I'm seeing people mean (at least) two different things when they use the phrase "flatten the curve" and they have different (somewhat opposite) implications for when the peak will be and whether it will come sooner or later.

1) Under one interpretation, you accept it as inevitable that a certain fraction of the population will eventually get COVID-19, until you reach herd immunity. But you want to spread those cases out over a longer period of time. So the disease is still growing but not super fast.

In practice, this means aiming for an R (reproduction number) a little bit *above* 1. Eventually, enough people have gotten it so that many are immune, which knocks R below 1, and new cases start to fall. This could take several months; the peak will take longer to come.

2) Alternatively, "flatten the curve" can just mean "reduce new cases as much as possible" which usually implies more aggressive social distancing/etc. This means getting R *below* 1, if you can, so new cases immediately start to fall. Under this strategy, the peak comes sooner.

In fact, the peak basically happens whenever you implement the new policy, though it may take time to appear in the data.

The catch is that many people are still susceptible (you haven't reached herd immunity) so you could have a *new* peak once you relax the restrictions.