Estimating the risk for university students and staff

More universities have communicated to offer-holders and/or implemented special action to handle the Admissions situation in the past two weeks (cf. my previous post). However, there are still hesitations among some institutions on whether to open campus next autumn or not, and if so which measures should be applied.

Are these hesitations supported by data ? Let’s do a bit of fact-checking.

According to NHS England’s reports, there have been approximately 10-20 Covid-19 deaths in the 20-24 age group so far. As 50% of this age group are students, let’s assume that about 5-10 students might have been among them (probably less, taking into account socio-economic factors).

Around 500 students die every year in England and Wales (ballpark number), so we’re talking about a maximum of 1-2% of annual student deaths. By comparison, suicides and drugs poisoning/misuse each represent roughly 100 student deaths. That’s about 200 in total, i.e. 40% of student deaths.

Let’s look at it from another angle, using a source that has more portability into the future, for example the University of Bonn study I referred to in a previous post. It was conducted in real conditions in a hotspot (Gangelt), so it cannot be accused of minimizing mortality. This study yielded a mortality rate (probability of dying if infected by the disease) of 0.37%, which is pretty much in line with most common estimates. Please note that the average age in Gangelt (43.7) is higher than in the UK (39), so we would expect mortality rate in England and Wales to be a bit lower, but let’s keep the higher value, this will only make the demonstration more valid.

Let’s apply this overall mortality rate to the current age distribution of Covid-19 deaths from the latest data published by NHS England. Through age-based regression, the estimated Covid-19 mortality rate for the 20-24 age group is approximately 0.0041%. In comparison, the estimated flu mortality rate in Europe for the same age group (obtained using the same regression method as for Covid-19) would be about 0.0027%.

Therefore, for the 20-24 group, the Covid-19 mortality rate is only roughly 1.5 times the normal flu mortality rate, even with unfavourable hypotheses.

This makes complete sense. Of course, Covid-19 is significantly more dangerous than flu overall. But this lethality difference is much more marked for older age groups, whereas for younger age groups the gap is quite small.

Let’s now use the same method to compare estimated mortality rates for staff, using the HE staff age pyramid published by HESA. The estimated Covid-19 mortality rate for this age structure would be about 0.1040%, versus 0.0529% for flu.

Therefore, for a typical HE institution, the Covid-19 mortality rate for staff is roughly twice the normal flu mortality rate, there again with conservative hypotheses.

Incidentally, this factor of 2 is exactly the H1N1 2009 average mortality rate compared to normal flu’s. I cannot recall that any university closed for swine flu, (although 80% of the H1N1 deaths occurred in the under-65 age group, which is precisely the opposite of Covid-19).

Ultimately, it will be for British universities to assess whether the associated risk level is acceptable or not, and whether social distancing should be maintained, bearing in mind the many mitigation possibilities that will be available, such as testing, tracing, protecting students and staff with conditions, self-isolation, etc.

Friends and colleagues to whom I have mentioned these numbers are a bit surprised. Given what they hear daily about the Covid-19 crisis from the media, they expected much more spectacular gaps with flu. Even an unmitigated ratio of twice the flu mortality rate is unimpressive and well below any major cause of death for the adult population. Within the viral domain, SRARS 2003 was 96 times the flu mortality rate, MERS 2012 was 356 times, Ebola 500 times, and plague (so much for those who ventured to use that term to describe the current pandemic) 600 times, i.e. 60% mortality rate.

I understand their surprise: how can members of the public NOT be confused by Covid-19 data ? Being exposed to a daily mixed bag of correct and incorrect information, unchecked or mis-commented figures and erroneous conclusions, sometimes within the same source of information, is confusing. As this confusion is set in the context of the media’s natural tendency towards inflationist sensationalism, this accumulation erodes the public’s sense of scale and creates a general misrepresentation of the situation which, powered by fear as it is, becomes extremely difficult to challenge.

The problem is not just a few tabloids selling a good story. It’s deeper than that. The latest analysis published by the Financial Times and subsequently relayed by much of the high-end press illustrates this peculiar situation.

The article sets out to estimate Covid-19 excess mortality. This is a major step in the right direction: as I explained some weeks ago, excess mortality is the only measure that gives a sense of scale to the current crisis.

Unfortunately, the headline (‘UK coronavirus deaths more than double official figure’) and opening statement (‘The coronavirus pandemic has already caused as many as 41,000 deaths in the UK’) are both wrong. The error lies in three methodological problems that lead to an overestimate:

(1) There isn’t necessarily ONE cause of death, therefore this raises the question of what we define as a coronavirus-attributed excess death. That is the difference between dying ‘from’ and dying ‘with’ coronavirus. Even the NHS is not so clear about it and has changed its counting method several times. Having worked on data appertaining to causes of death in the past, I confirm this is more complicated than it looks, as explained by Carl Heneghan, professor of evidence-based medicine at Oxford University: ‘You get the death certificate, but you’d also need to have the medical notes to hand, and coroners’ reports… That is actually a large job. A very big research study’.

(2) More importantly, the cause of current non-attributed excess deaths, referred in the article as ‘mystery’ deaths, is still unclear. Some might be due to people not being able to (or being unwilling to) access care because of the Covid-19 crisis. More generally, they could be assigned to the health system’s burden, resulting in the difficulty to deliver on both Covid-19 and other usual conditions. This is not unknown in epidemics to have also higher mortality from other causes. However, the FT analysis takes a one-sided vision and assumes these are all related to Covid-19. At best, they can be counted as indirect deaths, not direct. By indirect, we mean possibly dying ‘because’ of Covid-19, not ‘from’ or ‘with’. It’s a different count and cannot be included in a ‘UK coronavirus deaths’ headline.

(3) Much more importantly, a complete estimate of Covid-19 excess mortality should take into account gaps to average mortality over a whole year period starting in autumn 2019, not just a few weeks, because spring mortality, autumn mortality and so forth are not independent: those who die now didn’t die before, and some of those who are dying now because of the virus might have died later, nobody dies twice !

I was initially surprised to find that the experts that relayed this information did not mention the third issue, because that kind of mechanism literally jumps at you when you’re used to analyzing such numbers (especially given the Covid-19 age bias).

As it seems unlikely they didn’t notice it, I’ve been thinking about the possible reasons behind this singular omission:

  • One of the features of the current crisis is that no scientist wants to be seen as the one who is underestimating gravity and risk. If you’re wrong, it’s OK to be wrong by going over the top, not the other way round. This influences the way scientists communicate.
  • Issue (3) is about current excess mortality being compensated by future under-mortality. If we say that Covid-19 is causing some people to die earlier, this means we are storing under-mortality for the rest of the year. In which case this future under-mortality should be deduced from the current coronavirus-attributed excess mortality. But who wants to be caught in the media explaining that sombre reality ?
  • Worse, the evidence for issue (3) will be muddied by the future excess mortality we are currently storing because of the NHS burden. To take but one example, around 1,000 cancers are normally diagnosed every day in the UK: that’s not happening at the moment, so if you count lockdown time, plus the necessary time for the NHS to absorb the backlog, that could mean about 60,000 undiagnosed cancers, with many implications on delayed treatments as well. Consequently, future under-mortality and excess mortality will be adding one another and compensating in some way, but we don’t know in what proportion. There will be months, perhaps years, and considerable statistical work, before we can unravel these many causes and quantify them.

