Thread by @KennyMathieson

Yesterday, I learned a new Covid-related skill, how to calculate the doubling time for an exponential growth curve (in this case related to #Omicron cases growth in the UK).

Yesterday, that value worked out at 2 days.

Adding in today's data, now makes it a value of 1.4 days! 😱

My instruction manual for learning how to do this calculation, was this amazingly helpful video by @pk_kent 🙏🏻

How do you do the calculation Kenny?

Thanks for asking.

Here's the underlying data.

So, you begin by looking at the values at the beginning of the time period and also at the end of the time period of interest.

On 27/11/21 there were only 2 confirmed Omicron cases in the UK.

Today this total had increased to 3137.

We need to work out the Growth Factor.

There's an equation.

Final value (CF) = Initial value(CI) * e(^k*(tf - ti))

where:
tf = final time point (Day 16 - 12/12/21)
ti = initial time point (Day 1 - 27/11/21)
k = Growth Factor
e = natural logarithm (approximately equal to 2.718)

Final Value = 3137
Initial Value = 2

We need to rearrange the equation to work out k (the only unknown variable).

Ah, algebra...you old dog! I've missed you. 🤓

Dividing both sides by the initial value, we get:

CF/CI = e(^k * (16 - 1))

To get rid of e, we take the logarithm (ln) of both sides, giving us:

ln (CF/CI) = k * (16 - 1)

or

ln (CF/CI) = k * 15

The left side of the equation is:

ln (3137/2) = ln (1568.5) = 7.358

Therefore k (Growth Factor) = 7.358/15 = 0.4905 (unit is 1/days)

Paying attention? There may be a quiz, later. 🤓

Doubling Time = ln (2) / Growth Factor

ln (2) = 0.69315

Therefore the current doubling time for confirmed Omicron cases in the UK = 0.69315/0.4905

which gives a value of 1.413 days.

That's pretty alarming. 😬

But Kenny, why does any of this matter, I hear you ask...or possibly, it's just those damned voices in my head...AGAIN! 😉

Well, it matters a LOT.

We don't yet know how mild or serious Omicron is relative to Delta.

It's too soon, because serious cases take time to develop.

Let's try a thought experiment.

Assume Omicron only generates 1/10th as many serious (i.e. hospitalisations/deaths) cases as Delta.

We're saved, right?

Actually no.

The good news in this situation is that our individual chances of surviving Omicron without serious illness are improved significantly. Woo-hoo!

The bad news is there will be MANY more people infected and some of them will inevitably lose the Omicron Covid lottery.😢

For ease of calculation, let's round up the doubling time to 1.5 days.

Volume of cases

1.5 days = 2x
3 days = 4x
4.5 days = 8x
6 days = 12x

In less than a week, the benefit of a Covid strain that is only 1/10th as capable of causing serious illness, is more than negated. 😱

As already stated, we don't yet know how Omicron compares to Delta in terms of mildness, we'll learn that in the next couple of weeks.

However, we'd have to be VERY lucky for it to only be 1/10th as serious as Delta.

Also, any apparent greater "mildness" may turn out to be a mathematical illusion, as explained in this excellent thread by @nataliexdean

https://twitter.com/nataliexdean/status/1468988174693289994?s=20

The latest @UKHSA data shows that even someone who is fully boosted, is still about 5/6 times more likely to have a breakthrough infection from Omicron, relative to Delta.

And of course, only a minority of the population will be fully boosted as the peak Omicron wave hits us.

We are currently in the (relative) calm before the storm, but we do know enough to be sure that a major storm is about to hit us.

On the most optimistic projection, hospitals are going to be under massive pressure.

Volume (in terms of infections) matters...a LOT.

Common sense tells us a more deadly infection is a bigger threat than a (broadly equivalent) more transmissible version.

Alas, in any contest between the two, the cold equations of simple mathematics, will always trump common sense.

Buckle up, it's gonna be a bumpy ride. 😬

Correction: After 6 days (at a doubling time of 1.5 days) the multiplication factor is (of course) 16x rather than 12x.

You proofread a thread multiple times before posting and still! 🤦🏻‍♂️