Each infected person will come into contact with some other people. Testing allows three things—
- first, we can tell this person to stay at home and so stop them from infecting more people;
- second, we can tell the people they have seen to stay at home with good contact-tracing, so that even if they get it they don’t spread it further; and
- third, with enough tests and contact tracing, those who were exposed but not infected don’t have to stay at home.
We are winning so long as R<1, even if there is some chance the infection spreads; we do not need R=0.
The other way of reducing R requiring much less testing and contact tracing is a lockdown. This has obvious downsides. The point of a programme of testing and conyact tracing is that we can turn the cost of avoiding disaster from a lockdown to sticking some things up people’s noses.
edit: typo in first para