Monday, 12 July 2021

COVID-19: Are we Nearly There Yet?

As politicians in different countries of Europe make decisions about how far to unlock the COVID-19 measures and when, contradictory signals abound. So, I thought I would review the latest data, and provide some new graphs as well as updating some old ones. The purpose being, to try to answer the question: “Are we nearly there yet?”

I have produced new graphs of weekly growth in hospital and Intensive Care Unit occupancy by COVID patients, to go with the pre-existing graphs of weekly case growth. I have also taken advantage of the recent addition of an “excess mortality” column to the Our World in Data feed, to plot excess mortality for each country (as a percentage of the mortality for the same time of year averaged over the years 2015 to 2019).

For this analysis, I have returned to my list of 14 countries which together form the core of Europe: Austria, Belgium, Denmark, France, Germany, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Spain, Sweden, Switzerland and the UK. The data runs up to July 9th 2021.


I’ll start at the opposite end from usual, with vaccinations. Here are the graphs and ordered lists of percentages of people fully vaccinated (two jabs), and vaccinated (one or two jabs):

The gap between the UK and its challengers is narrowing steadily now.

I devised a measure I call “Susceptibles %.” This is an estimate of the percentage of the population in a country who are still susceptible to the infection, with all that it brings in its wake. Other things being equal, you would expect the weekly growth in new cases at a given time (and so the reproduction rate) to depend fairly linearly on the proportion of susceptibles at that time.

I calculate the susceptibles measure by, first, subtracting from 100% the percentage of the population who have been reported as cases. I assume that these people can be treated as no longer susceptible; I’ve read that, if you’ve had COVID once and recovered from it, the chance of getting it again is only about one in a thousand – even with all the different variants there are around. This is good news for those who, like me, had the damned thing way back in January 2020, before it was even proven to be in the country! (And have been locked down – unnecessarily – for almost 18 months now).

I then subtract from the figure the percentage of the population fully vaccinated, times an efficacy factor to allow for the possibility of a vaccination not “taking.” I found a Saudi paper that estimated this efficacy as 95%; in other words, 19 vaccinations out of 20 work, and one doesn’t. That sounds believable to me. But this paper was published before it was known that two jabs would be necessary. So, I’ve made a guess that one jab provides half the protection of two. Thus, I also subtract from my figure 47.5% times the percentage of the population vaccinated but not fully vaccinated. (Assuming the efficacies of the two jabs are independent, this is OK; because the expected value of the sum of the protection is the sum of the expected values). 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 resulting graph and list:

The Irish are suffering, not just from having been slower than others to roll out vaccinations, but from having locked down harder on average than others. They may have controlled the case count fairly well up to now. But if it turns out that the vaccines don’t actually do very much to stop the spread of the disease, that will be (to an extent) a case of shot-themselves-in-the-foot – they are still going to have to reach herd immunity. In contrast, the UK has reached a point at which I should be able to detect some effects of the vaccinations on the statistics for cases, hospitalizations, ICU occupancy and deaths.

Note that I have not tried to make any allowance for people who had COVID asymptomatically, and didn’t show up as cases because they didn’t take a test at the time. I found a paper that suggested you should add 28% to the actual reported case counts to allow for this, but I didn’t find this credible (it seemed to me to be averaging figures for different countries and different stages of the epidemic all into the same basket). And in the very early stages of the epidemic when it wasn’t even known whether the virus transmitted human to human, and tests were all but unavailable, there were also a lot of people (like me) who had COVID with mild symptoms, thought it was some kind of ’flu, and simply got over it. Both these factors mean that my susceptibles numbers are likely to be on the pessimistic (high) side.


I’ll start with a list of total cases per million, to give a feel for how far the virus has penetrated into the population in each country:

Here are the daily cases per million:

In recent weeks, new case counts have moved from a mainly downward trend to an upward one, and in several countries (most notably the UK – pink line!) a sharp upward one. This is reflected in the weekly case growths:

Much of the recent volatility, particularly in Sweden which accounts for all three of the excursions below minus 50 per cent per week and two of those above plus 200%, is down to relatively low numbers of cases in comparison to earlier in the epidemic. Larger countries such as the UK (pink line) show less volatility, but the cases are still often increasing by 50% or more per week.

