@Olivier5,
A flat line (eg Italy over the past week) means that the epidemic is
still progressing in the population but at a constant speed, with the same increment of new cases every day (linear growth). This is better than an exponential growth but it's still propagating. Only the
pace of propagation has been tamed at that point.
The next step is (hopefully, but look at South Korea...) a curve that heads down, indicating that propagation is slowing down in speed.
Only when the curve hits zero can one say that the epidemic has stopped progressing. China came close on day 55, deconfined itself a bit, and boom, it shoot up again, as noted by Chai, so now they are back to tighter lock down.