Fergal Reid, PhD. fergal.reid@gmail.com

Summary

Given publicly available data, Covid-19 is likely still on trajectory to kill tens of thousands in Ireland, over a period of months.

[Edit, 17th March — it’s not clear whether we’re still on this trajectory. While the infection-fatality-rates estimated below still seem valid, we’ve taken more social distancing measures since this was written; maybe these will reduce the growth rate sufficiently — see follow-on post.

Edit, 24th March: The authorities have closed several sections of the economy to prevent an uncontrolled epidemic, and individual Irish people are taking covid-19 seriously. Hence the scenarios here shouldn’t occur. I think the numbers below still reasonably describe the trajectory we were on earlier, and why we needed this action. It seems like we could have prevented a lot of economic damage if we had responded earlier, like Taiwan or Singapore did.]

It spreads more rapidly than the flu. If we don’t do more, it will likely infect 60% of the population, in the next 2–3 months, even after closing our schools.

Due to exponential growth, this will far exceed our health system’s resources to deal with it.

Covid-19 is reported to have an infection fatality rate of 0.5% across all cases, with healthcare support. I provide a simple calculation that argues this fatality rate could increase to 2.8% without healthcare, and hence that we might see 50k deaths in Ireland over a period of months.

It’s not clear there are any good options here, but we urgently need a hard-hitting and realistic public discussion.

Who am I

Machine learning PhD. Currently working in industry.

Google scholar. My LinkedIn.

I wrote a paper doing epidemiological models, in a non-medical context, so I understand basic epidemic processes and growth.

Should I be writing this?

Epidemiologists are the best experts in this situation. If one of them writes an article like this about Ireland, read that instead. But we don’t have many, and they are busy.

Treat me as an informed citizen. I’m going to break a lot of academic rules here due to time pressure.

There are political dimensions to the response that need to be understood and discussed, right now - for example the different trade-offs UK are making.

Main data-backed argument

How lethal is covid-19?

Lens 1: Case fatality rate

WHO: “Globally, about 3.4% of reported COVID-19 cases have died. By comparison, seasonal flu generally kills far fewer than 1% of those infected.” [As of 3rd March]

People take time to die, so the fatality rate increased to 3.7% in China since.

Italy is currently running about: 1,266/17600 = 7.6%

A recent letter in the Lancet attempts to correct for the time-delay of resolved cases, and estimates a 5.7% worldwide CFR, which seems high.

Lens 2: Infection fatality rate

However, Case Fatality Rate isn’t what we want to know.

First, CFR while in progress, like in Italy, underestimates final fatality rate (as people take time to die, after being discovered as ‘cases’.)

Separately, if you don’t detect mild cases, CFR looks worse than it is.

‘Diamond Princess’ Cruise Ship

The Diamond Princess cruise ship can be used as a lab here, as they tested almost everyone before letting them off ship. This lets us accurately estimate denominator — what to divide the number of deaths by, to calculate fatality rate. The population is elderly, so you need to correct for that. Russell et al. have done this and statistically estimate 0.5% infection fatality rate, on a population with the demographics of China.

However, this is using the Diamond Princess data, relatively wealthy passengers, and where there was plenty of medical care for everyone — the hospitals were not saturated.

Alternatively, Riou et al. estimate a higher 1.6% fatality rate among all cases in China, using a statistical technique using the ages of detected cases in China:

“We find that 1.6% (1.4–1.8) of individuals infected with COVID-19 during that period with or without symptoms died or will die”

How many will be infected?

The ‘attack rate’ is the percentage of population that gets infected (in total; not all at same time).

If we quarantined everyone to their house, like Wuhan, forever, this will be very low! But what is the attack rate without such measures?

It’s not 100%. As the population gets infected, then recovers, any disease finds it harder to spread to the now immune (or partially immune) people. You eventually reach an equilibrium, with less than 100% infected.

This equilibrium depends on how contagious it is. The R0 is a number that captures contagiousness.

How contagious is covid-19?

Kucharski et al, writing in the Lancet, estimate an R0 of 2.35. Researchers generally seem to be using values in the range 2–3. “(Rt) in Wuhan declined from 2·35 (95% CI 1·15–4·77) 1 week before travel restrictions were introduced on Jan 23, 2020, to 1·05 (0·41–2·39) 1 week after.”

