# One chart… and what it’s telling us (coronavirus – part 3)

I have looked at establishing further proof of the short-term impact of measures decided by governments in their attempt to control the coronavirus pandemic (such as social distancing, lockdown, etc.). Up to now, I felt the basic probabilistic logic (e.g. there is obviously an impact because these measures reduce propagation) was enough, but it seems there is some confusion around this, so it’s probably time for a bit more.

Looking at possible factors explaining differences between countries in terms of number of coronavirus deaths, I have found the following chart quite revealing.

[Edit 08/05: I have updated the chart using more recent data and counting all declared deaths, as several countries have changed their reporting systems since the publication of this post. Below is the updated chart. Gaps with the vertical values in the initial chart are due to (1) all deaths being taken into account, (2) changes in reporting systems and (3) slower comedown after peak in some countries. However, the pattern of the relationship between both ratios, and therefore, the following interpretations, remain unchanged.

End of edit 08/05]

A couple of caveats to start with: as explained in my previous post, I am looking at coronavirus deaths in hospitals only, there again because it is the only indicator that is reported relatively consistently over time on a daily basis in each country. Also, in order to compare what is comparable, this chart only includes Western European countries.

The horizontal axis represents the number of in-hospital coronavirus deaths per 100,000 inhabitants in each country up to the day when their respective government implemented their most restrictive measures. Example: France decided the lockdown on 17th March; up to that day, the country had recorded 175 in-hospital coronavirus deaths; given a population of 65,273,511 inhabitants, this means a death rate of 0.27 per 100,000 inhabitants at that date. This measures how advanced was the crisis in each country when their government made the decision – in other words, how quickly that decision was made, but using an objective metric rather than dates, as the propagation neither started nor progressed at the same pace across countries.

Why look at the ratio of deaths per 100,000 inhabitants, rather than just the number of deaths ? Because it enables us to compare countries with very different population sizes. For example, Germany has a population of nearly 84 million, versus 8.7 million for Switzerland, so you would expect the number of deaths to be lower in Switzerland than in Germany whatever the extent of the crisis: only the ratio per 100,000 inhabitants tells us what is happening comparatively in both countries. Switzerland implemented its most restrictive measures to-date on 16th March, at which date 19 deaths had been recorded (0.22 per 100,000 inhabitants); whereas Germany made a similar decision on 22nd March with 94 deaths recorded, but that represents only 0.11 per 100,000 inhabitants.

According to this metric, the UK was one of the latest countries to implement lockdown measures. At the other end of the scale (left-hand side of the chart), some countries like Portugal or Denmark implemented their measures even before the first coronavirus death was recorded on their territory.

The vertical axis represents the same ratio (number of in-hospital coronavirus deaths per 100,000 inhabitants) but based on the estimated total number of deaths at the end of the epidemic (from my own modelling). Please note that this model only predicts the outcome of the current wave of infections; a second wave or a resurgence would be another matter.

The third dimension of the chart is density (population per square kilometer), represented by the size of the dots. Density is an obvious factor in virus propagation. High density also results in problems beyond the actual propagation, with hospitals in hotspots unable to accept or treat patients accordingly. The density factor may explain why Netherlands (highest density in Europe with 409 inhabitants per square kilometer) is quite high on the vertical axis (which means a relatively high predicted death toll), despite taking measures quite early on.

This correlates with results we see every day in each country, as more densely populated regions are often hotspots (London and the West Midlands in the UK, for example). This is all the more true as national density is just an average over the whole population and territory. It does not reflect the differences in everyday life (density is obviously far higher on the Tube).

In terms of interpreting the chart, density is an interesting indicator when comparing countries whose dots are next to each other. For example, Switzerland is doing quite well compared to France. And of course, Germany is doing remarkably well, but that’s common knowledge by now and we all know why (mass-testing early on, among other reasons).

