I agree that this is a relative weakness of the model. I think part of it is that the division into vulnerable/invulnerable is a simplification. If for instance you injected somebody with COVID then everybody would be "vulnerable". So in some environments conditions are ideal for spread which makes many relatively immune people become infected.
I'm sympathetic to the case that education is signaling, but I think that case is less strong for early education. For instance this paper from Argentina uses teacher strikes to value a year of education at 6% of lifetime earnings.
That estimate is not wildly different and seems pretty immune to signaling.
Yeah, I don't think that HVAC in schools is something which will make a difference to their safety in time. My point was more
I would imagine that we could install experimental HVAC systems in a few hundred schools for not much money and get decent data.
I did not compute the odds precisely before writing up that section.
The two cases cited have attack rates of 53/61 and 104/122.
For a 25% cross immunity rate that would correspond to ~2% and .4% probability respectively.
For a 33% cross immunity rate that would correspond to a .02% and a .0001% probability respectively.
The actual claim of what percentage of the population is immune is fairly nebulous but anything beyond 25% would be hard to justify.