I can only speak for Israel, that the numbers went up as they relaxed regulations. We saw an immediate impact.
For all intents and purposes, NY is pretty much open, certainly in the Jewish communities, with hardly mask wearing or social distancing. Yet we haven't seen a major surge in cases.
Huge difference between Israel and NY: NY had people dying by the thousands, while Israel had hardly any infection the first time around. So once things “open,” Israel has plenty of vulnerable cannon fodder, while NY has already been “pruned,” so to speak.
Or, as I said to someone who was bragging how amazing NY is now, that everything is open and nobody is getting affected: “Saying that you’re immune to forest fires simply because anything flammable that you own has already been burned isn’t really much to brag about.” NY isn’t seeing a major surge because almost everyone who could be the victim of such a surge is already dead, unfortunately.