However, this silence is somewhat worrying because it indicates that even competent experts find it difficult to go against the inflationist trend, which leaves it unmoderated [edit 13/04: and even amplified, as the same mistake is repeated one week later]. In the case of the FT article, a critical review would have rather damped the ‘more than double’ claim, but it didn’t happen. That’s now in the headlines and that’s what the public will remember, growing more fearful than they probably should as a result, even though the claim is unambiguously wrong.

The ballpark I published one month ago still holds, i.e. in the region of 25,000-30,000 excess deaths at the end of the current wave. This is not only less than the ‘already 41,000 deaths’ of the FT article, it is also within the scale of a bad flu year concentrated over time.

This key difference between temporary burden and overall scale is also confirmed by Carl Heneghan, quoted in the same FT article: ‘The 2017-18 seasonal flu outbreak may have killed 50,000 in the UK but the reason we did not get alarmed then was that they were spread over many weeks’.

There is an important caveat: this episode might be within the scale of a bad flu year overall, but not so for the elderly. The lethality of Covid-19 is far greater than flu for the 70+ age group, which accounts for 85% of all UK Covid-19 deaths, as shown in NHS England’s reports and the new total number of deaths that include care homes. This will be the key factor behind ways to lift lockdown.

However, the caveat works both ways: a bad flu scale overall with a strong bias towards the elderly, therefore not much worse than a flu scale and risk for others, and that is exactly what the mortality rates estimated for university students and staff at the beginning of this post show. Which leads us to an inescapable and sad conclusion: the whole HE sector (students, staff and institutions alike) is a casualty of the blanket lockdown.

What this perspective also shows is that despite what the avalanche of daily coverage, death tolls and government briefings may suggest, there have been few new statistical facts on the Covid-19 crisis in the past six weeks. The first new item is that the comedown after the peak in some countries is a bit slower than expected, which has led to a revision of total deaths estimates (with previously identified relationships and patterns unchanged; all other predictions, including sources of likely under-reporting, UK’s high death toll and visible comedown by end of April, have followed their course).

The second new set of information is that we are now in a better position to locate the date of the peak in each country. From there on, there are many implications to analyse in terms of how the crisis has unfolded comparatively since the beginning of social distancing measures.

Maybe next week, if I — and the four fabulous friends (editor, data consultant, student, former HE colleague) that review and discuss these posts before publication — find the time… That’s all from me right now, cheerio !

[Edit 07/05: you might be interested in reading this, which just appeared today. Interesting views from Dr Banerjee, Pr Woolhouse, Pr Spiegelhalter and Stanford University. Nice not to be alone anymore… — Please note: the last chart in the BBC article mixes normal death rate (blue and orange lines), which is a probability to die, and Covid-19 mortality rate (red dots), which is a probability to die if you catch it, so for both to be comparable you need to multiply the Covid-19 numbers by the infection rate, which is going to make the Covid-19 percentages 5 to 10 times smaller, that’s how you can compare visually to the normal death rate, it’s much lower of course — also mind the log scale, differences between young and old are far greater than they look on the chart.]

[Edit 10/05: at last…. someone in the media who says things as they really are, thank you Professor Spiegelhalter ! Watch the interview or read the transcript.]

[Edit 13/05: interesting results in this study: not an easy read, but more complete and confirms the risk analysis of this post]

[Edit 14/05: the wind is turning, even the Telegraph is joining the realism bandwagon… better late than never]

Epilogue: from entry tariffs to integrative thinking

The most important event of the past week in the HE world has not hit the headlines. It hasn’t even been mentioned anywhere, as far as I know. Nevertheless, we should not underestimate its importance and broader significance.

Some universities have emailed their offer-holders with a ‘wherever you are’ message, whereby they are confirming that their campus will re-open in September AND that students will have the opportunity to start their degree online if they do not wish to (or are unable to) travel right away.

That is precisely the kind of action I hinted at in my previous posts, e.g. the feasibility of re-opening campuses at the beginning of the next academic year and the benefit of differentiated solutions that leave students the choice. Strangely, few universities have taken that step. Good for those who have, because by doing so they have filled the communication space left vacant by most institutions and gained a major competitive advantage in the admissions game that is about to unfold this summer.

Most importantly, what these universities have fully grasped is that, as far as next year’s admissions are concerned, this is no time to let someone else decide your future. In fact, the overall admissions perspective for the sector can be summarized in one sentence: the chips are down, so if you don’t call the shots it won’t come your way.

In this post, I will look at the dilemma some universities face on admissions for the next academic year. Even the word ‘dilemma’ might seem far-fetched, as many institutions feel they have very little choice but coping. However, further analysis shows that the current admissions situation can be approached at three possible levels: ‘plumbing’, strategy or integrative thinking. The ‘plumbing’ level concentrates on the most obvious tactic (entry tariffs). The strategic level goes beyond entry tariff tactics and looks at a range of possible strategies. The integrative approach embraces the limitations of the strategic level to engage with prospective students on an integrated vision of the learning ecosystem.


The plumber’s easy fix

The ‘plumbing’ approach consists in treating the problem as a compensation game between international students and home students operated by a tap called entry tariffs.

We are all aware that, taking into account restrictions on travelling, recession, cluttered planning horizon, UK’s poor Covid-19 ranking in Europe, potential issues with qualifications and visas, etc. British universities are facing a deficit of international students. Even for EU students, the theoretical hope of one last year of home fees does not change the overall psychologically unfavourable context. For international students as a whole, there is the possibility of lowering usual standards on qualifications and language levels, but even that may not be enough. Therefore, the solution could come from additional home students, which means lowering entry tariffs.

Obvious, isn’t it ? But does it work for all institutions ? Not necessarily. In fact, the effectiveness of the ‘plumbing’ approach depends on the position of each institution compared to other universities, as shown in the following chart.


