Gatherings: Up to 11-100 (Regional) Public transport: Recommended closed (Regional) Travel: Recommended not to travel (Regional)
20201007	61.57	Schools: Recommended closed (Regional) Events: Mandatory cancelled Travel: Mandatory restrictions
20201021	81.48	Schools: Some closed Workplaces: Mandatory closed Gatherings: Up to <=10 Public transport: Recommended closed Stay at home: Required with exceptions

Current (20201123): Schools: Some closed, Workplaces: Mandatory closed, Events: Mandatory cancelled, Gatherings: Up to <=10, Public transport: Recommended closed, Stay at home: Required with exceptions, Travel: Mandatory restrictions, International: Quarantine high-risk, Public info: Co-ordinated, Testing: If symptoms, Contact tracing: Comprehensive, Face covering: Required in some places.

Notes: The regional measures of August 8^th seem to have brought the immediate problem under control. After that, nothing seemed to have much effect until October 7^th. It was probably the national measures, “Travel: Mandatory restrictions” and/or the “Events: mandatory cancelled” that did the trick. And the (over?) draconian measures of October 21^st have certainly brought Rt down, and to well below 100%.

Italy

Date	Stringency	Measures
20200808	50.93	International: Ban some arrivals
20200817	54.63	Workplaces: Some closed
20200914	47.22	Schools: Recommended closed
20201006	55.56	Gatherings: Up to 11-100 Public transport: Recommended closed Contact tracing: Limited Face covering: Required when with others
20201014	50	Public transport: Open
20201023	66.67	Schools: Some closed (Regional) Workplaces: Some closed (Regional) Gatherings: Up to <=10 Public transport: Recommended closed (Regional) Stay at home: Required with exceptions (Regional) Travel: Mandatory restrictions (Regional) International: Quarantine high-risk Contact tracing: Comprehensive
20201106	76.85	Schools: Some closed Workplaces: Mandatory closed (Regional) Stay at home: Required with exceptions International: Ban some arrivals
20201110	79.63	Public transport: Recommended closed Contact tracing: Limited

Current (20201125): Schools: Some closed, Workplaces: Mandatory closed (Regional), Events: Mandatory cancelled, Gatherings: Up to <=10, Public transport: Recommended closed, Stay at home: Required with exceptions, Travel: Mandatory restrictions (Regional), International: Ban some arrivals, Public info: Co-ordinated, Testing: If symptoms, Contact tracing: Limited, Face covering: Required when with others.

Notes: The August 17^th closure of some workplaces did seem to have an effect. The package of measures on October 6^th did have an immediate effect, but not as strong as the Italians might have hoped. October 23^rd, for me, looks like the key date; and on that date, the only national measure was the restriction of gatherings to 10 or less. This looks like more evidence that restricting gathering sizes works.

Whether the strong restrictions added on November 6^th have made a difference, or are simply “over the top,” I – once again – cannot tell; and it doesn’t help that the Italians haven’t reported any Rt figures since November 20^th. But once again, an Rt consistently above 100% has nevertheless allowed case growth to drop significantly.

Luxembourg

Date	Stringency	Measures
20200807	31.48	Events: Recommended cancelled Stay at home: Recommended
20200812	34.26	International: Screening
20200821	39.1	International: Ban some arrivals
20200825	43.52	Workplaces: Recommended closed
20200913	40.74	Gatherings: Up to 11-100
20200926	43.52	Gatherings: Up to <=10
20201006	43.52	Contact tracing: Limited
20201020	52.78	Schools: Recommended closed Events: Mandatory cancelled
20201030	56.48	Stay at home: Required with exceptions Face covering: Required when with others
20201126	60.19	Workplaces: Some closed

Current (20201123): Schools: Recommended closed, Workplaces: Some closed, Events: Mandatory cancelled, Gatherings: Up to <=10, Stay at home: Required with exceptions, International: Ban some arrivals, Public info: Co-ordinated, Testing: Open, Contact tracing: Limited, Face covering: Required when with others.

