Why aren’t we talking about the single most important number in the #Covid19 crisis?

Why aren’t we talking about how many people are infected with #COVID19?

How many in every train, every park, every shop, on every street?

Estimating the total number of #COVID19 infected people, not just the “confirmed cases” iceberg tip, would help encourage lockdown compliance and hygiene measures. It’s critical to planning intensive care capacity, to determining how deadly the disease is and to understanding how fast it will spread. Yet governments, the press and even the many brilliant data analytics sites aren’t talking about it.

Using a simple model, I’ve estimated the following for actual infections as of 10th April:

~1 in 12 in UK (~8.1%)

~1 in 7 in London (~13.9%)

In other words, there may now be approximately 5.5 million UK people infected with the Covid-19 CoronaVirus.

Governments need to start sharing this type of estimate to cut through the widespread complacency we’re still seeing.

Epidemiologists can’t agree on the infected %. Their estimates range from 0.07% for the UK to over 50%. Some claim the number of infected is “unknowable” — so they resist making estimates at all.

This level of uncertainty isn’t helpful given the % population infected is central to our response. On one extreme, not many people have got the disease but it’s very deadly and we’re in this for the long term — managing multiple future waves. On the other, most people have already got it but it doesn’t kill many. In the latter case, once we’re through the painful peak of the next few weeks, the crisis would largely be over assuming recovered people retain immunity. It’s important to know.

A poll-style sample of the general public, then rapid testing of this sample, would help cut through the confusion. This isn’t about testing ill people, it’s testing random samples of the general public to determine how many are infected. Even samples using the current PCR “point in time” tests would tell us — we don’t need to wait for serological or mass testing capabilities.

In the meantime, I calculated this simple model based on the 10th April report of 8,958 UK hospital fatalities, using the following data and assumptions.

Concerns have been raised about the UK death statistics — both re: time consistency and completeness. I’ve added an additional 60% fatalities to account for Covid19 deaths at home / in care homes of non-tested people (~7%) and to account for the reporting time-lag (70% as of 27 Mar, but this gap should reduce as the curve starts to flatten). Regardless, deaths remain our most reliable guide to the numbers infected and Covid’s deadliness. This results in an estimate of 14,333 deaths.

Infection Fatality Rate 1% (death % of all infected, not just positively tested cases). This rate will jump if our intensive care facilities run out of capacity, but for this early stage in a country with high quality health facilities, this seems a reasonable estimate given experiences elsewhere in the world.

Median days from infection to death 23.5. This corresponds to data gathered in China. For earlier estimates I was using an adjusted figure of 18, given the exponential growth in numbers of infections meant the deaths to date were driven more strongly by more recent infections than a simple median would suggest. Given the growth rate has now slowed, this adjustment is no longer necessary.

On that basis, we can assume ~1.4m people must have been infected up to around 23.5 days ago to drive 14,333 deaths.

Days to double infections: 12 days, so ~1.96 doublings have occurred since that point 23.5 days ago. We can’t determine the actual doubling rate of infections without population sample testing, so I am using a combination of the observed case doubling rates (7.5 days adjusted to 8 days given assumed daily recoveries) as well as an assumption the UK is following Italy’s lockdown flattening (cases now doubling every 16 days) with a two week lag.

That doubling rate implies ~5.5 million people are infected today.

We can also estimate how many were infected but have now recovered. Bizarrely, the UK government has not reported on case recoveries for over two weeks. If we assume the average disease duration is 18 days, we can exclude “new cases” before that period on the assumption those people have now recovered. On that basis, ~10% of total cases might have recovered. Given cases are only the most serious, I’ve assumed ~15% of all infected have recovered. This implies ~6.5m have ever been infected and ~1m have recovered to date.

The estimates are very sensitive to uncertain inputs, so low confidence and very wide ranges apply.

London has ~23.4% of UK cases, which implies ~1.3 million total infections. That’s ~13.9% of the London population infected.

If the infection fatality rate is higher, the number of infections is lower. If the virus is less deadly, more people must have been infected to drive the deaths we’re seeing.