The R-rates, which usually correlate well with weekly case growth, are as follows:

In the countries with the highest R-rates, they are now up to levels not seen since the first wave in April last year, except for peaks in certain countries in the lesser waves of June, October and January. This raises the question: do the vaccines do much, if anything, to lessen the transmission of the virus? The answer seems to be that, despite an apparently greatly lowered proportion of susceptibles, the vaccines don’t do much if anything to control the spread of the latest “delta” variant. I’ll need to look deeper, into hospitalizations, ICU occupancy and deaths, to find a “fingerprint” of evidence that the vaccines are doing their job.


All this said, the lockdown decisions being made (or not) look rather different from last year’s:

There has been a general downwards trend in stringency since March of this year, with Portugal being the only exception. Most of the countries now seem to be playing a “waiting game,” either keeping stringency roughly constant, or lowering it cautiously (although the Netherlands has taken a gamble, and unlocked a lot of things all at once).

It seems from this that the governments (except Portugal) currently have sufficient confidence in the vaccines to allow people a few of their freedoms back for the summer; or, perhaps, are too scared of the people’s likely reaction to yet more lockdowns to do anything else. What they will do after the summer is anyone’s guess.


Here are the numbers of hospital beds occupied by COVID patients, per million population, over the course of the epidemic:

Almost all the countries are on a downward trend. The two which are obviously not are Portugal and the UK. Here is the ordered list of hospitalizations per million now, followed by the peak values from earlier in the epidemic for comparison:

So, all the countries’ hospitalization figures are well below their earlier peaks; even France’s. However, the UK and Portugal, at least, are rising. Here’s the new graph of weekly hospital occupancy growth. This is, in essence, the derivative of the hospitalized patients per million graph above:

Although the levels of hospitalizations in the UK (pink) and Portugal (light brown) are still relatively moderate, both have been rising since the middle of May. (The darker brown line with the two recent peaks is not either of these, but Luxembourg – which, because of its small size, is always likely to show more volatile growth than larger countries).

Here is the corresponding ordered list:

It looked until quite recently as if the UK’s hospitalization rates were not increasing nearly as fast as they had been earlier in the epidemic for similar numbers of new cases. This might have been due either to the vaccines lessening the average seriousness of the symptoms in the vaccinated, or to the virus infecting generally younger and healthier victims than before, or a combination of the two. However, recent increases in the weekly hospital occupancy growth have brought any such theories into doubt. My only conclusion is, wait and see.

Intensive Care Units

Here are the corresponding graphs for ICU occupancy:

Again, Portugal and the UK are rising, while the rest are going down.

Still only a fraction of the earlier peaks, but needs watching. Particularly since it was pressure on the ICUs that was the main objective justification for the January lockdowns.

A remarkably similar picture to the hospital occupancy as a whole! Again, wait and see.


Here are the daily deaths per million:

Now, that looks pretty good. Everyone on a downward trend since April; until the UK started to edge upwards in the middle of June. So, here’s another new graph – of weekly deaths growth. (The noisiness of this graph is caused by most countries having far lower death rates now than earlier in the epidemic):

Those three excursions down at the bottom right – from Ireland, Luxembourg and Sweden respectively – represent periods of a week or more without any COVID deaths. That’s good. But the UK (pink line) is more concerning. Here it is, plotted for the UK on its own, together with the weekly case growth and hospital and ICU occupancies:

Now, that doesn’t look very good, does it? Mid-May to now is rather reminiscent of last August and September. Except that the deaths growth peaks are keeping just underneath the cases growth peaks this time.