The chart

The chart (epilogue)

  • This chart focuses on the 15 best-ranked universities in England in the CUG 2020 league tables (Complete University Guide) — Scottish universities are not included as their academic fees system is different. These 15 universities may not be a representative sample of the whole HE sector, but they are nevertheless diverse in their history and values, which is enough for our purpose.
  • The horizontal axis is a measure of the International Risk faced by each of these 15 top universities. This measure is based on the respective amount of academic fees paid by home students versus other students in the 2018-19 academic year, as well as the percentage these academic fees represent in the institution’s total income (Source: I am indebted to two excellent Wonkhe articles by David Kernohan and Martine Garland, which both present interesting charts based on HESA data). The International Risk measure I am using is the percentage income loss in the event of a 50% decrease in international students. The ‘50%’ is not an estimate, only a benchmark to rank each university’s exposure (coming from their percentage of international students) and vulnerability (coming from the importance of academic fees in their income) to a loss of international students. Three caveats:
    • Please note that I only apply a cut in academic fees, not residence revenue, therefore the underlying assumption is that residences will be filled with additional home students (which may or may not happen).
    • This measure of ‘International Risk’ focuses on the risk linked to admissions, not the multiple consequences of the current crisis on other financial areas of the university (such as Council funding, research budgets, etc.).
    • The measure is a ballpark average for each institution as a whole: exposure and vulnerability are bound to vary across faculties and subjects.
  • The vertical axis is the Entry Tariff metric as published in CUG 2020.
  • The size of the dots is the CUG ranking of each institution: the bigger the dot, the higher the rank. My main reason for using CUG rather than other league tables is that CUG is subject-weighted but not subject-based, which gives it better consistency over time. Other league tables seem more obsessed with being ‘uncrackable’ (which they’re not – they can all be more or less replicated) than reflecting a true picture of the sector. I am not against subject-based league tables. On the contrary, it is clear that some metrics make more sense at subject-level and others at institution-level. However, the current methodology of subject-based league tables falls short of their ambition, with many inconsistencies and biases cropping up as soon as you crack them.
  • The colour of the dots reflects the Student Satisfaction metric as published in CUG 2020 (derived from the annual NSS survey).


What the chart is saying

The position of a university on the horizontal axis represents how exposed and vulnerable it could be to a decrease in the number of international students. The further on the right-hand side of the chart, the higher the International Risk. For example, the most exposed institution of the group is LSE, whereas the least exposed are Cambridge and Oxford.

From an action perspective, the horizontal axis reflects the need to make up for a possible international shortage. For example, there is no urgent need for Cambridge and Oxford to lower standards (no surprise), whereas the more exposed LSE could be tempted to do so (which does not mean this is the only available strategy, as we will see).

The vertical axis reflects the possible implications of making up for the international deficit by lowering standards to attract more students, particularly home students. At the bottom of the chart, we see that Loughborough and Lancaster are already among the lowest entry tariffs of the top 15 (but rank highly on other metrics such as student satisfaction). For these institutions, there could be a greater danger to lower standards as this could impact negatively on their achievements and relegate them beyond the top 15, where rankings become both less attractive and more volatile. Of course, there is a bit of game theory involved: if everyone lowers tariffs, then there is a general downward move and rankings are not impacted too much. Nevertheless, as the behaviour of the competition is not so predictable, these are typically situations where lowering standards should not be the only strategy.

You may think this is not really the time to ponder over hypothetical rankings in distant league tables, and least of all over one single metric (entry tariffs), which is just one ingredient of their complex formula. Well, not only is it particularly relevant to think forward and look at possible implications on future league tables when considering scenarios involving international students (as it is notorious that league table rankings is one of the main decision factors for international students and their families); it is also a good idea to look at entry tariffs because this is one of the league table metrics that is understandable by everyone, even at a superficial level, unlike many other metrics (spend, value added, outcomes, etc.) which are either more complex or less in touch with the reality they are supposed to describe.

The existence of possible alternatives to the ‘plumbing’ approach is illustrated by the size and colour of the dots. The bigger the dot, the higher an institution is ranked, therefore the higher its reputation. Also, institutions with green dots have the best record in Student Satisfaction, which reflects their capacity to deliver on student experience.

I could have added other dimensions beyond that. These are all qualities that institutions can leverage beyond the mere entry tariff approach, building their own strategy to gain competitive advantage.

From this chart, it emerges that there isn’t one right strategy, because (1) all institutions are not exposed in the same way to a deficit in international students, (2) they already have different entry tariffs and (3) their record and power of attraction with students are different.


Which alternative/complementary strategies for which institutions ?

Beyond lowering entry standards for home students and/or international students, what are the options for institutions to attract more students in these difficult times ? Here are just a few:

  • Send out a message to confirm re-opening campus in September: at this stage, few institutions have been clear on that point, which creates a communication void with offer-holders. Such a simple statement would provide reassurance in a world dominated by uncertainty.
  • Even better, the ‘wherever you are’ message, e.g. combining re-opening with a possible online transition. ‘Wherever you are’ is even more powerful than Dominic Cummings’ ‘take back control’ and ‘whatever it takes’, because it actually means something.
  • Leverage what your university is best known for: institutions can adapt quickly to a new context at the operational level, as shown by thousands of dedicated of lecturers in the past few weeks; but reinventing its DNA is another matter, if only because ethos and core values materialize through people, budgets and structures. Therefore, universities with a good track record on student experience, widening participation, raising student attainment through learning development and support centers, are best equipped to communicate to offer-holders on four key themes:
    • Safety
    • Community
    • Student experience
    • Academic Support


You may have noticed that these are all communication strategies. Are we overlooking other dimensions of the marketing mix ? Yes and no. It’s just that, for one reason or another, other courses of action are not so straightforward. For example:

  • More unconditional offers ? That could have been a possibility for the lower half of the top 15, but the moratorium on unconditional offers has been extended again, so that option seems a wee bit out of favour.
  • UG versus PG redistribution ? Lowering standards for PG courses is actually easier than for UG entries, as the admissions process is more flexible. But if such a strategy is applied, PG course convenors are in for a tough couple of years.
  • Price repositioning ? There again, the possibility exists for some PG courses, to some extent.
  • Finance for international students ? There have been debates about this question in the recent past. Some ideas may come to life under the spur of necessity.


From strategy to integrative thinking

Are we saying that universities have a limited choice of strategies ? That may be so, but reality suggests a different and more relevant question: is this limitation a problem or a solution ?

Let me explain. I opened this post by referring to an event that actually happened. Not something that might happen. There is currently a lot of talk about the future of the HE sector. Fine, I understand that. What about focusing on the future of students instead ? Isn’t that where the real solutions are ? In other words, instead of wondering what the solutions may or may not be, isn’t it preferable to talk to those who are the solution ?

Emailing offer-holders to announce both the re-opening of campus AND the possibility to start online is a shining example of integrative thinking as explored in Roger Martin’s remarkable book The Opposable Mind. – which is Martin’s term for the human brain’s ability “to hold two conflicting ideas in constructive tension”, a process through which decision-makers can synthesize “new and superior ideas”. In our example, the constructive tension proceeds from an understanding of the current state of mind of offer-holders.

Let’s face it: prospective students are one of the major hostage groups of the crisis. Nobody has ever seen the scientific evidence for shutting down schools. We are not sure it actually exists. For all we know, the main reason for closing schools was because they were facing staff shortages with the Covid-19 crisis. Even then, it would have made sense to keep schools open just for students in exam years, wouldn’t it ? And not to cancel the only gatherings that operate with social distancing even in normal times: exams. But that didn’t happen.

