I did some calculations of basic herd immunity thresholds based on fractal risk (without an infection model) a few months back, and the difference between splitting the population into high exposure vs low exposure captures more than half the change from the limit of infinite splits. The threshold stopped changing almost entirely after three splits, which was only 6 subpopulatuons.
With many other variables as exist here I’m not confident that effect would persist but my default guess is that adding fractal effects to the model will less than double the change from the homogenous case, and possibly change very little at all as the herd immunity threshold and therefore level of spread reduction will be changed even less (especially with control systems.)
That may end up being pretty significant in terms of actual number of deaths and infections at the end, but I would be very surprised if it changes whether or not there are peaks.
One could certainly split into low/high with a larger-than-actually-estimated division and call that close enough, or do something continuous in the middle with the assumption that the super-risky top is already spoken for, or something.
To me there’s still a big mystery of why it seems like herd immunity hasn’t done more work than it did.
A toy model that makes some sense to me is that the two population distinction is (close to) literally true; that there’s a subset of like 20% of people who have reduced their risk by 95%+, and models should really be considering only the other 80% of the population, which is much more homogeneous.
Then because you started with effectively 20% population immunity, that means R0 is actually substantially higher, and each additional piece of immunity is less significant because of that.
I haven’t actually computed anything with this model so I don’t know whether it is actually explanatory.
I did some calculations of basic herd immunity thresholds based on fractal risk (without an infection model) a few months back, and the difference between splitting the population into high exposure vs low exposure captures more than half the change from the limit of infinite splits. The threshold stopped changing almost entirely after three splits, which was only 6 subpopulatuons.
With many other variables as exist here I’m not confident that effect would persist but my default guess is that adding fractal effects to the model will less than double the change from the homogenous case, and possibly change very little at all as the herd immunity threshold and therefore level of spread reduction will be changed even less (especially with control systems.)
That may end up being pretty significant in terms of actual number of deaths and infections at the end, but I would be very surprised if it changes whether or not there are peaks.
One could certainly split into low/high with a larger-than-actually-estimated division and call that close enough, or do something continuous in the middle with the assumption that the super-risky top is already spoken for, or something.
To me there’s still a big mystery of why it seems like herd immunity hasn’t done more work than it did.
A toy model that makes some sense to me is that the two population distinction is (close to) literally true; that there’s a subset of like 20% of people who have reduced their risk by 95%+, and models should really be considering only the other 80% of the population, which is much more homogeneous.
Then because you started with effectively 20% population immunity, that means R0 is actually substantially higher, and each additional piece of immunity is less significant because of that.
I haven’t actually computed anything with this model so I don’t know whether it is actually explanatory.