Notes: Because Luxembourg is a small country, its weekly case growth will tend to be more volatile than in larger countries. There were also significant adjustments to the numbers of cases in late August. Since then, a significant drop in weekly case growth seems to have started since the October 20^th measures. I’m a little surprised by that, as school closures were only recommended, not mandated; perhaps the mandatory cancellation of events was a bigger factor.

The October 31^st “Stay at home: Required with exceptions” also produced a drop in Rt, as you can see by the “knee” on the graph. But since then, case growth hasn’t come down much, even though Rt has continued to drop. As to the November 26^th closure of some workplaces, we’ll have to wait and see.

Netherlands

Date	Stringency	Measures
20200818	50.93	Events: Recommended cancelled Gatherings: Up to <=10
20200920	48.15	Events: Recommended cancelled (Regional)
20200929	62.04	Events: Mandatory cancelled Travel: Recommended not to travel
20201104	65.74	Workplaces: Mandatory closed
20201122	56.48	Workplaces: Some closed Travel: No restrictions

Current (20201122): Schools: Recommended closed, Workplaces: Some closed, Events: Mandatory cancelled, Gatherings: Up to <=10, Stay at home: Recommended, International: Ban some arrivals, Public info: Co-ordinated, Testing: If symptoms, Contact tracing: Comprehensive, Face covering: Required in some places.

Notes: The August 18^th restriction on gathering size did seem to pull down the size of the next peak in case growth. How significant the recommendation to cancel events was, I don’t know. But Rt started to increase shortly afterwards, not to decrease!

The September 29^th measures, events cancellation and recommendation not to travel, did seem to get the cases coming down at last. Rt also started to drop significantly, a week or so afterwards.

All was well for a while; and by the middle of November, Rt had dropped well below 100%. But the November 4^th closure of workplaces seems to have had no beneficial effect at all. In fact, since the middle of November, Dutch cases have been dropping, but more slowly than before.

Portugal

Date	Stringency	Measures
20200801	65.28	Face covering: Required outside the home (Regional)
20200810	66.2	Events: Mandatory cancelled Stay at home: Required with exceptions (Regional)
20200825	55.09	Schools: Recommended closed Workplaces: Some closed (Regional) Stay at home: No measures
20200904	56.94	Workplaces: Some closed
20200915	58.8	Stay at home: Recommended (Regional)
20201002	56.94	Workplaces: Some closed (Regional)
20201023	60.65	Stay at home: Required with exceptions (Regional)
20201024	66.2	Schools: Mandatory closed (Regional)
20201030	74.54	Travel: Mandatory restrictions (Regional)
20201104	66.2	Travel: No restrictions
20201106	60.65	Schools: Recommended closed
20201114	69.91	Workplaces: Mandatory closed (Regional)
20201116	66.2	Workplaces: Some closed (Regional)
20201121	69.91	Workplaces: Mandatory closed (Regional)
20201123	66.2	Workplaces: Some closed (Regional)

Current (20201123): Schools: Recommended closed, Workplaces: Some closed (Regional), Events: Mandatory cancelled, Gatherings: Up to <=10 (Regional), Public transport: Recommended closed, Stay at home: Required with exceptions (Regional), International: Ban some arrivals, Public info: Co-ordinated, Testing: Open, Contact tracing: Limited, Face covering: Required outside the home.

Notes: Since early September, all the lockdowns have been regional. They have been quite stringent. And they do seem to be getting on top of the virus, albeit slowly.

The peaks and troughs in Rt in Portugal don’t seem to correspond to any particular lockdown measures being introduced or released at the time. Rt did, however, drop during September, a period when some workplaces were closed nationally. And, though Rt is still well above 100%, new cases have started to drop significantly. The Portuguese must be doing something right; but I have no idea what it is!