If the doubling rate has been slower due to lockdown effectiveness, infections are much lower.

If the recovery % is higher, current infections are lower.

As an alternative illustration, if our lockdown has managed to reduce days to double to 16 days (not 12) over the last 3 weeks, and Covid19 kills 1.5% (not 1%), the number of infections today drops to ~2.6m.

The base estimates above imply a total UK death toll (including the ~14,333 to date) of ~69k over the coming weeks… but only if the IFR% remains 1% + we see zero new infections. Sadly, neither of the above are sound assumptions. If our ICU capacity is overrun, the IFR% will spike hard. New infection levels depends on how hard we maintain our lockdown + how quickly we can scale our test/trace/quarantine capability.

Why is estimating the total number of infected people more important than just tested “cases”?

First — Infected people are doing the infecting. The “cases” are in hospital/dead/immune.

Second — If you know # infected and # deaths you can assess how deadly this thing really is (IFR%, not just “case” fatality).

Third — Telling public the % infected helps us comply with hard lockdown. Boris Johnson’s speech should have started: “There are infected people in every train, in every shop, in every park, in every tube… you might even be one of them… please take what I am about to say very seriously…”

Fourth — “Total infected” tells us how many people are going to be coming through our ICU capacity in the next few weeks and whether that will be overrun. If it is, #Covid19 will kill much more than 1%. When you run out of ICU beds / ventilators, many more die as in Italy/Spain.

If we’d started projecting total infected from day one (ideally via. regular pop. sample tests), we might have acted sooner. We might also have persuaded people to comply better with our weak lockdown. Instead, as the editor of the Lancet says… “a national scandal”?

Focusing only on the 74k “confirmed cases” (positively tested people) breeds complacency.

Complacency kills. It’s already happening.

Feedback, refinements or corrections are very welcome: Reply here or ping me at @JamieWoodhouse.


This University of Goettingen paper estimates UK cases are detecting only 1.2% of infections.

This CMMID paper estimates UK cases are detecting only 3.4% of symptomatic cases. Asymptomatic cases then need to be added to estimate total infected.

The “JoinZoe” Kings College symptom tracking app estimates 1.4m symptomatic infections (down from 1.9m). To get to total infected estimates we would need to add figures for people between 0–20 yrs and over 69 years. We would also need to add all asymptomatic infections (50%?).

This Telegraph article summarises a similar, but more granular model, estimating ~1.6m were infected as of 26th March.

This Evening Standard piece referenced 1 in 10 Londoners potentially being infected. https://www.msn.com/en-gb/news/newslondon/up-to-one-in-10-londoners-may-be-infected-with-coronavirus-expert-warns/ar-BB11HBdk

This recent Imperial College report takes a similar, but much more detailed and professional approach. Their estimates are already out of date given only 758 deaths as at 28th Mar and because they excluded non-hospital and reporting lagged deaths. However, their estimates imply similar ranges to those I’ve set out in this piece. http://www.imperial.ac.uk/news/196556/coronavirus-measures-have-already-averted-120000/

This UnHerd piece also takes a top-down, work from deaths approach and comes up with estimates in similar ranges: https://unherd.com/2020/04/how-likely-are-you-to-die-of-coronavirus/.

This Metro piece referenced 2–3% of UK population being infected, much higher in London https://metro.co.uk/2020/03/30/coronavirus-slowing-uk-thanks-social-distancing-measures-12476442/.

Finally, and way too late, some seem to be talking about this. Still not our government.

Data sources:

Deaths and case recovery rate: https://www.gov.uk/guidance/coronavirus-covid-19-information-for-the-public

Infection Fatality Rate: https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf and http://www.imperial.ac.uk/news/196556/coronavirus-measures-have-already-averted-120000/.

Days to cause death: https://www.sciencedirect.com/science/article/pii/S0140673620305663

Doubling rates: https://ourworldindata.org/coronavirus#the-growth-rate-of-covid-19-deaths

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