Researchers estimate the R0 of flu (depending on strain) at about 1.2–1.6, which is a lot less than 2.35. (We also have some herd immunity for flu, and vaccines.)

E.g. “comparable to R0 values estimated for seasonal strains of influenza (mean R0 1.3: range 0.9 to 2.1).” in the BMJ.

Early estimates of pandemic swine flu were 1.2–1.6: “The pandemic (H1N1) 2009 influenza virus has a R0 of 1.2 to 1.6 (Fraser, 2009) which makes controlling its spread easier than viruses with higher transmissibility.” Fraser et al.

With a higher R0, it is completely reasonable to expect a higher attack rate for covid-19 than for flu.

Projected attack rate

Health authorities are using figures of 50–70%: https://www.theguardian.com/world/2020/feb/28/australian-doctors-warn-of-overwhelmed-public-health-system-in-event-of-coronavirus-pandemic

UK chief science office talks about 60%: https://www.theguardian.com/world/2020/mar/13/herd-immunity-will-the-uks-coronavirus-strategy-work

Numbers for Ireland, v1

With this data, we can estimate a number of deaths for Ireland, assuming we have health care, and without new stricter countermeasures:

60% of the population infected, 0.5% die:

4,800,000 * .6 * .005 => 14,400 deaths

BUT: This is using the data from Diamond Princess, where all had access to healthcare.

Modelling if healthcare runs out

From WHO final report on China:

“Approximately 80% of laboratory confirmed patients have had mild to moderate disease, which includes non-pneumonia and pneumonia cases, 13.8% have severe disease (dyspnea, respiratory frequency ≥30/minute, blood oxygen saturation ≤93%, PaO2/FiO2 ratio 50% of the lung field within 24–48 hours) and 6.1% are critical (respiratory failure, septic shock, and/or multiple organ dysfunction/failure).”

Let’s assume that the 6.1% of critical cases die if the health system is overwhelmed, and half the 13.8% severe cases, for a total of 6.1+6.9 = 13%

Now, remember, we think China is not finding all its cases, because it’s hard to find all the mild ones. What percentage did it find?

From the Russell et al. Diamond Princess paper again:

“As the raw overall nCFR reported in the China data was 2.3% [7], this suggests the cCFR in China during that period was 1.1% (95% CI: 0.3–2.4%) and the IFR was 0.5% (95% CI: 0.2”

So, they are correcting the raw CFR of 2.3 down to an IFR of 0.5% (dividing it by 4.6).

Lets then divide the 13% of by 4.6 = 2.8% infection fatality rate without healthcare.

This would imply that in Ireland we would see

4,800,000*.6*.028 = 80k deaths, if no one has healthcare, and everyone gets sick at once.

If we assume no serious cases die, and just critical cases die, then the number is ~40k. Doctors can better estimate the exact number here, but it’s large.

That’s if we could treat no-one, and all cases happened at once. How many of these 80k could be treated in Ireland?

Ireland’s healthcare capacity

We don’t have a lot of ICU beds:

“There are 240 critical care (ICU or HDU) beds in HSE-funded hospitals in Ireland (Critical Care Programme, 2018). Private hospitals have an additional 43 critical care beds.” https://jficmi.anaesthesia.ie/wp-content/uploads/2019/02/Irish_National_ICU_Audit_Annual_Report_2017_FINAL.pdf

Many of these ICU beds will be already occupied.

We obviously have more non-critical care beds (15k-16k, public and private): (HSE) (Statista)

According to the WHO report “Remarkably, more than 40,000 HCW have been deployed from other areas of China to support the response in Wuhan”, to deal with their 80k detected cases. No one is going to send 40,000 health care workers to Ireland.

I don’t know how many patients we can treat at once, but it’s nowhere close to the number we might need, if this hits all at once.

Over what period will it hit?

Timeline

Unfortunately, this is growing exponentially, so it will effectively hit at once, if not arrested.

Other European countries are seeing a doubling every 3-6 days.

If that trajectory persists, and we don’t arrest it, in the 1-2 weeks closest to peak rate, we’ll have seen >75% of our cases emerge.

This would mean we have a peak need to treat upwards of 50k critical cases.

Clearly this would lead to tens of thousands of deaths, maybe many tens of thousands.

How quickly will this happen?

Analysis of speed has been done better before.

Read Chart 4 (easily verifiable from public sources), and Chart 7 (published in JAMA).

