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I propose a less effective, but easier to implement, way to optimise who to test. It relies upon a simple result from network/graph theory that I will outline here. Assume, if you will, that typical social networks contain a small number of people who are highly connected (hubs) and a large number of people who are much less connected (spokes). The hubs could be e.g. your GP/physician, your teacher, or even just your popular friend. It would not be surprising if these people have a much high transmission rate for a virus than people who have a much smaller social circle - all other things being equal, and also crucially, they often connect mutliple sub-networks (GP is a good example here). We would of course like to ensure that we test (perhaps regularly) the people who are at the center of these networks - the hubs. How do we find out who these people are? It turns out that you can do this probabilistically. First, I pick someone at random from the population. I then instruct them to pick a contact/friend at random. The person they pick is statistically much more likely to be a 'hub' than a 'spoke', even though we have no explicit knowledge of the network and carried out this process randomly. A good way to visualise this is to imagine a toy network of say one person in the middle, connected to everyone else, and 10 other people, all connected to the person in the middle but nobody else. You can see that in 10/11 cases, a 'spoke' is selected who then goes on to select the 'hub' (what we want) whereas in only 1/11 cases the hub is initially chosen, who then chooses one of the other 10 contacts at random. A practical implementation of this could be to choose N people at random and send them a letter or text message instructing them to pick e.g. the (modulo) 5th person from their contacts list whose name begins with R. They would then contact this person and inform them that they should present themselves at a doctor and be tested should they develop any symptoms. There are obvious optimisations to be made here in terms of name distributions and other subtleties of course, and certainly providing a list of fallback randomiser instructions, if they can't find someone fitting that criteria. Bottom line is, even if many people don't comply, you can increase the probability that you end up prioritising testing of people who are very connected, and thus likely to spread disease, which can be invaluable when your testing capacity is constrained. |
I'm sorry but in modern America, you can count on the average person screaming bloody murder when confronted with a scheme like that. No one likes to be part of someone else's mathematical model but a random electrician or hairdresser is toss that away or maybe put out an angry tweet that will get more leverage than this idea.