If you think that it can be stopped then you trace every case, you find everyone who they touched, you confine every possibly contagious person, you wash everything they've come into contact with, and if you're very very lucky you completely eradicate the disease.
The other approach is the one you take when you no longer believe that to be possible. When you come to believe that it has spread too widely, that it is loose in too many countries, that there are too many holes in the net, and containment has failed.
At that point you know - everyone is going to catch this disease. The only question is when.
Everyone catching it at once will be much much worse than if you can spread the cases over several months. But even worse would be to make it look like you'd stopped it, but only a small proportion of the population had been through the disease and developed immunity.
Because then when it does, inevitably, spread through the population again (once people start traveling again), it does so at a time you have no control over, and quite possibly in a massive spike. So your want to slow it and spread it over the summer, not stop it entirely.
The question is no longer "How do we keep everyone alive?" - that ship has sailed. The question is "How do we keep as many people alive as possible?"
And that is why people in the UK are being told to self isolate if they get a fever - to slow it down. Why they aren't being tested - there is no cure, so testing is irrelevant except for statistical testing to give an idea of the disease spread. Why care homes are to be "cocooned" until the disease has gone through the healthy parts of society and left us with hopefully enough herd immunity that the virus can't spread any more.
There is no doubt that we are in a worse situation than if we hadn't hollowed out the NHS through 10 years of austerity, bringing it to the point where there is no spare capacity to deal with a situation like this. And we should have started sooner - containment might have worked if we'd started a few weeks earlier than we did. But unless we shut society down for the next few months - not just here, but worldwide, so that there's no new Patient Zero anywhere to restart things - then we need to deal with containment having failed, and we're now having to work out how to delay and control the spread.
China built hospitals, they cleansed city blocks, they locked up infected people away from their families until they were no longer infectious. They did everything they could to take the first route out of the epidemic.
I wonder how angry they'll be when we spread the disease back to them.
(I'd share some useful links, but they're all over on Pinboard, where you can filter by "disease". This one is probably my current favourite though.)
Original post on Dreamwidth - there are comments there.