Spain

Date	Stringency	Measures
20200810	60.65	Stay at home: Recommended (Regional)
20200814	62.5	Workplaces: Some closed
20200907	60.65	Schools: Some closed (Regional)
20201007	64.35	Schools: Mandatory closed (Regional)
20201013	64.35	Contact tracing: Comprehensive Face covering: Required outside the home
20201022	58.8	Schools: Recommended closed
20201025	71.3	Events: Mandatory cancelled Gatherings: Up to <=10 Stay at home: Required with exceptions Travel: Mandatory restrictions

Current (20201129): Schools: Recommended closed, Workplaces: Some closed, Events: Mandatory cancelled, Gatherings: Up to <=10, Stay at home: Required with exceptions, Travel: Mandatory restrictions, International: Ban some arrivals, Public info: Co-ordinated, Testing: If symptoms, Contact tracing: Comprehensive, Face covering: Required outside the home.

Notes: The two sets of lockdowns during July do seem to have had an effect on both Rt and weekly case growth, but they were regional only. Another “sea change” seems to have taken place around October 25^th. The measures introduced then were event cancellations, reduced gathering size, stay at home, and travel restrictions. All four of these have been seen to be effective elsewhere, so the Spaniards are probably on the right track as far as dealing with the virus is concerned. Here, too, we see Rt consistently above 100% during November, and yet a significant drop in new cases.

The face covering requirement introduced on October 13^th – the most stringent in all the 14 countries – does not appear to have had any effect on Rt. And any effects it might have had on case growth will have been eclipsed by the measures of October 25^th.

Sweden

Date	Stringency	Measures
20200817	55.56	Schools: Recommended closed
20201110	58.33	Travel: Recommended not to travel (Regional)
20201111	50	Gatherings: No restrictions
20201124	53.7	Workplaces: Some closed

Current (20201124): Schools: Recommended closed, Workplaces: Some closed, Events: Mandatory cancelled, Public transport: Recommended closed, Stay at home: Recommended, Travel: Recommended not to travel (Regional), International: Ban some arrivals, Public info: Co-ordinated, Testing: If symptoms, Contact tracing: Limited.

Notes: The weekly case growth has come down since the end of October, with no particular lockdown measure being an obvious cause. However, Rt – which is unusually smooth, like Denmark’s – has been rising since July, and now seems to have just about peaked. The November 24^th closure of some workplaces hasn’t been in force long enough yet to draw any conclusions.

Switzerland

Date	Stringency	Measures
20200917	43.06	Face covering: Required when with others
20200918	43.06	Testing: If symptoms
20201010	33.8	Schools: Recommended closed (Regional) Events: Recommended cancelled (Regional) International: Quarantine high-risk
20201019	35.19	Gatherings: Up to 11-100
20201020	40.74	Events: Recommended cancelled International: Ban some arrivals
20201029	45.37	Workplaces: Some closed Events: Mandatory cancelled (Regional)
20201102	49.07	Schools: Some closed (Regional)

Current (20201123): Schools: Some closed (Regional), Workplaces: Some closed, Events: Mandatory cancelled (Regional), Gatherings: Up to 11-100, International: Ban some arrivals, Public info: Co-ordinated, Testing: If symptoms, Contact tracing: Comprehensive, Face covering: Required when with others.

Notes: This is an odd one. Rt went up enormously during September and early October, perhaps due to the re-opening of schools after the summer break. (There was a similar rise back in May, when schools re-opened after the first lockdown). Weekly case growth and Rt have been coming down almost continuously since then, and Rt is now down almost to 100%. Yet there was no national lockdown measure in early October to trigger that!

New cases peaked and started coming down around the time of the October 29^th closure of some workplaces. Looking at Rt, there is a “knee” at precisely that time; so perhaps this measure added to the already existing downward trends in Rt and weekly case growth.

