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! 😱 Image
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. Image
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

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! 🤦🏻‍♂️

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More from @KennyMathieson

14 Dec
@SashaSagan It's just as well that there is no charge (I hope! 🙏🏻) for quoting someone, or I would have incurred significant debt by now, given how often I have quoted your father.

e.g.

I'm sure you already know his profound impact on so many of us.

My first "encounter" (via TV) with him was when he did the Royal Institution Christmas Lectures in 1977. I was a geeky schoolkid interested in science.

Your dad was inspirational.
I didn't become an astronomer, but I did subsequently navigate my way through a couple of chemistry degrees.

His beautful book dedication to your mum in "Cosmos", is my favourite such dedication of all-time. 😊
Read 5 tweets
14 Dec
Humanity is a bewildering species. 🤔

Since Covid first manifested its ghastly presence on these shores, I think it fair to say that most of us have gained an understanding of the R number.

In simple terms:

R < 1.0 = Good! ✔️ 👍🏻
R > 1.0 = Bad! ✖️ 👎🏻
Obviously, it has ebbed and flowed in response to: lockdowns beginning; lockdowns ending; vaccine rollout; and social bubbles etc.

However, by this point, few can be in any doubt that R being significantly above 1.0, say around 1.5, is VERY bad indeed. 🤮
#ExponentialGrowth
We have been incredibly lucky to have several highly effective vaccines appear, so quickly.

Just imagine what 2021 would have looked like in the face of the #Delta strain, without ANY vaccines? 😱

But our “leaders”, basically opted for a “vaccine only” strategy. 🙄
Read 24 tweets
14 Dec
Ye Gods!

Who is briefing @NicolaSturgeon?

Once again, she quotes an #Omicron doubling time of 2-3 days. 🤬

It’s under 2 days, and certainly nowhere close to 3 days.

By all means, let’s see the working behind a calculation of 3 days?

I’ll wait and then point out the error. 🙄
You can get some variation in the calculation of doubling time.

It depends on which exponential curve you’re measuring.

For example, growth in Total #Omicron cases...OR growth in Daily Omicron cases.

Clearly they are related, but will result in (not very) different values.
The sinplest method of calculation (which I use) works it out from a formula using the starting value and the current value.

You can make it more complicated by working out a best fit exponential curve to the data.

Again, you’ll get a (not very) different number via that route.
Read 4 tweets
13 Dec
So, arguably there are two ways you could calculate the doubling time for #Omicron

1. Doubling Time of Total UK cases

and

2 Doubling Time of Daily UK case totals

I’ve just calculated both, using the latest data.

The values are 1.43 and 1.66 days respectively. 😬
Last week, there was much talk about a doubling time of 2-3 days.

I knew nothing about how to calculate this value until Saturday evening, but it’s a simple formula.

The 3 day estimate is (and was) nonsense, unsupported by the data.

It looks to have arisen from a basic error.
The calculation itself is very simple (assuming you know basic algebra) and is outlined in this thread from yesterday.

Read 7 tweets
13 Dec
Exponential growth, BUT you can still go to panto? 🤦🏻‍♂️

As a nation, we’re approaching the idyllic halcyon period between the moment the brakes get slammed on for an emergency stop, and the moment we fly through the windscreen (because, as you know, seatbelts are only for wimps).
I just heard @SCrabbPembs on #DailyPolitics saying Plan B measures were already in effect in Wales and hadn’t curbed the spread of Delta (which is true).

Logic might then suggest, that FAR greater restrictions might be needed to curb the spread of a MORE transmissible virus? 🤔
Apparently not. It seems that (for now) is just crazy talk among our political class. 🤷🏻‍♂️

Watching the news coverage on the Plan B shenanigans tomorrow is just surreal. 🤦🏻‍♂️

“Will there need to be more restrictions before Christmas?”

Abso-fucking-lutely...and you may quote me. 🤬
Read 8 tweets
13 Dec
Remember those glorious days when @BBCNews could state (with confidence) how many children a certain politician had? 🤔

“If anyone says I was speeding, I want to see the evidence.” #SafetyFirst

As convincing statements of total innocence go... 🤦🏻‍♂️

news.bbc.co.uk/1/hi/uk_politi…
“For a man who wants to be Prime Minister, Boris Johnson is in danger of developing a reputation for breaking the law.”

Rules (and safety) are for...lesser mortals, apparently.

dailymail.co.uk/news/article-3…
‘But Boris Johnson may have a get out from claims he broke the law - because there is an exemption for “a vehicle being used for police, fire and rescue services”.’

An utterly selfish, narcissistic, arsehole always looking to play a “get out” card. 🤬

mirror.co.uk/news/politics/…
Read 4 tweets

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