Has over half of the UK already been exposed to COVID-19?



Stuart McDonald  is my hero. He is able to speak about complicated things in a simple way and his analysis of trends in the development of the pandemic has been consistently proved right.

Here is his latest observation

But lest we get carried away, Stuart is keen to scotch rumours that we are mass-immunised. The recent media suggestion that over half of the UK may have been exposed to the virus which causes COVID-19 is firmly dismissed in this excellent article, published with Stuart and his group’s kind permission

this second bulletin from the newly formed COVID-19 Actuaries Response Group, we discuss the recent media suggestion that over half of the UK may have been exposed to the virus which causes COVID-19.

Screenshot 2020-03-27 at 07.46.03

Screenshot 2020-03-27 at 07.43.51


The Oxford study describes a simple but widely used Susceptible-Infected-Recovered (SIR) epidemiological model framework. A forthcoming bulletin will describe this model in more detail, so we will not summarise it here. We have no particular concerns about the choice of model structure.


Combinations of model parameters have been chosen which closely reproduce the pattern of deaths during the first fifteen days when death counts were above zero in Italy and the UK. For Italy this was a total of 197 deaths between 21 February and 6 March; for the UK this was a total of 144 deaths between 5 March and 19 March.

These are small numbers of deaths to use to calibrate a model, particularly one which seeks to project backwards from the first death to estimate the date that transmission began. We note the study authors’ stated intent to avoid any potential effects of local control strategies, but we are of the view that a longer time series could have been used given the lag between the introduction of control measures and observed deceleration in the rate of increase of confirmed cases or deaths.

Parameter Choices

Most of the parameter choices, such as the assumption that the transmission rate (R0) is in the range 2.25 to 2.75, seem to be reasonable and supported by the literature.

The authors take a two-step approach to modelling mortality:

  • Proportion of the population vulnerable to severe disease (ρ)
  • Probability of dying having contracted severe disease (θ)

The assumption used for θ looks reasonable and well supported by earlier studies. However, this is not the case for ρ. Values of ρ between 10% and 0.1% are considered, with no justification being provided. This is a crucial assumption since the modelling approach leads to an inverse relationship between this parameter and the proportion of the wider population assumed to have had the disease.

The first sentence in the results section is absolutely key: “Our overall approach rests on the assumption that only a very small proportion of the population is at risk of hospitalisable illness. This proportion is itself only a fraction of the risk groups already well described in the literature​, including the elderly and those carrying critical comorbidities (e.g. asthma).”

So, the whole study is conditional on the validity of this assumption. But, as implied above, some of the values of ρ considered seem implausibly low. Analysis carried out in 2015 showed high levels of disease in England’s over-65 population – for example, almost half had hypertension, nearly one in five had heart disease and a similar number had a chronic respiratory disorder. Whilst it is likely that not all of these individuals would be classified as being vulnerable, given these statistics it is unclear why the authors would consider that the vulnerable proportion might be as low as 1%, let alone 0.1%.

Screenshot 2020-03-27 at 07.40.37

When ρ is assumed to be 10% (dark red line below) the susceptible proportion looks to be around 95%, i.e. the model indicates that just 5% of the population have been exposed to the virus.

When ρ is assumed to be 1% (orange lines) the susceptible proportion is as low as 60%, i.e. the model indicates that up to 40% of the population have been exposed.

When ρ is assumed to be 0.1% (yellow line) the susceptible proportion is just 32%, i.e. the model indicates that up to 68% of the population have been exposed.

The results are even more extreme for Italy, with the ρ = 0.1% scenario implying that 80% of the country had already been infected by 6 March. We struggle to comprehend how the authors concluded that this was a plausible scenario to include in the paper in light of the 7,000 additional deaths which have tragically occurred in Italy since that date, and the significant differences in confirmed cases and deaths between the Lombardy region and the rest of the country.

Media Reporting

The study authors make no explicit claim that the scenarios with a very low vulnerable population, and therefore a very high wider population exposed, are the most likely scenarios. They do however say that “Importantly, the results we present here suggest the ongoing epidemics in the UK and Italy started at least a month before the first reported death and have already led to the accumulation of significant levels of herd immunity in both countries.”

