Given your expertise in solving DEs for money, and knowledge of chaos theory, why did you earlier mention "Yes, you can get chaotic behavior solving certain PDEs and stuff" and seemingly exclude the ordinary differential equations which started chaos theory?

We know that transmissions rates are not fixed. While R0 models the average, sometimes 1 person infects 100 other people, and sometimes no one is infected.

These 100+ events are rare, but not extraordinarily rare.

If it happens early in a simulation, then your simulated model will result in a higher growth than one where that event occurs later.

So sometimes you'll have a large outburst early, and sometimes it will be delayed a week or two.

> My superficial understanding of Ferguson's model is that it's an extended SIR model, with different classes of patient with different behaviors, geographical grouping, etc. From my intuition, it doesn't seem like that kind of DE would be too chaotic

The paper "Impact of non-pharmaceutical interventions (NPIs) to reduce COVID- 19 mortality and healthcare demand" appears to be the one which has influenced many. It cites https://www.nature.com/articles/nature04795 as the model used, which cites https://www.nature.com/articles/nature04017 which gives a summary:

"We constructed a spatially explicit simulation of the 85 million people residing in Thailand and in a 100-km wide zone of contiguous neighbouring countries. The model explicitly incorporates households, schools and workplaces, as these are known to be the primary contexts of influenza transmission .. Random contacts in the community associated with day-to-day movement and travel were also modelled."

I expect that sort of agent-based modeling, by nature, to be chaotic, along the lines I outlined above.

You write: "So when such behavior is present, modelers are usually aware that it is, since it has consequences well beyond floating point reductions. I haven't seen that discussed in any of Ferguson's papers"

How many papers of his have you read? The paper I quoted from, https://www.nature.com/articles/nature04017 , includes:

"Multiple assumptions are inevitably made when undertaking preparedness modelling for a future emergent infection. Sensitivity analyses are therefore critical for assessing the robustness of policy conclusions. Here, critical assumptions not already discussed include (1) the ratio of within-place to community transmission, (2) the expected generation time, Tg, of a new pandemic strain (largely determined by the duration of viral shedding and therefore infectiousness), (3) the level of heterogeneity in individual infectiousness (for example, ‘superspreaders’20), (4) antiviral efficacy/take-up, and (5) the sensitivity and specificity of case detection during the control programme."

You rhetorically asked "Would you at least agree that in a perfect world, with unlimited resources, that's something you'd fix?"

That's a bogus argument. If I had that sort of unlimited resources there are many more things I would rather use it on than making this simulation be the way you want it to be.

For one, the noise and induced chaos are certainly far less than which result from the uncertain input values to the program.