I want to say a little bit more about @joel_c_miller's point below, and explain why, like several more knowledgeable people I follow (such as @nataliexdean), I am sceptical about the idea that we can let the virus spread amongst younger healthier people while ... 1/ https://twitter.com/joel_c_miller/status/1257561054780915712

protecting the vulnerable. The argument is based on very basic maths, so I do not rule out that I have missed some important consideration that invalidates my conclusion. I am always interested to hear about such considerations, and ready to change my mind. 2/

Consider a network with the following properties. It's largely homogeneous, but contains a few "vulnerable clusters" (such as care homes), where infection spreads rapidly. Let's also assume that these clusters are well isolated, but not *perfectly* isolated. 3/

For concreteness, let us imagine a care home with 50 care workers, administrators, cleaners, etc., who do not live at the home. Let's also suppose that with all the precautions in place, if one of these staff members is infected, there is only a 10% chance ... 4/

that they will set off an outbreak at the care home. Then if the prevalence in the outside population is, say 1%, then (simplifying a bit) the expected number of care workers infected is 0.5, so the probability of an outbreak is around 0.05, or 1 in 20. 5/

But if the prevalence is 10%, then that rises to more like 50-50. (It will be a bit less than 50-50 since the different sources of infection are not exclusive, but I'm talking order of magnitudes here.)

One can put in all sorts of different numbers of course, ... 6/

but the point is that when strenuous efforts are made to protect vulnerable clusters, whether or not those clusters become infected typically depends on a large collection of low-probability events. If the prevalence of infection outside increases a lot, then ... 7/

those probabilities can change from very low to merely low, and then the probability that at least one of them occurs can change from low to high.

But don't the precautions at least *help*? Sometimes they do, certainly, but one can conceive of situations where they ... 8/

achieve almost nothing. Suppose, for example, that a vulnerable cluster has 200 independent opportunities to become infected, and at each opportunity the chances of infection are 10%. Then the chances of avoiding infection are 0.9^200, which is about 0.0000000007. 9/

Suppose we manage to reduce the chances at each opportunity to 2%. Then the chances of avoiding infection leap up to about 0.0175. In other words, with all the precautions in place, the chances of the cluster being infected drop from roughly 100% to roughly 98%. 10/

My guess is that there are many such situations already. And it's a safe bet that with a significantly increased prevalence among the healthy population, there will be many more of them. 11/11