So, here’s the elephant in the room: offer-holders are not only prospective students, they are young people who have been sacrificed. And they know it. Now they are waiting, wondering what will happen next. That is their state of mind. It doesn’t take much finesse to see that failing to communicate to them in such a situation is a major psychological mistake.

Will prospective students turn to anyone who reaches out to them with a positive and confident message on the next academic year ? Well, why wouldn’t they ? At last, someone is talking to them about their future. They are young people: their future is their life, not Covid-19.

Right now, everything around them is in a ‘no future’ mood. They are not only under lockdown, they are also mentally and emotionally immersed in the wider dimension of the lockdown: the world has frozen itself. Young people want a future, they don’t want a frozen world.

Therefore, institutions that occupy this communication space are not only delivering a message of hope, they are positioning themselves as the source of hope. If you are the VOICE of the future, you ARE the future. This operates at two levels: the rational level (the message) and the symbolic level (the source of the message). More than ever, the future belongs to those who will proactively consult, understand and communicate with students.

In making this point, I am looping back to the conclusion of my first post: student experience begins NOW.



In previous posts, I have written about the general coronavirus crisis and its implications on the HE situation. Why ? Because I feel everyone has a right to understand what is going on and deserves clarity. The feedback I have received in the past few weeks (including, in one particular instance, resulting action taken by an institution) suggests they have reached their goal.

In this last post, I have focused on the HE situation only. As far as the coronavirus situation is concerned, I have nothing to add on the statistical front and will happily defer to two experts who are infinitely more knowledgeable, clear-minded and useful than I will ever be. The first item is an article by Katherine Xue, postdoctoral fellow in microbiome evolution at Stanford University. The second is a video interview of Sarah Gilbert, Vaccinologist at Oxford University, on the Andrew Marr Show. The first explains the complex inner workings of this specific viral epidemic, while the second provides a first-hand perspective on the successive steps of vaccine research. Highly recommended.

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.

The chart

[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.

The chart (updated 10-05)

End of edit 08/05]


Reading and understanding the chart

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

Country Date Decision made (source: Wikipedia)








On 9 March, the government announced (…) in a press conference that all measures previously applied only in the so-called “red zones” had been extended to the whole country, putting approximately 60 million people in lockdown. Conte later proceeded to officially sign the new executive decree.[116][240]




On 12 March 2020, the Portuguese government declared the highest level of alert because of COVID-19 and will maintain it until 9 April.[8]










12 March: the government announced new measures that will be in effect through the end of the month. All events (concerts, sports) and all meetings with more than 100 people are now forbidden and the RIVM is encouraging people to work from home. The restriction also applies to museums. All Dutch universities will suspend physical teaching until 1 April, but online teaching will continue. Schools remain open.[30]






On 12 March, a national lockdown was announced, effective from 18:00 the same day. For two weeks, schools, kindergartens, fitness centres, hair salons etc. are closed. Sports and cultural events and gatherings are banned and restrictions apply to restaurants.[20]
























Starting on 13 March 2020, all people working in non-essential functions in the public sector were ordered to stay home for two weeks.[7] In the private sector, employers are urged by the authorities to allow their employees to stay home in the same period and work from there if possible, although this should not affect functions that are essential to the society (such as pharmacy workers and people working with sale of food and maintenance of critical infrastructure).[86] On that same date, all secondary education (like gymnasiums), universities, libraries, indoor cultural institutions and similar places were closed, initially for two weeks. Starting on 16 March, all primary schools, daycare and similar places were also closed for two weeks.[7] Virtual (online) schooling was used to some degree.[87] The municipalities are establishing limited daycare for children where the parents could not stay home and take care of them. Because of the vulnerability of elderly to COVID-19, it was strongly recommended that grandparents should not take care of their grandchildren.[88]












On 15 March the national lockdown due to the State of Alarm becomes effective.[108][109] All residents are mandated to remain in their normal residences except to purchase food and medicines, work or attend emergencies.[110][111] Lockdown restrictions also mandated the temporary closure of non-essential shops and businesses, including bars, restaurants, cafes, cinemas and commercial and retail businesses, while also announcing that the government will be able to take over private healthcare providers, if needed.[108][112]
























On 15 March, a ban was also announced for public gatherings of more than five people, and restaurants were ordered to close beginning on 17 March.[26] In addition, Günther Platter, the governor of Tyrol, announced a one-week lockdown for the whole province.[27][28] Residents in Tyrol were required to remain in their homes except for necessary reasons such as purchasing food or medicine, visiting the doctor, withdrawing cash, or walking a dog.[27]

As of 16 March, nationwide, homes may only be left for one of the following reasons:[29]

·       necessary professional activities

·       necessary purchases (groceries or medication)

·       assisting other people

·       activities outside, alone or in the company of people living in the same household



















On 13 March 2020, the Federal Council decided to cancel classes in all educational establishments until 4 April 2020, and has banned all events (public or private) involving more than 100 people. It has also decided to partially close its borders and enacted border controls.[34][35][36] The canton of Vaud took more drastic measures, prohibiting all public and private gatherings with more than 50 people, and closing its educational establishments until 30 April.[37][38]

On 16 March 2020, the Federal Council announced[39] further measures, and a revised ordinance.[40][41][42] Measures include the closure of bars, shops and other gathering places until 19 April, but leaves open certain essentials, such as grocery stores, pharmacies, (a reduced) public transport and the postal service.[43

















On 12 March, French President Emmanuel Macron announced on public television that all schools and all universities would close from Monday 16 March until further notice. The next day, the prime minister Édouard Philippe banned gatherings of more than 100 people, not including public transport. The following day, the prime minister ordered the closure of all non-essential public places, including restaurants, cafés, cinemas and nightclubs, effective at midnight.[11] On 16 March, President Macron announced mandatory home confinement for 15 days starting at noon on 17 March.[12]

















On 22 March, the government and the federal states agreed for at least two weeks to forbid gatherings of more than two people and require a minimum distance of 1.5 metres (4 ft 11 in) between people in public except for families, partners or people living in the same household. Restaurants and services like hairdressers were to be closed.[205] Individual states and districts were allowed to impose stricter measures than these. Saxony joined Bavaria and the Saarland in prohibiting residents from leaving their dwellings except for good reasons, which are similar to the ones in the other two states; outdoor exercise is permitted under the new rules only alone or in groups of maximal five members of the same household.[206]


















On 23 March, Boris Johnson announced in a television broadcast that measures to mitigate the virus were to be tightened further in order to protect the NHS, with wide-ranging restrictions made on freedom of movement, enforceable in law,[28] for a planned “lockdown” period intended to last for at least three weeks.[109] The government directed people to stay at home throughout this period except for essential purchases, essential work travel (if remote work was not possible), medical needs, one exercise per day (alone or with household members), and providing care for others.[110] Many other non-essential activities, including all public gatherings and social events except funerals, were prohibited, with many categories of retail businesses ordered to be closed.[28][111]




















On 24 March, Taoiseach Leo Varadkar announced from Government Buildings the extension of all existing measures until 19 April—as well as stricter measures, among which were: the limiting of social gatherings to four people (unless members of the same household); the shutting of all non-essential retail outlets still open—effective from midnight—bringing an official end to hairdressing, theatres, gyms, leisure centres, betting offices, marts and other market places, casinos and bingo halls, playgrounds, holiday caravan parks, organised indoor and outdoor social events of any kind, including all sport (some of which, such as horse racing, was then still being held behind closed doors); the limitation of cafes and restaurants to takeaway and delivery services. Varadkar stopped short of calling it a “lockdown“, the term used in other countries.[346][347][348][349][350]



What will next October look like for British universities ?

