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Welcome to my blog, which was once a mailing list of the same name and is still generated by mail. Please reply via the "comment" links.

Always interested in offers/projects/new ideas. Eclectic experience in fields like: numerical computing; Python web; Java enterprise; functional languages; GPGPU; SQL databases; etc. Based in Santiago, Chile; telecommute worldwide. CV; email.

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[Covid] Extended SIR Models

From: andrew cooke <andrew@...>

Date: Thu, 1 Jun 2023 22:09:34 -0400

I just went to see a talk on mathematical modelling of pandemics.  It
was largely a rehash of the SIR model along with simulations (although
I got lost near the end, so may have missed what was new).

Anyway, I got to thinking, and really it seems like the SIR approach
really misses the heart of the poblem.  I mean, we know that if
everyone isolates then infection rates will drop.  It's fucking
obvious.  The reason why it's controversial to actually put that into
practice is because there's a large collective cost.

When you see the word "collective" you start to look at the SIR model
and think how "free market" it is.  Lots of independent little people
all doing their own thing.

So I started wondering how you could extend it to include social cost.

The simplest solution I can see is to have a global state that
represents "common good" that is incremented on every interaction,
but that decays over time.

In addition, it seems that you need to add some kind of consequence
for this good becoming lower.  The simplest I could think of was that
you randomly kill individuals (so this would need to be SIR + births
and deaths I guess) at a rate connected to how low that gets.

I imagine that if you ran this then for most reasonable death
probability functions you get little happeninn until some threshold,
and then collapse.

So maybe it wouldn't be very interesting.

One extension might be to have two groups (in the same overall
population) with different functions / probabilities (eg rich and
poor).  Maybe that would show something more interesting.

Has anything like this been done?

Andrew

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