My model calculations for Covid-19 cases for an earlier UK lockdown

Introduction

A little while ago (14th May), I published a post entitled What if UK lockdown had been 2 weeks earlier? where I explored the possible impact of a lockdown intervention date of 9th March instead of 23rd March, the actual UK lockdown date.

That article focused more on the impact on the number of deaths in those two scenarios, rather than the number of Covid-19 cases, where the published data is not as clear, or as complete, since so few people have been tested.

That post also made the point that this wasn’t a proper forecast, because the calibration of the model for that early an intervention date would have been compromised, as there was so little historic data to which to fit the model at that point. That still applies here.

Therefore the comparisons are not valid in detail against reported data, but the comparative numbers between the two models show how a typical model, such as mine (derived from Alex de Visscher’s code as before), is so dependent on (early) input data, and, indeed, responds in a very non-linear way, given the exponential pattern of pandemic growth.

Cases

I present below the two case numbers charts for the 9th March and 23rd March lockdown dates (I had covered the death data in more detail in my previous post on this topic, but will return to that below).

In the charts for cases here, we see in each chart (in orange) the same reported data, to date (24th May) but a big difference in the model predictions for cases. For the 9th March lockdown, the model number for cases by the 23th March is 14,800.

The equivalent model number for cases for 23rd March lockdown (i.e. modelled cases with no prior lockdown) is 45,049 cases, about 3 times as many.

The comparative reported number (the orange curve above) for 23rd March is 81,325 (based on multiplying up UK Government reported numbers (by 12.5), using Italy’s and other data concerning the proportion of real cases that might ever be tested (about 8%), as described in my Model Update post on May 8th). Reported case numbers (in other countries too, not just in the UK) underestimate the real case numbers by such a factor, because of the lack of sufficient public Coronavirus testing.

As I said in my previous article, a reasonable multiple on the public numbers for comparison might, then, be 12.5 (the inverse of 8%), which the charts above are reflect for the orange graph curve.

Deaths

For completeness, here are the comparative charts showing the equivalent model data for deaths, for the two lockdown dates.

On the right, my live model matches reported deaths data, using 84% lockdown intervention effectiveness, for the actual March 23rd lockdown, quite accurately. The model curve and the reported data curve are almost coincident (The reported data is the orange curve, as always).

On the left, the modelled number of deaths is lower from the time of lockdown. By 23rd March, for 9th March lockdown, it is 108, lower than it is for lockdown at the 23rd March (402) (with no benefit from lockdown at all in the latter case, of course).

These compare with the model numbers for deaths at the later date of May 13th, reported in my May 13th post, of 540 and 33,216 for March 9th and March 23rd lockdowns respectively (at virtually the same 84.1% intervention effectiveness).

As for the current date, at 84% effectiveness, of 24th May, the numbers of deaths on the right, for the actual 23rd March lockdown data and model is 36,660 (against the reported 36,793), and for the 9th March lockdown, on the left, would have been, in the model, 570 deaths.

That seems a very large difference, but see it as an internal comparison of model outcomes on those two assumptions. whatever the deficiencies of the availability of data to fit the model to an earlier lockdown, it is clear that, by an order of magnitude, the model behaviour over that 2 month period or so is crucially dependent on when that intervention (lockdown) happens.

This shows the startling (but characteristic) impact of the exponential pandemic growth on the outcomes from the different lockdown dates, for an outcome reporting date, 13th May, just 51 days later than the March 23rd reporting date, and for an outcome reporting date, 24th May, 62 days after March 23rd.

The model shows deaths multiplying by 5 in that 51 day period for 9th March lockdown, but 82 times as many deaths in that period for the 23rd March lockdown. For the 62 day period (11 days later), the equivalent multiples are 5.2 and 339 for 9th March and 23rd march lockdown respectively.

My 9th March lockdown modelled numbers are lower than those from Professor Rowland Kao’s research group at Edinburgh, if their Scottish numbers are scaled up for the UK. Indeed, I think my absolute numbers are too low for the March 9th lockdown case. But remember, this is about model comparisons, it’s NOT an absolute forecast.

In terms of the long term outlook (under the somewhat unrealistic assumption that 84% lockdown effectiveness continues, and in the (possibly more realistic assumption of) absence of a vaccine) deaths plateau at 42,500 for the actual March 23rd lockdown, but would have plateaued at only 625 in my model if the lockdown had been March 9th (as covered in my previous post).

Conclusions

For cases, the modelled March 9th lockdown long-term plateau, under similar assumptions) would have been 41,662 cases; but for the actual 23rd March lockdown, the model shows 2.8 million cases, a vastly higher number showing the effect of exponential behaviour, with only a 2 week difference in the timing of the intervention measures taken (at 84% effectiveness in both cases). That’s how vital timing is, as is the effectiveness of measures taken in the pandemic situation.

These long-term model outcomes reflect the observation of a likely deaths/cases ratio (1.5%) from the “captive” community on the cruise ship Diamond Princess.

But as I said earlier, these are comparisons within my model, to assess the nature and impact of an earlier lockdown, with the main focus in this post being the cases data.

It is a like-for-like comparison of modelled outcomes for two assumptions, one for the actual lockdown date, 23rd March, where the model fits reported data quite well (especially for deaths), and one for the earlier, postulated 9th March lockdown date (where the model fit must be questionable) that has been discussed so much.

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