Following my previous post, a colleague (from another institution) asked me whether I thought British universities would be able to resume offline teaching next October.

My first reaction was to think: ‘yes, of course they will’. Then I wondered: is that so obvious ? And if it is, which data would support this view ? So let’s give it a go.

There are actually two practical questions to answer:

  • Should British universities prepare to resume offline teaching next October ?
  • If so, will it be business as usual ?


To begin with the beginning: will it be safe to welcome students back on campus next October ? There are several indications that make this prospect quite likely.

Such a prediction might sound somewhat out of sync for British readers as the island is now in its highest coronavirus burden period, with still high daily death tolls. To explain this, I need to go one step further than my previous post, which was deliberately lean on statistics (that couldn’t last forever, could it ?), and explore three concepts: burden, timescale and scale.



In epidemiology and health statistics, there are several ways to define burden. However, in the case of the Covid-19 pandemic, it is the number of deaths that is the least unreliable indicator of the evolution of the situation in each country.

As mentioned in my last post, the number of identified cases is the key indicator for any country to monitor the situation and lead the fight, but not so for making predictions of final outcomes. At any stage, the number of identified cases depends on how much testing is done and the capacity of the country’s health system to report and process these cases. Therefore, in terms of flow over time, it is a  more complex and multi-dimensional measure than the evolution of the number of deaths.

‘Least unreliable’ does imply some imperfections, though, and there are quite a few. For example, some countries only report hospital coronavirus deaths. Two recent adjustments published by France and the UK suggest that the total number of coronavirus deaths could be about 30% higher (France’s public health organization now publishes two daily numbers : hospital deaths and total deaths). My educated guess is that this gap could increase in the next few weeks as more deaths are reported outside hospitals, particularly care homes (edit 10/04: this increase can now be seen in France’s latest figures, where total number of deaths is now 1.5 the number of in-hospital deaths, therefore the coefficient there is already 50% — edit 24/04: the coefficient seems to stabilise at approximately 60%, but could rise again with delayed death recording, so educated guess was correct, unfortunately). It will definitely be much bigger for countries where a large proportion of the population has no access to health care. Some countries also experience longer time lags to centralise and report deaths. However, in this post I am only looking at neighbouring European countries, so the assumption that this bias is relatively homogeneous across countries is not unreasonable. Also, what matters most to our question is not necessarily the absolute correctness of reported numbers but their trend, assuming that these biases are relatively consistent over time in each country.

There is also the question of how much of these coronavirus reported deaths exceed the normal mortality at a given time of year. That is the concept of excess mortality, which is used to measure all causes of death. I will discuss this question further in the post, but for our purpose the number of coronavirus deaths as reported daily by public health organizations is still the indicator to follow.



In all countries affected by coronavirus, the epidemic picks up more or less quickly, then reaches a peak and gradually comes down. In the middle of that curve is the High Burden period where 80% of coronavirus deaths happen. For any country, it is the period after the first 10% of deaths have been recorded and before the last 10% of deaths. When this most important period occurs and how long it may last will be crucial to answer our initial question, because once this period is over governments may start thinking of easing lockdown (which will also depend on the number of cases by then; that’s public health management, not forecasting).

I have modelled the evolution of the number of reported coronavirus deaths in European countries. Although the evolution in some countries is not entirely predictable yet, it is nevertheless clear, looking at countries where the epidemic is more advanced than the UK (China, Iran, Italy, Spain), that this High Burden period lasts between 3 and 5 weeks (edit 24/04: that interval is correct for most countries, but data published since writing this post shows that the later social distancing measures have been taken, the slower the comedown after the peak, so late-deciding countries like the UK could go through a 6-week High Burden period). It so happens that the UK is currently in its High burden period. Therefore, by the end of April (at the very latest), the number of daily deaths in the UK will have substantially decreased (edit 24/04: this is also turning out to be correct, although the comedown is not as pronounced as if the UK had followed the curve we see in countries that took decisions earlier). It does not mean that there will be no coronavirus deaths at all after that, but these will gradually dwindle to nought. This should also be the case for most European countries, which means that by October the European peak should be well behind us.

However, there are two conditions for this to happen according to prediction.

The first condition is that no large-scale second wave of infection (or worse: a later seasonal resurgence of the virus) will get in the way of a return to normality. That is difficult to predict at this stage and will depend on a combination of various factors: immunological, political (how governments handle the situation) and behavioural. If everyone starts hugging frantically on their first day out, that might be asking for trouble.

The second condition is that no scale effect will result in the epidemic getting suddenly out of hand.



Fighting epidemics means controlling hotspots. Scale effects can happen when a sufficiently big hotspot (a region or town, for example — Wuhan, Lombardia, New York, London, Birmingham, etc.) gets out of control for too long. Looking at countries which are near the end of the epidemic (China) or near the end of their High Burden period (Italy, Spain, Iran), it seems that so far measures have prevented this from happening.

This is, so to speak, the underlying mechanism of the epidemic, and that’s where the sheer number of daily deaths is not enough to appreciate the situation. A benchmark is necessary to give a sense of scale.

To understand this, let us compare the number of deaths due to the coronavirus so far to the number of deaths we usually get from flu in Europe in a given year. There are several methods to calculate flu-caused ‘excess mortality’, e.g. the number of additional deaths caused by flu compared to the ‘normal mortality’ over a period of time. In this post, I will refer to a 2019 study based on the 2017-18 season (, which was close to average by European standards. According to this study, the flu death rate per 100,000 inhabitants was 25.4. For coronavirus reported deaths at hospital, by the end of the epidemic the corresponding rate in Europe will be somewhere between 20 and 30 (according to my model — too early to be more precise — edit 10/04: Sweden is the last European country where the evolution of the current wave is unpredictable, due to the uncertainty around government policies and inconsistencies in daily reports), with some countries above their usual flu rate and some below.

Even that comparison is not strictly relevant because a proportion of reported coronavirus deaths is part of the ‘normal mortality’ that occurs at any point in time, whereas past flu numbers are ‘excess mortality’, e.g. the number of additional deaths caused by flu. In other words, the final excess mortality of Covid-19 in Europe will be lower than what we would think looking at the current burden on health systems (edit 24/04: at this stage, information released on excess mortality is not consistent statistically, let’s wait until reporting contradictions clear up).

