On Approximate Estimates for End of April Infections

[danieldwilliam]

Posting mostly to check my maths and the not-craziness of my assumptions

930 newly reported coronavirus deaths yesterday. Allowing for reporting lag, approximately 1,000 casualties.

Total deaths approximately 7,000.

Estimate of the peak of deaths occuring 20th April. Assuming approximately 1,000 deaths a day until the peak, followed by a two week period on the other side of approximately a 1,000 deaths a day. With roundings takes us to 35,000 deaths within a few weeks.

Assume 1% of symptomatic cases result in death. That implies 3.5 million people have had coronavirus with symptoms. The next bit is a guess on my part but assume for every one person with symptoms there is another person who is asymptomatic. Total number of UK residents infected with coronavirus approximately by the end of April, 7m.

Ball park. A little over 10%.

Which if I have understood the literature correctly

a) doesn't help much when using antibody tests with a 95% accuracy rate in sorting the genuine positives from the false positives. You'd see 1 false positive for every 2 real positive reports. (This is going to turn in to some real life and death version of the Monty Hall problem)

b) doesn't help much with reducing the speed at which the virus spreads. If each infected person infects 3 other people and only 0.3 of those people have already had it then 10 infected people infect 27 people who in turn infect 73, compared to 3>>30>>90.


If, at the end of April the transmission rate is 0.9 due to movement restrictions then I estimate 9 blocks of 3 weeks, 27 weeks in total from 1st May, until the total number infected persons reaches approximately 2/3rds of the population which seems to be the lower limit at which the chains of transmission start to break down because of herd immunmity.

Other than the fact that I finally understand the Monty Hall problem I'm not seeing a whole lot of good news here.

Comments

[mountainkiss]

Nate Silver is estimating 30% asymptomatic, based on aggregation of experts as I understand it.

[danieldwilliam]

Thanks.

30% is less cheerful than my guess of 50%.

[mountainkiss]

That said, I think you're underestimating deaths. Only hospital deaths are reported (as opposed to e.g. care homes) and there will also be deaths before people go to hospital, or people who choose not to admit themselves or their loved ones, or undiagnosed deaths.

[danieldwilliam]

I saw an update from the ONS which (assuming I understood it properly) suggested that 80% of coronavirus deaths were taking place in hospitals.

Which would imply that my estimate was 25% too low.

Correctly for the two errors leaves the overall estimate about the same, perhaps 30 weeks rather than 27.

[cmcmck]

What's puzzling me is that some of those recorded deaths were recorded almost a month back which plays hell with the stats.

[danieldwilliam]

I *think* that the additions from prior days are approximately equal to the missing entries from today's list - more or less.

[andrewducker]

How do you feel about this in retrospect?

[danieldwilliam]

I think the guess that there would be 35,000 coronavirus deaths "within a few weeks" was reasonably close.

Where scenario diverged from reality was the R rate. If I read myself correctly I was projecting an on-going R rate of 0.9 to see when we mightexpect any meaningful herd immunity. Looks like the various social distancing measures reduced the R rate quite a lot below 0.9. So we've been able to reduce the total number of ill people and onward transmission a lot. More in Scotland than in England I think for "some reason".

[andrewducker]

Yes, it's definitely been less bad in Scotland.

[danieldwilliam]

And I think will continue to be less bad in Scotland over the next 12-18 months.

[andrewducker]

I'm hoping Aberdeen is a wake up call to organisations that think they can get away with flouting the rules.

[danieldwilliam]

I hope that the authorities get tore in to them and then their customers likewise.