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1/n Back in March @nntaleb had a tweet about SIR models that got me interested studying models of virus spread a bit more. https://twitter.com/nntaleb/status/1239171413342289921
2/n As I often do, I started by trying to explain a bit about the models to my kids: https://mikesmathpage.wordpress.com/2020/03/18/sharing-nassim-talebs-ideas-about-virus-models-with-kids/
3/n Nassim followed up with a 3 min video about the models, too, which is definitely worth watching. That video and one whose work he references are in this follow up project I did with my kids: https://mikesmathpage.wordpress.com/2020/05/13/sharing-ideas-from-nassim-talebs-point-estimate-for-pandemics-video-with-kids/
4/n Continuing down the path of learning more about the virus models, I stumbled on this amazing - and I mean amazing - post on agent based virus models from Christopher Wolfram:
https://community.wolfram.com/groups/-/m/t/1907703
https://community.wolfram.com/groups/-/m/t/1907703
5/n As Wolfram shows in his post, (and I'm sure is well known) there's sort of a phase transition when you model how a virus spreads across a network. With just a seemingly small change in interaction between nodes, the virus goes from not spreading to spreading everywhere
6/n Wolfram illustrates the point with this picture - but, yo, definitely check out his post:
7/n I thought it would be interesting to study these agent based models a bit more and wanted to look at the distribution of outcomes for network configurations near where the phase transition happens.
8/n Following Wofram's code, I started with this pretty graph with 1000 nodes
9/n Then I used Wolfram's model to run ten 5,000 run simulations starting with 10 randomly selected infected nodes on the graph and assuming the average interaction for each node went from 0.21 nodes per step up to 0.3 in the 10 runs.
10/n With 0.21 interactions per step on average the virus doesn't spread that much - infecting from 1% of the network up to around 20% (the percentage spread across the network is the x-axis)
11/n At 0.3 interactions per step on average the virus spreads almost completely through the network - in fact hardly ever does less than 60% of the network get infected.
12/n At 0.25 interactions per step on average the distribution is surprisingly wide - basically from 1% to 60% can get infeced
13/n Here's a gif showing how the distribution of infections changes as the interactions move from 0.21 per step on average to 0.3 - sorry it isn't labelled. But the steps are 0.21, 0.22, and up to 0.3.
14/n Part of my interest in these models stems from trying to understand with the corona virus infection looks so different in different places in the US. What I learned from this little exercise is that the spread of a virus on a network can look totally different +
15/n even when you are running random simulations on the same network leaving everything but the initial infected nodes fixed. In some cases the width of the distribution was very surprising to me (though I'm sure this is all well-known to people who study this stuff, btw).
16/n I don't know how well these models work for the spread of a real virus, but at least some of the papers I've seen on the corona virus are using agent based models.
For me this little back of the envelope study reinforces a few of the things that Taleb said back in March -
For me this little back of the envelope study reinforces a few of the things that Taleb said back in March -
17/17 The variation in these models is so large depending on the inputs that I can't see how you could possibly use them for prediction. For risk management - sure - you can definitely see how bad things can get, but the overall outputs are all over the place! /end