Crucially, and somewhat predictably, reporting has focussed on these high exposure scenarios. For example, the headline in the Financial Times was “Coronavirus may have infected half of the population – Oxford study”.

We feel that this message is potentially misleading and could undermine key public health messages about social distancing. Whilst it is important to communicate and discuss the uncertainty in how the virus has spread (and possible ways of understanding it better), given the seriousness of this situation, both academics and journalists need to take great care to communicate their messages in a clear and balanced way.


Fundamental principles of epidemic spread highlight the immediate need for large-scale serological surveys to assess the stage of the SARS-CoV-2 epidemic, Lourenço​ et al, 24 March 2020

By Stuart McDonald FIA CERA for

COVID-19 Actuaries Response Group – Learn. Share. Educate. Influence.

Stuart mc

About henry tapper

Founder of the Pension PlayPen,, partner of Stella, father of Olly . I am the Pension Plowman
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6 Responses to Has over half of the UK already been exposed to COVID-19?

  1. Brian G says:

    That is so brilliantly explained.

  2. John Mather says:

    My concern is the way the new cases are reported

    If the tests are only applied to those exhibiting symptoms then models and media are open to political manipulation and the Ministry of Truth at number 10

    If you look at the Spanish Flu experience of 1918 ( best book Pale Rider by Laura Spinney) Trump is clearly trying to tell the tide not to come in

  3. DaveC says:

    What is most baffling is that this doesn’t have to be an unknown variable.

    It could be nailed down much more firmly with a sample. Much like exit polls, tv viewing stats, etc… the right sample would give an idea of what is going on.

    Currently we just look at hospitalisations/deaths and use heavily biased data from Wuhan/China/Italy to gauge things.

    Iceland’s data gives validity to the 0.1% claim. So perhaps sars2 really is already well spread?
    Italy’s data gives validity to the 10% figures, so perhaps sars2 will wipe us all out?

    How about we use 25,000 test kits and find out, to actually properly gauge policy that is critical to the economy and lives being saved?
    Perhaps they do have this information but don’t feel the need to clarify it.

    I think John is partially correct. Better to not know so you can manipulate the message sufficiently… rightly or wrongly.

    Given the behaviour of the population in some instances, I’d say managing them is more critical than anything else.

    I’ve a feeling this’ll all be over in 8 weeks. Lockdown finished up in 3-4. And the p value indeed will turn out to have been well into sub 1% range.

  4. Julie Richards says:

    I’m not a data scientist or researcher although my son is and we have had some interesting discussions over the last few weeks, reflecting the fact that my husband spent three weeks in China over November and December, in the area between Macau and Hong Kong, mixing with Chinese and US colleagues.

    The significance was not appreciated at time, but in the two weeks prior to Christmas he and I showed the Covid-19 symptoms, particularly the constant dry cough, aching limbs and high temperature: I was particularly ill with bronchitis. We put the experience down to unusually early, severe flu (he always has flu vaccine, I never do): we’ve not been tested and clearly recovered.

    Coronaviruses are around us all the time so it could have been anything but the co-incidence is worthy of note. If Covid19 is what we were exposed to, that is consistent with the point that China knew of the full virus impact long before it became public and the likelihood that it has already extend beyond Wuhan long before the news broke. Apparently, Chinese research shows it was identified and the risks of it jumping to humans known in 2013 and re-reinforced as a high risk in 2016 (see New Scientists this week).

    Trade with China is extensive and there will be many like our family so it is not unreasonable to suggest that the incidence of the virus could be significantly underestimated, given the exponential nature of its spread, but perhaps so too is the recovery rate. It would also mean, not surprisingly, that much of the modelling may be flawed.

    Final observation – it has been nigh on impossible for me to find a way of altering NHS or Public health to our experience. Sad fact is both have been badly resourced (i.e not necessarily lacking in money but certainly in spending it efficiently) and the medical profession’s warning on the ability to cope with an unusual surge in illnesses have been well founded.

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