This could be quite different outside Europe, for example in India or some African countries, which we cannot model because the number of deaths is not reported reliably at this stage.

The point here is not to try and predict whether coronavirus will eventually kill more or less people than flu, but to give the current situation a sense of scale by comparing both epidemics (one being regarded as exceptional, the other annual) from a quantitative standpoint.

I am aware that these numbers might surprise some readers, least of all because we are hearing how overwhelmed most European health systems already are, including the NHS. However, there is no contradiction between both views, here’s why. When there is a flu peak, health systems are already under pressure. In the case of Covid-19, what makes the pressure on hospitals much higher is that, due to pathological complications of the virus’s acute symptoms (and the resulting mortality risk), the number of coronavirus-infected patients ending up in A&E and ICU is higher than for flu. In European countries, the proportion of coronavirus deaths occurring in hospitals might be somewhere between 50% and 80% (edit 24/04: this range of percentages holds, according to latest stats), whereas for flu that percentage is much lower. Also, the coronavirus epidemic seems more concentrated over time in each country. Flu annual outbreaks usually occur over 5-6 months with varying intensity, whereas coronavirus burden lasts about 3 months in each country (but not at the same time in all countries). These two factors explain the intensity of the coronavirus burden on health systems.

Therefore, both past quantitative facts and current news reflect the reality of their respective context, but in one case (daily coronavirus news) we are looking at burden, particularly peak burden, whereas in the other (annual flu statistics), we are looking at scale over an epidemic cycle.

In the UK alone, flu has killed over 17,000 people every year in average over the past 5 years (Source: Public Health England). Here’s a little thought experiment: as I write, there are 6,159 coronavirus reported hospital deaths; according to my model, it is unlikely that the final toll will exceed 3 times that number (edits 09/04 and 24/04: extra hospital capacity + slower comedown after the peak in countries where lockdown has been decided later ⇒ higher proportion of Covid-19 deaths in hospitals; which could mean a 4.5-5 factor in the end for the UK); allow 50% extra for non hospital deaths (edit 24/04: this is still the current official figure, there are indications this could rise as a result of the situation in care homes, but this has not materialised yet in data), then remove 30% of the total for normal mortality (not precise estimates, just ballpark percentages — edit 24/04: the data that is piling up on the question of excess mortality is highly contradictory, to say the least, but appears more favourable than initially thought; some more recent estimates have been published, they are very interesting in terms of calculations but there are at least three potential flaws: see my full analysis here — nevertheless, using these more recent sources with a correction factor still places our conservative ballpark at about -30 to -40%); compare the result to 17,000 (edit 24/04: the estimated maximum goes from 6,159×3×1.5×0.7 to 6,159×5×1.5×0.6, higher but still on the same scale as a bad flu year). That’s as high as it (edit 10/04: e.g. the current wave, which does not exclude the possibility of additional deaths through resurgence or by-effect) can possibly get, most probably lower (edit 02/05: that possibility still holds, but difficult to prove at this stage).

You may then wonder whether official epidemiological forecasting models overestimated the number of coronavirus deaths, or whether the difference with reality is the effect of lockdown measures. That will be for scientists and public health specialists to answer when the time comes. I think it’s both: official models were scenario-based and probably overestimated the outcome (worst-case scenarios predicted 250,000 potential deaths in the UK, e.g. 15 times the average annual flu death toll – here again, the comparison will give readers some appreciation of scale), AND lockdown measures are having an effect (through a straightforward probabilistic mechanism reducing propagation), particularly in hotspots.


Second practical question: will it be business as usual, even if universities teach offline again next October ?

That’s less likely.

As already analysed by many university professionals from Admissions or Planning departments, the student supply chain is long and complex, which means we may have already lost many students with the current crisis, particularly international students.

The second reason is that, even supposing European countries are free from coronavirus in October, that may not be the case for other regions. It is possible that countries and continents like India or Africa, where local conditions make it more difficult to control both propagation and contamination, may have to remain in lockdown longer. More generally, the coronavirus may end up polarising the world in a dividing line between wealth and poverty (again).

There is also the unknown of how the virus will behave over the winter in the Southern hemisphere.

Thirdly, many implications of the current crisis are yet to unfold: to get students in, we need enough borders to re-open, which requires countries to accept each other’s testing standards, we need airplanes back in service, etc. Plus the financial and psychological aftermath. We need families to recover from financial hardship. We also need people to switch back to a mindset where they can start planning again.

Finally, there is the issue of trust and image. On that record, British universities may not be in a great place if you add up the effects of the virus crisis, this year’s strikes, Brexit and a notoriously underfunded health system (coronavirus inevitably spotlights how health systems are coping across the globe).

To make things worse, some British universities are now cancelling summer exams. Although made in the name of inclusion, this is the least inclusive ‘one size fits all’ decision they could possibly make. ‘No detriment’ is undeniably the right way forward, but ‘no detriment’ does not mean ‘nothing at all’. The students I’ve spoken to may not openly articulate their views, but they are not happy.

First year students are particularly affected. Some of them came a long way to join a British university. With the strikes and the virus, they have barely received more than one term of tuition. That’s not much for their money, and even less so for the debts they or their families are contracting through student finance schemes.

For all these reasons, it may not be enough for British universities to say ‘we’re back in business’ for business to come back.

Top universities with historically high QS World rankings will remain attractive. Those who are most at risk of losing out by leveraging entry tariffs and filling their places with lower-qualification home students are institutions from the 5th-20th band in British league tables, because once you drop out of the top 20, rankings become much more volatile. But as with every challenge comes an opportunity, universities that are able to rebuild a positive student experience after this crisis despite the financial loss will have an advantage. In this new context, widening participation and raising attainment will be hot topics.

One possible evolution is for universities to move some activities online, offer more online degrees, etc. This is a highly complex matter that every university, indeed every faculty or department, will decide according to their own strategy. But it is no mystery that much will happen there in the next few months and years.


What will ‘going to University’ mean if you can’t ‘go’ to University ?

Since writing my last post four years ago, I have not given a thought to restarting this blog, let alone in circumstances like these.

My reason for posting today is that when I have engaged lately with family, friends or colleagues about the current pandemic, I have realized how confused everyone is, whereas the mechanism is actually quite simple when you know the background.

I am not interested in theories, socio-political science-fiction or scenario-based speculation. Nor do I pretend to have any solution. I just want to recap a few basic facts that explain the situation we are in. Some of my friends have asked me my statistician’s point of view, but to be honest the answer would stretch any listener’s patience, although no numbers or advanced stats are involved. So here it is, for those who are interested.

Before starting, let me also say that there is no contradiction between ‘thinking’ and ‘feeling’. Apologies for going against the current media-induced emotional state, but you can be genuinely compassionate about the hardships many people experience at the moment and still keep your head about what’s going on.

