Re: No use
"A person walking through Oxford Street station to change from one tube line to another during the rush hour will typically be inside the infectious range (under 1 metre) of lots of people (possibly over 100). If the person is a non-symptomatic carrier ..."
It's a probabilistic thing which is why tracking is supposed to check for a sustained presence rather than just walking past. However, to reverse your situation, consider an uninfected person walking through the station. They will encounter a lot of people and if several percentage of them are infective then the probability of catching a sufficient inoculum from the totality, if not from a single one, is going to be greater. A tracing app would need to take that into account.
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What worries me about such an approach is this:
AIUI the way this would work is that it starts by an individual being tested, presumably when they start displaying symptoms. The system then works back through their previous contacts and warns them. However, because it is probabilistic some of these warnings will be false positives. If the system then works forwards to secondary and tertiary contacts all the initial false positives will be false and some of the secondaries from the initial true positives will also be false. It will cascade false positives through the population. The only way to counter this would be for all those warned to be tested promptly to stop the propagation and maybe revoke false positives already propagated. The converse also applies - there will be carriers insufficiently ill ever to get checked and encounters with them will be false negatives.
The whole system would depend on a very efficient testing system, one capable of doing far more tests than the present system and doing them far more quickly than the PCR method. The tracing system itself would get a reputation for being untrustworthy in terms of its results as well as being regarded by the likes of ourselves as untrustworthy in terms of handling PPI. The real benefit would be the testing system needed to support it - so why not concentrate resources on the testing system and forget the tracking?