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.