From papers I have read, bc the virus was of an animal origin, ( hence our immune systems not recognising it & fighting it) they can't confidently say we WILL get herd immunity in the traditional way.
NY was one of the first hardest hit areas & have suffered dreadfully, but now they are coming out of it, ironically, as many parts of the US are climbing the peak.
Gov Cuomo has today impose quite strict restrictions on people visiting from certain high risk states. It won't be popular with many & possibly a PITA to enforce , but you can't blame him & the move seems popular amongst NY residents.
We can only watch through our fingers from over here.
My feeling is that as much as Boris has completely mishandled our crisis in many ways ( a discussion for another day) we Brits have, on the whole been sensible & it is THAT which has stopped it being worse than the horrendous shit show it already is & to date is nowhere near as bad as the US. But we shall see.