UK

UK wide measures

Date	Stringency	Measures
20200801	69.91	Travel: Mandatory restrictions (Regional)
20200813	66.2	Schools: Some closed (Regional)
20200830	66.2	Contact tracing: Limited
20200901	64.35	Schools: Recommended closed
20200914	65.74	Gatherings: Up to <=10
20200924	67.59	Stay at home: Recommended
20201012	60.19	Stay at home: Recommended (Regional) Travel: Recommended not to travel (Regional)
20201019	65.74	Schools: Mandatory closed (Regional)
20201022	67.59	Stay at home: Recommended
20201023	75	Stay at home: Required with exceptions (Regional) Travel: Mandatory restrictions (Regional)
20201106	75	Workplaces: Mandatory closed (Regional) Stay at home: Recommended Travel: Recommended not to travel International: Ban some arrivals
20201110	63.89	Schools: Open Workplaces: Some closed

Current (20201116): Workplaces: Some closed, Events: Mandatory cancelled, Gatherings: Up to <=10, Public transport: Recommended closed, Stay at home: Recommended, Travel: Recommended not to travel, International: Ban some arrivals, Public info: Co-ordinated, Testing: If symptoms, Contact tracing: Limited, Face covering: Required in some places.

Notes: The UK seems to have the best correlation between Rt and weekly case growth of all the countries. There was a sea-change from a rising to a falling Rt trend some time in September, only broken by the huge spike in early October. “Gatherings: Up to <=10” and “Stay at home: Recommended” may have helped with this.

Here is the new cases graph for the UK as a whole:

The “tiered” local lockdowns in place in the second half of October seemed to have just about stabilized the new cases. When a new national lockdown was introduced in early November, cases suddenly went up again! But they peaked around November 13^th, and have been going down ever since.

The UK data is particularly difficult to analyze, not only because of the tiers system (a version of which comes back into force on December 2^nd), but also because England, Northern Ireland, Scotland and Wales each have their own separate additional lockdown rules.

England (84% of UK population)

Date	Stringency	Measures
20200801	66.2	Stay at home: No measures Travel: Mandatory restrictions (Regional)
20200827	66.2	Face covering: Required in some places
20200901	62.5	Schools: Recommended closed
20200914	63.89	Gatherings: Up to <=10
20200925	63.89	Face covering: Required in some places
20201012	65.74	Stay at home: Recommended (Regional)
20201105	74.07	Stay at home: Required with exceptions Travel: Mandatory restrictions
20201117	66.67	Stay at home: Required with exceptions (Regional) Travel: Recommended not to travel
20201130	68.52	Schools: Some closed (Regional)

Differences from UK wide measures (20201130): Schools: Some closed (Regional), Stay at home: Required with exceptions (Regional), International: Quarantine high-risk.

Notes: The August 27^th “Face covering: Required in some places” almost exactly coincided with the start of the second wave. And after the September 25^th tightening, cases went soaring! Not good evidence for the efficacy of face coverings. And despite “Schools: Recommended closed,” most schools did in fact re-open, and the results are visible in the cases graph.

Of the November measures, the most likely to have brought about the drop in cases were the stay-at-home requirement and the travel restrictions.

Northern Ireland (3% of UK population)

Date	Stringency	Measures
20200810	62.96	Face covering: Required in some places
20200824	57.41	Schools: Some closed (Regional)
20200831	55.56	Schools: Recommended closed
20200911	54.17	Gatherings: Up to <=10 (Regional)
20200922	55.56	Gatherings: Up to <=10
20200925	55.56	Face covering: Required in some places
20201014	77.78	Schools: Mandatory closed Stay at home: Recommended Travel: Mandatory restrictions
20201102	68.52	Schools: Some closed Travel: Recommended not to travel Contact tracing: Limited
20201110	66.67	Schools: Some closed (Regional)

Differences from UK wide measures (20201123): Schools: Some closed (Regional), International: Quarantine high-risk.

Notes: Due to the low proportion of the population, these measures are unlikely to have contributed much to the UK wide picture.

