The things is, if we can only close schools for, say, a 3 week stretch, it would be better to do it now to limit spread. I know we always need nurses, but we won't need them as much now as we will later.
Anti-intuitive as it may be, I think it's better to close sooner than at the peak. Closing schools at the peak will do nothing to stop spread.
My maths earlier was too complicated. Lets say we can halt spread totally for 3 weeks by closing schools.
Do you want:
New infections:
1, 1, 1, 1, 2, 4, 8, 16 Total cases = 34
1, 2, 4, 8, 16, 16, 16 Total cases = 63
If you freeze growth early, you get less total cases than freezing it at the peak.