The first point is that there is nothing new in this pandemic from an epidemiological standpoint. Back in 1957, between 2 and 3 million people died of the flu, including several hundred thousands in Europe. There was a lesser but nevertheless mass epidemic 10 years later, followed by other ones in the 90s and 10 years ago. By nature, the flu virus mutates. It has mutated before and will mutate again. Therefore, despite what the mass media coverage would have us believe and the restrictive measures we all have to comply with, this outbreak is neither exceptional nor the worst in living memory.

The second point, of which I know from working on epidemiological modelling and policies in the past, is also the most important: the only strategy that works when it comes to fighting against an epidemic is identifying and tracing cases, e.g. testing. That is a constant, whether you are talking about flu, TB, malaria or aids. It has been known for a long time. Would early mass-testing have helped avoiding mass confinement and economical destruction in the UK, France, Italy, Spain, etc. ? The answer is yes, because it would have enabled millions of healthy people to return to their work, as well as helping the more vulnerable. It would have also prevented shutting down schools and shattering young people’s lives. But mass-testing requires both preparation and quick decision processes on a national scale. It is no coincidence that the two countries which have successfully implemented this strategy (South Korea, Germany) are among the most organised democracies in the world. Three weeks ago, when I told friends that most Western governments were doing exactly the opposite of what they should have done, they thought I was a loony. Today, this view seems more palatable, for some reason.

The third point is that no health system can safely cope with an outbreak like this, whether it’s the NHS or any other health system. If it could, then it would mean that it is oversized in normal times, which it clearly isn’t, so that’s a no-brainer.

The fourth point is another no-brainer: social distancing and restrictive measures on people’s movement reduce (or slow down) the propagation of the virus and help health systems to cope. No need to be a great mathematician to understand that. So, when governments claim that they are making science-based decisions, they are correct in that sense. It’s also a spin, as it would be more accurate to say that these measures are a common-sense unavoidable last resort given that they first ignored (or were unprepared for) the one sensible strategy, which was mass-testing.

From there on, it’s just a ‘more or less’ story: health systems will cope more or less well, there will be more or less casualties, it will take more or less time, etc. In that intrinsically relative context, the British media’s blame game of putting pressure on the UK government by comparing their measures with France’s or Italy’s is highly dubious, for one simple reason: every time you cross a frontier, be it national or regional (London versus less populated areas in England, for example), three things change: scale (population size), density and culture. This makes it impossible to make actionable comparisons of ‘performance’ across countries. In their zeal, the UK media tend to forget this is a global pandemic, not Masterchef.

My last point is about confinement. As I said before, it is a necessary short-term measure given the absence of mass-testing (let’s keep our head in the way we comply, though: whether you go out and exercise for 20 minutes or 2 hours makes no difference to the propagation, it’s the social distancing that counts!). But the longer-term immunological and wider health-related consequences of mass confinement are very much uncharted territory. To the best of my knowledge, confinement hasn’t been used on a large scale since the cholera epidemics of the 18th century, which were quite specific. This time, the final equation will be complex and, to say the least, highly interdependent and multi-dimensional. I would be very wary of anyone who claims to know the bottom line. Even looking at the practical side only (and that’s just one aspect of it), the way out of this situation will depend on how quickly and effectively mass testing will be implemented in each country (and not only in the UK, as we are all in this together).

The question of the ‘way-out’ is, of course, a critical point for universities right now (

Since the beginning of the crisis, universities have mostly cascaded government decisions. But there are now major business model questions ahead: what will it mean to ‘go to University’ when you cannot actually ‘go’ there ? Will prospective students still adhere to the offline togetherness of student life on campus ? Or will they switch to providers that already sell online degrees and have huge fast-growth potential ?

Should we try and adapt in the (wishful?) hope that no major mutation will happen in the way HE is delivered round the globe ? Or should we totally re-think what we can offer in this new world ? In other words, should we just seek to adapt our provision within the same business model ? Or accept the possibility that the virus might have damaged the business model so badly that it will soon be obsolete ?

For a start, let’s rephrase those questions from the general to the quantitative (‘how many students will etc.’ rather than ‘students will…’). Campus life and offline academia will still be attractive for a number of students, but the problem is: how many are we going to lose over the next few months and years as a result of this crisis ? Any decrease in student numbers would be regarded as problematic in normal times, but now we are looking at change on a totally different scale. As for the validity of such metrics as continuation, value-added, outcomes, etc. in next year’s league tables: excuse my French…

I do not have the answers to these questions more than anyone else, but there’s one thing I know: it’s student experience that will make the difference, and student experience is NOW, not in the distant future. I hear that some universities are already restricting next term’s provision (even online) or cancelling exams altogether: is that the right approach ? By doing so, aren’t they (to use an expression from my native culture) buying matches for their own cremation?

Online degree providers are rubbing their hands at some universities’ dithering process-driven approach over next term’s exams and assessments – they’ve done this online successfully for years.

The core problem here is that universities are not always very good at making decisions which are both student-driven and data-informed. The data is there, but it must be looked at differently, otherwise decisions could miss the main point, which is that this crisis has put our current (and prospective) students in different situations and we owe them ALL a solution that matches their aspirations.

This is not the time to be paralyzed by the search of a ‘one size fits all’ solution. If we do not segment our solutions (as all good businesses do) to adapt to these situations, this will be just another let-down.


Open-ended Maths: a selection of 101qs favourites

The 101qs website was created in 2012 by Dan Meyer, a great Maths teacher and dedicated apostle of open-ended Maths.

‘Open-ended Maths’ is an expression that sounds pretty scary to many Maths teachers. A lot worse than ‘out of the textbook’, which is rather trendy and flattering. Dan Meyer’s first paragraph on his About page does not seek to cajole them back to their comfort zone either:

We don’t care how well you lecture. We don’t care how well you engage us. We aren’t impressed by your fancy slide transitions or your interactive whiteboard. We care how well you perplex us.

This sets the tone perfectly: open-ended Maths is about stimulating students by presenting them with a perplexing picture or video — perplexing in the sense that it raises questions. Students have to formulate the questions themselves and subsequently solve them, which often means developing appropriate resources on the way.

If you are a regular reader of my posts, you know by now that this blog is not about being ‘for’ or ‘against’, but understanding precisely WHY and HOW an idea is potentially useful for teaching Maths. In this instance, it so happens that open-ended Maths is not only cool, it is also an essential teaching tool — for reasons I shall explain in a later post — on the condition that it is not used systematically (for reasons I shall also explain).

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Introducing (some) problem-solving skills

Problem-solving is not only a prominent Maths activity, as shown in the Maths ability pyramid. It is also a discipline of its own, with its specific know-how. In other words, the specific skills of problem-solving can be learnt too. By doing so, students will not only learn to solve problems more efficiently, they will also make the best of problem-solving’s high educational value.