You may have noticed that Belgium, the second most densely populated country in Western Europe (380 inhabitants per square kilometre) does not appear in the chart. The reason is that it is still difficult to predict with some precision the final number of coronavirus in-hospital deaths in Belgium. We already know it’s going to be bad (at least in the region of 40-50 deaths per 100,000 inhabitants), we just don’t know how bad. (Note: the other missing country in the chart is Sweden, where the government has taken a more liberal approach with no significantly restrictive measures to-date; the evolution in Sweden remains difficult to model at this stage). (edit 01/05: further analysis shows that my comment on Swedish measures was not entirely accurate: Sweden did take measures, but they were not necessarily enforced in the same way as other countries)

What is this chart telling us about the current situation ?

The general shape of the plot shows that the lower the ratio on the day measures were implemented, the lower the final death toll is likely to be (examples: Denmark, Norway, Germany, Austria, Portugal). Similarly, the higher the initial ratio, the higher it is likely to be in the end (UK, Spain, Italy). [Edit 21/04: one of my readers kindly looked at the results of my modelling a couple of days ago and suggested that the values on the vertical axis are slightly underestimated. In view of the most recent data received since the publication of this post, that’s a fair comment. This is mainly due to the comedown being a bit slower than expected in each country once they pass the peak. However, because the model is mechanistic and not causal, this small bias will be similar between countries, so the overall shape of the graph, the correlation and its possible interpretations are unchanged].

Does this provide a proof that the earlier the measures, the more lives saved in each country ? Strictly speaking, this is not a proof, just a correlation between two significant ratios. Also, we should not overlook the approximate nature of both ratios. However, there is no doubt the chart strongly suggests that interpretation.

Another possible interpretation of the chart is that countries that take decisions earlier are also those who handle the crisis more effectively, thus saving more lives in the end. Both interpretations are possible. Although not equivalent, they are nonetheless linked because taking measures to reduce propagation is definitely crucial in managing the crisis.

If we accept the first interpretation, which is that early measures have a positive impact, there is an interesting conclusion to be drawn with reference to the question of scale I was discussing in my previous post. The main point here is that the vertical axis expresses results GIVEN THAT lockdown measures have been decided. The resulting scale in number of deaths is not out of proportion with a more or less bad flu year (although different from flu in nature and intensity). If we follow that logic, what the chart suggests is that these measures have played a key role in keeping the crisis on that scale, and even more so when they have been taken early on.

There are two important things, however, that the chart is NOT telling us. First of all, it does not tell us what the final outcome will be after the current wave has dwindled. In other words, it does not tell us whether lockdown measures have reduced the number of deaths, or just slowed it down and spread it over time. Our knowledge of the immunological implications of Covid-19 is still insufficient, therefore epidemiological scenarios remain difficult to predict with any certainty.

Secondly, it does not say which measures have been more efficient. Each of these countries have taken different measures at different times and only the date of the most restrictive measures (to-date) is used. This level of detail will be for local experts to analyse. Their conclusions, however, will be crucially important. Here’s why.

What is this chart telling us about the future ?

Let’s look ahead at the next outbreak, whether from the same virus (second wave, resurgence) or a different one. This is a matter of “when”, not “if”: in these uncertain times, the only certainty we have is that it will happen again sooner or later.

In that perspective, the first possible reading of the chart could be: “Great, early lockdown works, so that’s the silver bullet: let’s do it again if it happens and we’ll all be safe !”

Such a reading would spell disaster, considering the damage lockdown does to the economy and its wide-ranging consequences. It is also out of touch with the world we now live in, which is evolving from a zero-risk-pursuit to a risk-management world. This change of logic will apply at all scales (to governments and universities alike). This is not about leaders covering their backs anymore, but making the best decisions based on measured risks in a rapidly changing world.

A more hopeful (or less hopeless) reading of the chart is: “Early lockdown works, fine, let’s see how we can avoid it in the future.”

With that concern in mind, what this chart emphasizes first and foremost is the need for preparedness and mass-testing at an early stage, because (as explained in my first post), that is the first and best alternative to large-scale lockdown. What this chart is also telling us is that, precisely because some restrictive measures will remain necessary and because they will have to be decided early, the key to the future will be to apply only the most effective measures (social distancing, self-isolation, etc.), avoiding large-scale nationwide decisions whenever possible (or only for a very short time and with appropriate contingency plans).

