A while ago, I mentioned that the cost of delaying lockdown by a week was to increase illness and death by a factor of 5, based on the doubling time of 3 days that the virus seemed to have at the start.

Human cost of delayed action – a short thread prompted by a tweet from @dougmcneall asking what the effect of a changing lockdown date (eg by a week) would be. Not long enough for a blog post! 1/

— James Annan 🇪🇺 (@jamesannan) April 21, 2020

It’s a simple result but quite striking and perhaps counterintuitive, so here it is in more detail (and with slightly different numbers).

I’ve been fitting the SEIR epidemic model to the daily death data, and here is the latest hot-off-the-press version.

The magenta line is the median of my model fit, and the red circles are the data, though I have smoothed them a little to reduce the huge weekly cycle in reporting (Sun/Mon are always really low, then Tuesday really high).

This model allows the reproduction number to change at the lockdown date, and estimates the two values (which I call R0 and Rt) by fitting to the data. Taking that central magenta estimate, it is easy to re-run the model assuming the same change happened a week earlier. And this is what we get:

Magenta is as above, and blue is what happens if I make the change in R one week earlier, on the date of the blue vertical line. How did I know it would cause such a large reduction in deaths? The doubling time in the early phase is 3.5 days here (not 3 days as I got previously, told you the numbers were slightly different). So the size of the epidemic on this new lockdown date is exactly 1/4 the size it was on the later date. And the behaviour of exponentials (both growing and declining) is such that every day before or after the lockdown, the total size in the hypothetical case is also 1/4 what it was the same number of days before or after the lockdown in reality. The next plot shows this more clearly. I have just shifted the blue line forward by 1 week to make the lockdown dates coincide.

See the same shape, just lower? The logarithmic y-axis that I’m using means that a constant vertical distance between the solid blue and magenta lines corresponds to a constant ratio in numerical values, of 4 in this case. So the total number of deaths is also smaller by a factor of 4. The dashed blue line is the same model output as the solid blue line, only I’ve multiplied it by 4. You can see it overlies the original magenta almost exactly. Just towards the right hand edge of the graph there is a small mismatch, which is due to the magenta case benefiting from a slightly enhanced decline from a hint of the “herd immunity” phenomenon. That is to say, a with roughly 10% of the population having suffered from the disease in that scenario, these people (assumed to be immune) reduce the spread of the disease just enough for the lines to look a little bit different.

So, with these numbers that represent an initial doubling time of 3.5 days, we see that implementing the lockdown one week earlier would have saved about 30,000 lives in the current wave (based on official numbers, which are themselves a substantial underestimate). It would also have made for a shorter, cheaper, less damaging lockdown in economic terms. And this is all quite simple maths that every single modeller involved in SAGE was fully aware of at the time.

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What if lock down had started March 1st? Would that have been 75% fewer deaths and cases?

Would earlier lock downs mean greater cases in second round expected in the fall?

From my own quite crude attempts at data wrangling there is some co-relation between the length of time between first case reported and date of lockdown against an estimated infection rate. You can only do this for a limited number of countries but it does include the UK. How you define lockdown and the differences in each country muddy the waters but it is there.

From everything I’ve seen Belgium has the most transparent data and similarity to the UK, using their case rate and mortality rate indicates an estimated UK number of probably over 325,000 cases & 53,000 fatalities.

I can’t see any way to attempt to predict any 2nd wave numbers, too many variables.

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As you say, SAGE modellers are surely aware of this. However, this blog from one epidemiologist indicates why even given this knowledge, earlier lockdown is not always a good idea: https://personalpages.manchester.ac.uk/staff/thomas.house/blog/blog.html

Reducing R at lockdown and never changing it back again (which is what I understand the graphs above show) is surely modelling an indefinite lockdown, which we cannot sustain?

Hi Raf, yes it’s funny you should say that, it was that particular blog post where I got my model code from 🙂

It’s true that indefinite lockdown is unsustainable, and if literally our only option was a 3 week spell and nothing else then his modelling would be correct. However in reality we have more options than that. Whatever our future choices are, we could have reached this point with many fewer total deaths and a shorter lock-down.

If sage were aware…why didn’t the government act then?

You’ll have to ask them.

Agreed, we could have reached today (May 20th 2020) with many fewer deaths to date. However, *if* by locking down later, enough of the UK was infected (and has gained some immunity that is retained) such that a second wave of infection this winter is kept no larger than the first, then it is still possible that the later lockdown has saved lives and minimised the total lockdown time.

Of course, if the strategy of “lockdown until cases fall to a low level, then aggressive contact tracing indefinitely to keep R1 after lockdown (and drops to <1 only through herd immunity) and yours assumes R can be retained at the lockdown level Rt < 1. Neither of these is realistic, and as you say we have some sustainable options short of full lockdown, so the true value of R after lockdown is going to be somewhere in between these.

It's not clear to me:

– what amount of physical distancing and contact tracing infrastructure is needed to get R<1 indefinitely without herd immunity, and

– whether the amount of surveillance/intrusion this entails will accepted by the UK public.

It looks as though the measures currently in place in China may be sufficient to keep R<1, but the extent of non-anonymous surveillance and enforced quarantine (away from home) used there is far beyond what I think is possible in the UK, without a seismic shift of public opinion towards authoritarian government.

Of course, the toy model we are talking about assumes homogeneous mixing of people and a single value of R for the whole country. A climate model of similar complexity would assume that the temperature was the same everywhere on the globe… and I'm not sure we would want to make many quantitative predictions or policy recommendations based on the outcome of that model…

So what would the model now say by removing/waving the lockdown

Whoops, the above is missing some text. Meant to write in the second paragraph:

Of course, if the strategy of “lockdown until cases fall to a low level, then aggressive contact tracing indefinitely to keep R1 after lockdown (and drops to 1 after lockdown (and drops to <1 only through herd immunity) and yours assumes R can be retained at the lockdown level Rt < 1….

If we end up with the virus going right through us, maybe we could argue it doesn’t matter much what the policy is….except….the hospitals didn’t treat care home patients due to worries about capacity, so we ended up infecting the care homes with *more* cases rather than shielding them to achieve *less* as the basic mitigation plan implied.

If we were to go back to business as before, there will be a big second wave, but with so many now working at home etc, I don’t expect people will go back to business as before regardless of what the law says.

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