For Maths teachers, it means that it is possible to choose problems for students not only according to a particular Maths topic (fractions, algebra, trigonometry, etc.) but also with a view to practise one or several problem-solving skills.

In order to do this, it is necessary to identify and name these skills. This post covers 10 problem-solving skills, which you can see in action in UKMT JMC 2015 (cf. my JMC 2015 teacher’s notes).

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UKMT (teacher’s notes) – JMC 2015

This is the first post presenting my teacher’s notes of past UKMT papers, starting with JMC 2015.

The objective of these teacher’s notes is not to provide solutions — UKMT already provides an excellent Pdf of solutions and further investigations, which you can download here — but to provide insights to teachers as to how UKMT questions can be used in the classroom.

In other words, these teacher’s notes are about making the best of the educational value of UKMT questions. Which, by the way, extends the scope of UKMT questions beyond their target age group. For example, some JMC questions, although intended for Year 7-8 students, can be used for educational purposes up to GCSE, sometimes even with A level students with the addition of relevant extensions and investigations.

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What is a logical progression ?

Maths makes a lot of sense when it is taught in a way that makes sense. If you teach something that makes sense in a way that doesn’t, at the end of the day it doesn’t make sense.

In other words, if we teachers don’t get our conceptual thinking right, then we can’t really expect students to, can we ?

The most important dimension of this conceptual thinking depends on the age group you are teaching to. However, there is definitely one dimension of conceptual thinking you cannot overlook from secondary school on: the logical progression.Read More »

Are Maths exams robbing students of the fun ?

After weeks of writing and talking to teachers about behaviour management, I am back (with relief) to posting on my favourite topic: Maths teaching. That is no doubt the effect of meeting two highly inspirational people (one Maths teacher and one Headmaster) within a few days.

I would like to start this post with a seemingly remote comment which was kindly sent to me by a reader concerning the Maths ability pyramid, pointing out that the pyramid does explain ‘what we do in Maths and why we do it’, but not HOW we do it.

Which is absolutely true: the HOW question is extremely important and it will require several posts to develop this (inexhaustible) point. One could even say that, for Maths students, it’s the ‘HOW we do Maths’ that makes a huge difference.Read More »

Go for hybrids ! (How to spark off a Maths topic ? – Part 3)

This is the last part of our review of possible ways to spark off a Maths topic (preliminary note: it is recommended to read the 2 previous posts: How to spark off a Maths topic ? – Part 1: concept processors and How to spark off a Maths topic ? – Part 2: memory reinforcers).

Actually… the best sparks are often hybrids. It’s quite nice to have logic (conceptual processor) + emotional engagement in order to activate memory (memory reinforcer).

Let’s look at a few examples…Read More »

Memory reinforcers (How to spark off a Maths topic ? – Part 2)

We continue our review of possible ways to spark off a Maths topic (it is recommended to read the previous post: How to spark off a Maths topic ? – Part 1: concept processors).

Today, we are talking about the second category of sparks: memory reinforcers.

The idea of memory reinforcers is to spark off a topic with something that engages beyond the intellect in order to reinforce memory. What you choose may not seem logical, but that is beside the point if you reach your goal of memory reinforcing.

As memory champion Josua Foer explains: ‘We remember when we are able to take a piece of information and experience it. We remember when we pay attention. We remember when we are engaged’.

A memory reinforcer can be…Read More »

How to spark off a Maths topic ? – Part 1: concept processors

This post is about sparking off the core topic of a Maths lesson. (NB: This is different from starting a lesson with a Do Now or Starter, which are often used (and quite rightly so) as retrieval activities or stimulating/settling activities, but are not necessarily related to the core topic of the day’s lesson). Therefore, the spark will often be the second item in the lesson, but it is the first point of contact with the main topic.

Choosing the right spark to introduce a topic is important for 3 reasons:

  • First of all, the spark should totally serve the core topic, either through raising a question that will inevitably lead to the new concept or skill being introduced, or by catching attention and reinforcing how the lesson will be remembered.
  • Secondly, the spark should be in direct correlation with the way the main point of the lesson will be wrapped up (more about that in a future post).
  • Thirdly, the spark should introduce the first increment on prior knowledge, i.e. building up on what students already know.

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How to develop fundamental abilities

This post provides a few practical tips on how to develop fundamental abilities (i.e. the first level of the Maths ability pyramid), thus helping students to become more confident by increasing their awareness and fluency with the mental manipulation of objects and processes such as order, numbers, causes and consequences.

There is a double benefit in working on this development: not only does it help teenagers to focus and develop mental resources, but it does so by involving them in a series of lively exercises that look very much like collective games with relatively little Maths involved. In other words, developing fundamental abilities is both low-cost and high-benefit.Read More »

Stephen Hawking, the ultimate teacher

This post is an ‘extension’ of the previous post concerning the Magic of Q&A beyond expectations.

Back in May 2015, thousands of people gathered at Sydney Opera House for a talk by Stephen Hawking. Appearing in 3D hologram form, beamed in from Cambridge University, the physicist was asked the following question by an audience member: ‘What do you think is the cosmological effect of Zayn leaving One Direction, and consequently breaking the heart of millions of teenage girls across the world ?’Read More »

The magic of Q&A beyond expectations

It is always very stimulating when questions and answers in a Maths lesson suddenly go beyond all expectations.

This might sound like this is something that only happens exceptionally. Not so. In a class where a climate of questions and answers has been set in mutual trust, exceeding expectations happens almost every day.

In this post, I would like to show two such examples, one where my expectations as a teacher were exceeded, and another where a student improved his own conceptual understanding starting from a misconception – which was of great benefit to the whole class.Read More »

Three things your Maths students should not be afraid of

For many students, Maths is not fun, it’s fright !

That is not necessarily what they will show in the classroom. When students experience difficulty in Maths, they might appear bored, annoyed, rebellious, ironic, puzzled, defiant, etc. but not afraid, because they are proud.

It’s adults that tell you how frightening the experience was when they were kids. Adults are not in the classroom anymore, they can let the fright out and even laugh about it.

But where does this ‘Maths fright’ really come from ?Read More »

Why is it so important for students to have a sound number foundation ?

Yes, you’ve heard it before… ‘Students can’t do sums anymore’.

You had heard it before, hadn’t you ? Well, just in case you hadn’t, that’s exactly what someone was telling me last night at the pub: ’Oh, you’re a Maths teacher, eh ? Well, I’ll tell you one thing, mate: kids can’t do sums anymore !’

That was just in case you hadn’t heard it before.

True or not true ? Important or not ?Read More »

The Maths ability pyramid


The Maths ability pyramid is a communication tool I have created in order to explain more easily to students and parents what we do in Maths and why we do it.

The initial idea behind the Maths ability pyramid is not only to access a better understanding of what learning Maths is, but also to get rid of this highly misleading fiction: the one monolithic so-called ‘Maths ability’ (you know, when parents or students tell you: ‘Sir/Miss, I’m not good at Maths anyway’…).Read More »