This will spread super fast, if current rates are maintained.

The >25% growth per day, like other European countries are seeing, if sustained, turns 100 cases into 1M cases within 42 days. (This is conservative: Spain grew an average of 48% a day over the last 7 days. That growth turns 100 cases into 1M cases within 25 days.)

This sort of growth falls normally and predictably from basic epidemic modelling.

There is no reason to think this growth won’t be sustained, until we get close to the saturation point (the attack rate), unless we change society to curb it.

This is the idea of ‘flattening the curve’.

However, closing schools doesn’t seem to have meaningfully slowed this in Lombardy (see below).

Where is Ireland in this process?

It’s very hard to know where Ireland is in our epidemic, as our surveillance is just getting in gear:

“It had been the case that if people had returned from an at-risk area and had symptoms, they were to contact their GP.

Now, the at-risk area is no longer a condition and if people have symptoms, they should contact their GP.” (13th March).

https://www.rte.ie/news/coronavirus/2020/0313/1122004-coronavirus-ireland-health/

Up to now, we’ve generally required travel as a testing criterion, so have poor visibility into community cases.

Our response

We just closed the schools.

Note that Lombardy in northern Italy, population 10M, closed schools across Lombardy, and isolated the worst affected towns, on 23rd Feb, when it had 79 cases.

“Schools and universities will also be closed for at least a week in Lombardy, Veneto, Emilia-Romagna and Piedmont, while similar measures have been taken in Liguria and Alto Adige.” https://amp.theguardian.com/world/2020/feb/23/italy-draconian-measures-effort-halt-coronavirus-outbreak-spread (article is from next day when case numbers went up even more).

Ireland has a similar number of cases now, so it’s not clear we are in fact acting early by closing schools when we did.

Now, there is a lag time to observe the impact of any measure, and every country is different. In Wuhan, it took about 2 weeks after lockdown before they saw reductions in cases (see chart below), so we should expect a 2-week lead time for any social distancing to impact observed new case figures.

JAMA note lag time between 24th Jan shutdown and case peak Feb 7th

However, Lombardy has enacted similar measures to Ireland for 23 days and Italy is not seeing a day-on-day reduction in new cases.

Hence there isn’t yet a good reason to think we won’t be in the same situation as Italy is, in 2–3 weeks — and a substantially worse one in 5–6 weeks — given our current measures, given publicly available data.

It’s possible folks working in surveillance in Ireland know things I don’t, in terms of how clustered cases are.

But it seems possible we’re just blind, and going to see big increases in cases as we roll out better testing over the next week. Media articles like this are not encouraging. ‘Earlier today, the HSE said it working to ensure “sufficient testing facilities” are in place by Monday for the Covid-19 coronavirus following “high demand” in recent days.’ [14th March].

Tricky policy tradeoffs

Not speaking with any expertise at all here, but this disease presents some really hard policy tradeoffs:

I see three strategies:

1) Maintain extreme social distance while the world finds a vaccine.

To stop the epidemic, we likely need much higher social distancing than just closing schools, bearing in mind Lombardy’s experience. We don’t know exactly how much distance is required here, but it may be very economically expensive to sustain. At some point the economic damage of this distancing will become higher than the cost of the disease. It may take a year to test a vaccine.

2) Singapore style measures

Build a very aggressive testing and contact tracing system, and quarantine anyone coming in. Maintain large but not extreme social distance (to allow economic productivity). This requires a lot of social compliance, and serious surveillance machinery. It’s not clear if we could achieve this.

Even if we could, we may have too many cases already. Perhaps we could do extreme social distance until case numbers reduce, then implement Singapore-style measures.

3) Accept attrition of old and vulnerable until we have herd immunity; tell those who can to isolate, and let the epidemic take its course. It looks like the UK is going down this path. Maybe it is the most rational path, but maybe it’ll be viewed as monstrous when history is written.

We obviously have some exposure the UK strategy, via Northern Ireland.

If we are planning to do 2), we should have closed down movement earlier, as it gets much more expensive to contain an epidemic as it grows exponentially.

In Wuhan, it took about 2 weeks after house-by-house lockdown before they saw reductions in cases, so we should expect a 2-week lead time to see the impact of any social distancing.

I don’t understand the current response in Ireland. I worry that there’s no coherent plan, or that the delay in enacting 2) will lead us into 3).

