It's quite important semantically because for people who don't stay well informed 'second wave' might imply that areas which have "gone through" the wave are be

It's quite important semantically because for people who don't stay well informed 'second wave' might imply that areas which have "gone through" the wave are benig hit again, which so far is not the case. Essentially a lot of news reporting on this at the moment seems to be fearmongering and maybe an attempt at face-saving from politicians, who will at some point not be able to escape the reality that many of the measures they instituted were not the ones which would actually have saved lives (such as stricter policies about care homes).