Dr Duncan Robertson Profile picture
Apr 12, 2021 14 tweets 5 min read Read on X
Herd Immunity.

I've built a model to show the concept of herd immunity.

It shows why we need to not leave hard-to-reach parts of the population unvaccinated.

A thread.
Herd immunity, also called population immunity, is the protection for the population that comes from when a proportion have been vaccinated.

With more vaccinations, we move towards this herd immunity threshold.

(We're not there yet, even though some say we are.)
Here's my model. Imagine a population in a country.

People are either susceptible (they may not be vaccinated or have had the virus). We colour these green.

People may have had the vaccine. These are blue.

And there's one (near the bottom left in purple) that is infectious
Now, in my model, they will infect anyone who is susceptible (green) within that little circle surrounding them. And those will infect people surrounding *them*
After a few generations, more and more are infected.
Eventually, almost all (although not all - some are fortunate) are infected.

That's bad. And it's because we haven't reached the herd immunity threshold.
So - what happens when we reach the herd immunity threshold (or get close to it)?

We have many more vaccinated (they're blue).

Let's see what happens when the infectious person (this time in the middle) infects others.
Well, in this case, there's a local infection, but the infection can't be sustained (that's good). Herd immunity.
But.

What happens when those vaccines are not spread out equally across the country?

Let's vaccinate *the same number of people* just in the bottom half of our population.

There we are - lots of vaccinated people in blue. That infection (right middle) doesn't stand a chance.
Now let's see what happens when that infectious person is in the top half among the unvaccinated population (remember, we have the same number of vaccinated people in the population as a whole).
Well, that infection spreads...
... and spreads ...
... and spreads ...
until huge numbers of people are infected *even though we have overall reached the herd immunity threshold*

And that is why we need to vaccinate evenly, not leaving pockets where infection can spread.
If anyone would like to work with me on this, do let me know. I've built the agent-based model and would be happy to work with others turning it into a paper.
@chrischirp @AdamJKucharski @GrahamMedley
If anyone is interested in the seemingly different ways we can model spatial transmission, here's a paper I wrote pre-Covid showing the similarities between the different approaches of:
- population
- network
- agent-based
- cellular
models

Download here: duncanrobertson.com/research/Risk_…

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More from @Dr_D_Robertson

Jul 18
The UK Covid Public Inquiry has published its first Report, on Resilience and Preparedness. It is the most urgent report, as we are still ill-prepared for the next pandemic.

🧵
This is the first of many reports, each reviewing a specific area, including healthcare systems; test, trace, and isolate; and the economic response to the pandemic.

The Module 1 Report sets out nine significant flaws from the Covid-19 pandemic: Image
The Report suggests 10 recommendations: Image
Read 11 tweets
Jun 9, 2023
Data thread from today's @IndependentSage briefing including a discussion on sick pay, the topic of today's discussion. 🧵 Image
Cases and tests. Relatively low.
Caveat that the ONS Covid infection survey has been paused ImageImageImageImage
Hospital admissions. Trend not upward.
Caveat that testing has changed in hospital. ImageImageImageImage
Read 14 tweets
Apr 21, 2023
Covid data presentation for the @IndependentSage briefing on 21 April 2023 🧵 Image
Testing has changed from 1 April 2023, so it is difficult to compare before and after this date.
gov.uk/government/new…
The ONS survey has been 'paused', so we can look at the (less recent, less representative) data on PCR positivity

coronavirus.data.gov.uk/details/testin… ImageImage
Read 11 tweets
Apr 20, 2023
Alright. Another maths thread. And why it's non-trivial to ask exam questions.
🧵
OK. So the 'exam question' is:

"Inflation is currently 10%. If inflation halves, how much will a £1 pint of milk cost".

Sounds easy. It's not. It's ambiguous. It's not a good question. Unless it's designed to be a bad question. In which case it's a good question.
1. It talks about 'inflation'. But *what* inflation? At the moment, we have overall inflation at roughly 10% but inflation of food at roughly 20%. So is the overall inflation rate the same as the inflation rate for milk? It's not clear. Bad question.
Read 9 tweets
Mar 24, 2023
Data thread from today's @IndependentSage briefing. 🧵
First, the @ONS Covid Infection Survey is being paused, and @CovidGenomicsUK is being retired. This will have implications for data reliability and availability going forward.
Read 17 tweets
Mar 20, 2023
OK, I'm going to write a response to this maths problem, published in @DailyMailUK, that has caused a lot of comment, some thinking the answer is 1 and some thinking the answer is 9.

A thread. 🧵

dailymail.co.uk/news/article-1…
So, what answer is correct? Is it 1 or is it 9?

Many of us would go straight to the answer 1. That's because we know (or our children know, and have taught us), that there is a 'rule' for how you deal with the order of doing the calculation - do you do + first or ÷, for example?
Enter BIDMAS (or BODMAS).

"It stands for Brackets, Indices [or Order], Division, Multiplication, Addition and Subtraction."

That's the conventional order. Forget about indices [or order] for now - that's not important for this one.
bbc.co.uk/bitesize/topic…
Read 12 tweets

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