Coronavirus

[Simon B]

No - you don't need logs - just type 100^(1/12) = into the search bar in a browser - typically connected to Google search, and a result 1.46779926762 - that's a bit OTT - say 1.47 - appears. Works for any ratio - so Growth-Ratio ^(1/no-of-weeks)= will do.

Whether the computation is actually done using logs or not is unknown by this method - it might be - it might not be!

Good point! Force of habit - see an exponent, solve with logarithm. Probably CORDIC actually for a calculator to do logs or exponentiation which are sort of the same thing anyway.

So, yes, what Dave said.

[french frank]

To get from 41 to 4000 is 100-fold growth over 12 weeks and requires growth to 147% of the previous week's total, per week, every week. This won't be what happened, but it gives some insight.

1.47 * 1.47 * 1.47 (repeat 12 times) = 1.47^12 = 101.81, i.e. roughly 100-fold growth.

To work out the 1.47, you need logarithms so it's probably best not to go there .

On that basis, the figure is growing by about 50% a week.

I just added together all the percentage increases (or decreases) as reported daily, and divided the total by 75 (the number of days). Came to 50.7%. Was that a coincidence?

[Frances_iom]

I just added together all the percentage increases (or decreases) as reported daily, and divided the total by 75 (the number of days). Came to 50.7%. Was that a coincidence?

for ease of future reckoning use the engineering approximation that if x = doubling period in what ever units you are using then the rate of increase in % is 70 divided by x; likewise given y as the % increase per unit of time then the doubling period is 70 divided by y;

[french frank]

for ease of future reckoning use the engineering approximation that if x = doubling period in what ever units you are using then the rate of increase in % is 70 divided by x; likewise given y as the % increase per unit of time then the doubling period is 70 divided by y;

Not sure what conveys most to the Average Jo (non gender-specific non-mathematician): the average % increase per week over a period of x weeks has been 50%. Or the % increase over x weeks has been 10,000%.

[oddoneout]

Not sure what conveys most to the Average Jo (non gender-specific non-mathematician): the average % increase per week over a period of x weeks has been 50%. Or the % increase over x weeks has been 10,000%.

That depends on who is presenting the figures and for what purpose? The second option makes a better screaming headline, the first might be what the administration would prefer to admit to as being less likely to scare the horses.

[teamsaint]

Well the official figures are showing a sharp week on week decline, presumably(?) driven by lids being off school and not reporting test results.

Which hopefully is a good sign.

Re ZOE, the vital thing surely is the pattern that develops post the recalibration ?

[french frank]

Well the official figures are showing a sharp week on week decline

This must be patchy across the country. The Bristol rate of increase has been speeding up steadily in the last 7 days (July 11- July 18) from a recent lowest of 16.9% to 58.8% (latest) I suppose this does mirror the gradual decline in the previous week?

[Bryn]

Well the official figures are showing a sharp week on week decline, presumably(?) driven by lids being off school and not reporting test results.

Which hopefully is a good sign.

Re ZOE, the vital thing surely is the pattern that develops post the recalibration ?

Decline? https://coronavirus.data.gov.uk/

[teamsaint]

Decline? https://coronavirus.data.gov.uk/

Percentage change in recent 7-day case rates by specimen date, which will feed into the rate per 100k in the coming weeks.

[teamsaint]

Meanwhile the government seems hell bent on its insane ( domestic) covid passports scheme. One can only hope that Labour will find better ways to oppose than by saying that it is expensive and impractical, though of course it will be both of those things.

[muzzer]

This must be patchy across the country. The Bristol rate of increase has been speeding up steadily in the last 7 days (July 11- July 18) from a recent lowest of 16.9% to 58.8% (latest) I suppose this does mirror the gradual decline in the previous week?

I was in Bristol last weekend in glorious sunshine which will only have contributed to the rise in cases, even while doing my mental health the world of good. Their jab rates there are much higher than at home here in a comparatively vax hesitant part of London where our cases are up but the rate seems to be slowing. The second jab rate is still woeful imho and it’s a public scandal that the councils aren’t rounding people up to get them jabbed. But perhaps this sort of existential disaster is nature’s way of checking our hubris.

As others have observed, it is impossible to draw any meaningful conclusions from the data and this in itself is bad for one’s wellbeing. I was for example saddened to see Tim Spector this week basically saying, if I’ve got him right, that he’d been being too optimistic about the slowing rate of new cases.

The nightmare scenario is high number of cases plus relatively high vax rate equals perfect environment for more variants. Possibly vax resistant. And that will be seriously socially divisive imho. I have parted ways with any friends or acquaintances who won’t get jabbed. History is clear. We have minimal agency in the face of such a macro scale event. Science is our friend at this time.

With apologies for the ramble. Now then, a cross country ramble however, to a pub for lunch. With the promise of live music and company. That would be a treat.

[Dave2002]

Not sure what conveys most to the Average Jo (non gender-specific non-mathematician): the average % increase per week over a period of x weeks has been 50%. Or the % increase over x weeks has been 10,000%.

Of course these calculations are based on an assumption that the [average] rate of change is constant - for exponential growth. Not an unreasonable assumption as a first approximation, but there would be no peaks if the approximation were extended indefinitely. So although initially the rate of change appears to be exponential as the disease is unchecked and continues to spread as time moves on, other factors come into play which turn the growth around. So the curves we see and are shown to try to explain the pandemic are not exponential.

In a true exponential, the rate of change, the rate of change of the rate of change, and the rate of change of the rate of change of the rate of change (and so on) are all constant.

[Dave2002]

Spotted from another thread - where it was out of place ....

https://www.theguardian.com/commentisfree/2021/jul/20/if-johnson-didnt-believe-the-nhs-overwhelmed-stuff-why-was-he-clapping

Ouch!!!!!

[kernelbogey]

Spotted from another thread - where it was out of place ....

https://www.theguardian.com/commentisfree/2021/jul/20/if-johnson-didnt-believe-the-nhs-overwhelmed-stuff-why-was-he-clapping

Ouch!!!!!

Rachel Clake has written a number of brilliant articles in the Guardian about the NHS dealing with Covid, and excoriating politicians.

[Serial_Apologist]

In a true exponential, the rate of change, the rate of change of the rate of change, and the rate of change of the rate of change of the rate of change (and so on) are all constant.

That must explain why my rates keep going up.