Contrary to the narrative in the UK, the trade-offs between 1, 2, and 3 are necessarily political as well as scientific — how do we value the lives of the old and vulnerable vs. different levels of economic damage?

This needs urgent discussion, and we need to be realistic about the magnitude of the potential impact.

We might get lucky. Someone might discover a therapeutic, or the social distancing already employed might work better here, vs in Italy. If policy makers have a good reason to think this, they should explain this to the public; regardless a public discussion should be had.

EDIT: Follow-up piece I wrote, about new modelling from a leading group at Imperial College London: https://medium.com/@fergal.reid/irelands-covid-19-strategy-in-light-of-updated-uk-models-why-flattening-the-curve-might-not-87f78abfb6e

Appendix: arguments for infection fatality rate vs case fatality rate, without using models

You might still wonder whether there is a large unseen ‘iceberg’ of unobserved mild cases — it’s a key question. There is uncertainty here. But by the time there’s certainty, it’ll be too late to act.

However, if you are unconvinced by the Diamond Princess dataset (which is small), or by Riou et al’s technique using age distributions, then Bi et al have studied contacts of confirmed cases in Shenzen, testing all close contacts of confirmed cases.

Cases found by testing contacts are much more likely to reflect the real distribution of outcomes, vs. cases who present medically (which are likely to bias towards more severe).

If we look at the distribution of severities within the ‘discovered cases’, at the time of “first clinical assessment” it shows:

Mild: 20.7%, Moderate: 75.9%, and Severe: 3.4%.

The severity definitions used here are different than other work*.

Unfortunately, Bi et al. only break out the status of these ‘discovered cases’ at first clinical assessment; naturally some will progress. However, even so, the proportion of severe cases in the discovered group (3.4%) vs in the group who presented due to symptoms (10.3%) is not reassuring, as it would indicate a decrease of only a factor of 3 in severe cases due to hidden mild cases. (There will be random error in any inference on such a small sample — but it’s still valuable evidence.)

* “Cases with fever, respiratory symptoms, and radiographic evidence of pneumonia were classified as having moderate symptoms. Cases were classified as having severe symptoms if they had any of: breathing rate ≥30/min; oxygen saturation level ≤93% at rest; oxygen concentration level PaO2 /FiO2 ≤ 300mmHg (1mmHg=0.133kPa); lung infiltrates >50% within 24–48 hours; respiratory failure requiring mechanical ventilation; septic shock; or multiple organ dysfunction/failure.”

Bruce Aylward’s opinion

Bruce Aylward, who led the WHO mission to China, was interviewed in Vox.

The Bi et al. data above shows covid-19 is infecting children, so his comments are at least partly out of date. But his assessment that there are not many unseen mild cases, and comments on Chinese healthcare, remain relevant:

“More of a surprise, and this is something we still don’t understand, is how little virus there was in the much broader community. Everywhere we went, we tried to find and understand how many tests had been done, how many people were tested, and who were they.

In Guangdong province, for example, there were 320,000 tests done in people coming to fever clinics, outpatient clinics. And at the peak of the outbreak, 0.47 percent of those tests were positive. People keep saying [the cases are the] tip of the iceberg. But we couldn’t find that. We found there’s a lot of people who are cases, a lot of close contacts — but not a lot of asymptomatic circulation of this virus in the bigger population. And that’s different from flu. In flu, you’ll find this virus right through the child population, right through blood samples of 20 to 40 percent of the population.

Julia Belluz

If you didn’t find the “iceberg” of mild cases in China, what does it say about how deadly the virus is — the case fatality rate?

Bruce Aylward

It says you’re probably not way off. The average case fatality rate is 3.8 percent in China, but a lot of that is driven by the early epidemic in Wuhan where numbers were higher. If you look outside of Hubei province [where Wuhan is], the case fatality rate is just under 1 percent now. I would not quote that as the number. That’s the mortality in China — and they find cases fast, get them isolated, in treatment, and supported early. Second thing they do is ventilate dozens in the average hospital; they use extracorporeal membrane oxygenation [removing blood from a person’s body and oxygenating their red blood cells] when ventilation doesn’t work. This is sophisticated health care. They have a survival rate for this disease I would not extrapolate to the rest of the world. What you’ve seen in Italy and Iran is that a lot of people are dying.”