A majority of countries have been caught on the backfoot by the current outbreak. The chart is showing how much and what the consequences may be. It’s a ‘how quickly’ story. The future will not only be ‘how quickly’, but ‘how best’. It won’t be just about saving lives, but also minimizing disruption and preserving some togetherness in society.

What could it mean for British universities ?

If we are looking at managing risk and taking more discerning measures, the message for British universities could be: if we want campus life to continue, closing down and cancelling exams all-round just won’t do. There are voices in the academic world that are beginning to claim that shutting down schools and universities may not be necessary. I have not seen the data to support that view (edit 14/04: according to this article, the evidence for closing schools is challengeable, to say the least), all I’m saying is that it should be given some consideration because minimizing disruption for high-immunology lower-risk groups could make sense. Of course, if schools and universities should be allowed to remain open during an outbreak like this one, it would have to be closely regulated and monitored, hence the crucial importance of testing, tracing and self-isolating.

Last but not least, the warning I hinted at last week concerning the possibility of a global spotlight on the under-funding of the NHS has materialized: it is now notorious that the UK’s coronavirus death toll per inhabitant will be one of the highest in Europe (as shown in the chart).

This might cause a double problem for British universities. In the short-term, it could damage their attractivity. In the perspective of a future outbreak, it also means that universities may have to contend with decisions emanating from a government that doesn’t want to be caught acting too late. What decision space will be left for universities then ? I guess it will depend on how fiercely the world of offline education fights its corner. And how soon.

I am aware that not all my colleagues share my optimism about British universities reopening campus next October because the many possible epidemiological scenarios that could unfold in the next few months are still too uncertain. That’s a fair comment, as indeed immunity and resurgence scenarios are difficult to predict.

Here comes the risk management question. At the end of the day, one number could help inform decisions objectively: mortality, e.g. the risk of dying if you are infected.

Every epidemiologist will tell you that it is impossible to calculate the mortality of a new virus before the epidemic is over, not so much because of the number of deaths but of the difficulty to estimate how widely the virus has spread and how many people have been infected. That is the reason why there have been very few serious estimates of Covid-19 mortality so far. The first study that seems to bring an element of reliability in that respect comes from the University of Bonn. According to this study, 15% of the town of Gangelt (considered as one of the epicentres of the outbreak in Germany) have been infected with the virus. This would set the mortality rate at 0.37%.

Let’s pause on these figures for a second. Do they give hope ? Yes, they do. For one thing, they are based on real data obtained from systematic testing over a sample of 1,000 people, and therefore much more realistic than some of the infection rates and fantastical mortality rates of 3-5% one still sees here and there on the Web.

How do they compare with known epidemics ? On the contagion side, seasonal flu can infect up to 20% of the population, according to WHO. That’s not very different. Past mortality rates have been estimated at 0.2% for the 2009 H1N1 flu and 0.1% for seasonal flu worldwide (source: Statista). The latter is also close to European (approximately 0.16%, according to ECDC) and US statistics (0.13% over the past 5 years, according to CDC).

Let’s also bear in mind that this first estimate of 0.37% mortality is an average across all age groups. The mortality is much lower for young people. In the UK, for example, 84% of flu deaths occur in the 65+ years group and that proportion is usually even higher on a bad year (edit 14/04: this might be much higher for Covid-19: according to a study based on 1,625 coronavirus deaths in Italy, 99.13% of these occurred in the 50+ group — edit 03/05: this age concentration is also confirmed by NHS England figures: 91% of coronavirus deaths occurring in hospitals are in the 60+ age group, which suggests a much higher percentage when adding care home deaths).

Of course, 15% and 0.37% are not the last word. Even though the estimate is quite precise in its own context (with a 1,000 sample, the 95% confidence interval is +/-2%), it is nevertheless based on a single German town with 13,000 inhabitants. Nobody would venture to say exactly the same results will be found across Europe. Nevertheless, as a ballpark they give the situation a sense of scale.

Therefore, if these results are confirmed by further similar studies from other countries (as a transition towards the prospect of a vaccine, perhaps by the end of the year), there is hope.

(*) Appendix: table of dates used to determine ratio on horizontal axis of the chart