Of course, the numbers of deaths are quite small, compared with the earlier peaks. Daily UK COVID deaths are currently in the 30s, against daily cases in the 30,000s. Which suggests, that plotting deaths per case (with a 21-day offset, as before) might give a clearer picture:

In the UK, the deaths per case ratio (with 21-day offset) has been declining consistently, from over 3% at the New Year to around 0.3% now. That might, perhaps, be a “fingerprint” of the vaccines doing their job? If you look more closely at the spaghetti graph above, you can see that – excursions notwithstanding – there has been a general downward trend in the deaths per case ratio from the New Year until the end of May. But since then, some countries have been going up again – notably Germany, the light blue line at the top.

In fact, I think Germany deserves a bit more attention on this one. So, here’s their deaths per case, with the 21-day offset:

The Germans are lowest of all the 14 in cases per million; they seem to have controlled the spread of the virus quite well. But at the cost of a considerably higher deaths per case ratio than the UK, at least since last summer. That spike at the end seems to have come from a big drop in the number of new cases in Germany during June, which has since begun to reverse following the latest round of unlocks.

Excess Mortality

Another way of looking at the epidemic is to ignore the COVID statistics entirely, and simply look at excess mortality from all causes over the period of the epidemic. Our World in Data expresses the excess mortality as a percentage excess over the mortality at the same time of year, averaged over the years 2015-2019. These figures are normally provided on a weekly basis. Here’s the graph:

This shows the diverse timings of the epidemic in different countries. Almost everyone got hit by the first wave – Spain the worst, followed by the UK, Belgium and Italy. Portugal got hit in early July, then Belgium twice more in August and November, then Switzerland in late November. Since then, most of the big peaks have been from Luxembourg, which (as usual) tends to produce more volatile figures because of its small size. There is, I think, a general downward trend since around November. That’s good.

One useful plot is to average the excess mortality percentages over the whole course of the epidemic. This depends on the assumption that the excess mortality figures are being provided on a fixed, periodic basis such as weekly – an assumption which seems to be true in Western Europe, but might not hold for the rest of the world. Here’s the result:

All things considered, this looks about as good a measure on which to judge the politicians as any; at least, once the epidemic is over.

Denmark and Sweden have consistently performed better than all the other countries, even though Sweden has never had a face covering mandate. Ireland and Germany have controlled the spread of the virus relatively well, as shown by the numbers of cases per million. But in the case of Ireland at least, this was achieved through over-draconian lockdowns; and that may come back to haunt them yet, if the vaccines don’t prove as effective as claimed.

How far away is herd immunity?

It’s difficult to know what percentage of cases in the population is required to reach herd immunity for this virus. To date, no country has had more than 18.2% of the population known to have been cases (Andorra is the highest). The highest cases per population ratio in any country with population more than a few million is in Czechia, at 15.5%.

The Czechs have recently unlocked, to the extent that their latest state of lockdown is as follows: International: Ban some arrivals. Stay at home: No measures. Travel: No restrictions. Public transport: Open. Face covering: Required in some places. Gatherings: Up to 101-1000. Schools: Recommended closed. Events: Recommended cancelled. Workplaces: Recommended closed. That looks like the kind of unlock you would expect when a government crosses its fingers and hopes the epidemic in its country is all but over. So, I plan to look at Eastern Europe, and Czechia in particular, in my next COVID missive in a few weeks. One thing I will set down here is the Czech vaccination status: they have fully vaccinated 30% of the population, and part vaccinated another 18%. That means that my “susceptibles” calculation for Czechia would give a value of 44.6% as of July 23rd.

As far as my 14 countries are concerned, though, there is still a long way to go in the cases stakes to match Czechia. Only Luxembourg, Sweden and recently the Netherlands have yet reached cases per population of even 10%. The vaccinations should help reduce the cases per population required to achieve herd immunity, though. I’d expect the margin required to reach herd immunity to be lowered as the number of susceptibles decreases. By how much, is a question I can't answer yet.

There’s still a way to go. So, I’m not expecting to hear the fat lady singing the Rolling Stones’ “It’s all over now” any time soon. Unless we are all closer to herd immunity than I see any hard evidence to suggest.

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