Thread by @NTallapragada

Have you seen something like this on social media recently?

"Delta's so bad! A friend of a friend got COVID even though he got the vaccine."

It turns out this tells us more about social networks than it does about vaccines.

How? It's a small world after all! #scicomm 🧵(1/n)

Lots to unpack here, so let’s start from the beginning.

This is a social network. It helps us keep track of how people are connected.

In this picture, circles represent people, and the lines between them indicate who knows who. (2/n)

This social network has 5 people: 2 groups of 3 friends, with 1 friend in common.

Real social networks look a lot like this (but are much bigger, obviously). There's just enough overlap that lots of people are "friends of friends," just 2 hops away! (3/n)

So, what does this have to do with our perception of who's getting COVID, and how well vaccines work?

Basically, because we tend to know a lot of the same people – and we make comparisons between people we know – we can come to conclusions that conflict with the data. (4/n)

Let's say you're part of this social network, with 5 fully vaccinated people (circles) in Boston and 5 unvaccinated people (squares) back home in some other part of the country.

In this picture, you're the circle with the arrow pointing at it. (5/n)

Ok, now the delta variant shows up and makes a bunch of people sick. ☹️

Let's indicate these positive COVID cases in red.

As is the case in real life, more unvaxxed people than fully vaxxed people got COVID! (6/n)

In this example, the vaccine is 75% effective.

We say this b/c there's a 25% "relative risk" (RR) that someone vaxxed gets COVID:

1 / 5 fully vaxxed got COVID
----------------------------- = 1/4 = 25% RR
4 / 5 unvaxxed got COVID

Efficacy = 100% – RR = 100% – 25% = 75% (7/n)

But how effective does the vaccine look to *you*? (again, you're the circle with the arrow)

Just 33% effective, if you count yourself, and 0% if you don't!

And *every* fully vaxxed person in this network has a friend of a friend who is fully vaxxed but still got COVID... (8/n)

Let's do the math:

You know 3 fully vaxxed people including yourself, and 1 has COVID. You know 2 unvaxxed people, and 1 has COVID.

1 / 3 fully vaxxed got COVID
------------------------------ = 2/3 = 67% RR
1 / 2 unvaxxed got COVID

Efficacy = 100% – RR = 100% – 67% = 33% (9/n)

If you don't count yourself, it looks like the vaccine doesn't work at all, because half your friends got COVID – vaxxed or not.

1 / 2 fully vaxxed got COVID
------------------------------ = 1 = 100% RR
1 / 2 unvaxxed got COVID

Efficacy = 100% – RR = 100% – 100% = 0% (10/n)

But, if you zoom out and look at the entire network, the vaccine is 75% effective!

Our personal experience leads us to underestimate the power of the vaccine. (11/n)

Moral of the story: vaccines still work really well!

For every friend of a friend who got the shot and still got COVID, there are many more who didn't.

Be very careful when drawing conclusions from anecdotes! (12/n)

https://twitter.com/NateSilver538/status/1421894085137285127

And even if you do get COVID after getting vaccinated, your symptoms will be milder, and your outcomes *way* better, than if you didn't get the shot. (13/n)

https://twitter.com/NTallapragada/status/1417317209374855169

Back to social networks: all of this is closely related to "six degrees of separation," the idea that any two people on Earth are at most six social connections apart.

You and Kevin Bacon. You and a Fortune 500 CEO on LinkedIn. You and Queen Elizabeth II. (14/n)

All it takes is a few people with friends in unexpected places to connect the whole world!

So, it’s not inconceivable that you and your friends in LA are all thinking of the same 22 people with breakthrough COVID. (15/n)

https://twitter.com/bymeg/status/1420239197097500673

Want to learn more about the theory behind social networks?

Check out this article by @davidaustinm about work from @duncanjwatts, @stevenstrogatz, & many others!

(As an aging millennial, I love how there's a whole example involving LiveJournal.) (16/n)
ams.org/publicoutreach…

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