Scotland (8% of UK population)

Date	Stringency	Measures
20200805	71.3	Travel: Mandatory restrictions (Regional)
20200817	67.59	Schools: Recommended closed
20200821	73.15	Stay at home: Required, minimal exceptions (Regional)
20200824	70.37	Travel: Recommended not to travel
20200831	64.81	Stay at home: Recommended
20200923	64.81	Contact tracing: Comprehensive
20200925	64.81	Face covering: Required in some places
20201004	64.81	Contact tracing: Limited
20201102	67.59	Travel: Mandatory restrictions (Regional)
20201117	64.81	Events: Mandatory cancelled (Regional)

Differences from UK wide measures (20201123): Schools: Recommended closed, Events: Mandatory cancelled (Regional), Travel: Mandatory restrictions (Regional), International: Quarantine high-risk.

Notes: Due to the low proportion of the population, these measures are unlikely to have contributed much to the UK wide picture.

Wales (5% of UK population)

Date	Stringency	Measures
20200816	59.26	Stay at home: No measures
20200901	55.56	Schools: Recommended closed
20200908	62.5	Gatherings: Up to <=10 (Regional) Travel: Mandatory restrictions (Regional)
20200914	62.5	Face covering: Required in some places
20200925	62.5	Face covering: Required in some places
20200928	66.2	Stay at home: Recommended
20201013	67.59	Gatherings: Up to <=10
20201016	70.37	Travel: Mandatory restrictions
20201023	77.78	Workplaces: Mandatory closed Stay at home: Required with exceptions
20201109	64.81	Workplaces: Some closed Stay at home: Recommended Travel: Recommended not to travel
20201117	64.81	Contact tracing: Limited
20201123	66.67	Schools: Some closed (Regional)

Differences from UK wide measures (20201123): Schools: Some closed (Regional), International: Quarantine high-risk.

Notes: Due to the low proportion of the population, these measures are unlikely to have contributed much to the UK wide picture.

Some tentative conclusions

In many cases, it’s hard to establish a strong correlation between success against the virus and any one particular lockdown measure. Part of the reason is that governments like to make lots of different regulations all starting on the same date, so it’s hard to determine which worked and which didn’t. The following conclusions, therefore, can only be tentative.

While schools are well known to be a breeding ground for the virus, I couldn’t find any evidence that school closures, either recommended or mandated, have on their own caused a significant drop in case growth anywhere during the second wave.

Workplace closures appear not to have been beneficial in Belgium or the Netherlands, and their effectiveness in Germany is doubtful. There is, however, some evidence that they did make a difference in Italy; and perhaps in Portugal and Switzerland too.

In most of the countries, large scale events have been (and still are) cancelled. But when a country has relaxed this measure, re-imposing it often seems to have had a beneficial effect on new case counts; at least in Ireland, Luxembourg, the Netherlands and Spain. But there seems to have been no clear benefit from re-imposing this measure in Belgium.

The reduction in maximum gathering size to 10 or less seems to have been effective in Austria, Belgium, Italy, Spain and the UK. The only country where it doesn’t seem to have made much of a difference is the Netherlands.

Public transport closures do not appear to have been a significant factor during the second wave of the epidemic.

Stay at home requirements look to have had a significant effect. Even just recommending stay-at-home has produced effects in Austria, Germany and the UK. Mandating stay-at-home seems to have made a difference in Belgium and Spain, and perhaps in Luxembourg.

Travel restrictions, too, do make a difference. Even a recommendation not to travel has had beneficial effects in Germany and the Netherlands. Mandatory restrictions on travel have been effective in Ireland, and arguably in Spain. And a mixture of the two has, probably, had some effect in the UK.

The only countries which changed their international travel rules in October or November are Germany, Switzerland and Italy. I would expect that the effects of these changes will have been negligible; since international travel bans and quarantines would have far more effect in times when the virus is at a low level in a country, than when – as now – it is higher than in the rest of the world.

As to face masks for the general public, evidence from Belgium, France, Spain and the UK suggests that they have no beneficial effects. Indeed, it’s not implausible, given the data, that requiring the public to wear face coverings actually helps to spread the virus.