Instead of THE GUBBMINT being evil by LOCKING EVERYTHING DOWN in some scary QUARANTINE ZONE or the like, imagine a "got to build up zombie bite immunity" response, or one with pseudoscientific treatments, or pretty much anything so 
can feel like things are back to normal while zombies are just a thing that continues happening.
Add your own ideas if you like. 
The idea I've always had for a zombie story is actually the only one in which there is a cure for zombification. The thing is, zombies rot and fall apart with time, which means that if and when they get cured, they don't just regenerate, they come back as disfigured people with zero memories of the time they were zombies, as well as the added stigma of probably having killed and eaten somebody while zombified.
So the whole shtick is how do you reintegrate into society as a former zombie, scarred and treated like a monster, even though you're just supposed to be a normal dude again? I'm not mature, insightful or wise enough to do that premise justice, but I think it would be real neat in the hands of someone who's a better writer than I am.
Yeah, everything you are suggesting there ; BBC has you covered
I was thinking the same thing. There have actually been a few zombie films/shows that have a similar premise to what joaomarrom was suggesting, at least the part about a cure having been found and former zombies trying to reintegrate back into society. Along with In The Flesh, another one that comes to mind is The Cured which starred and was produced by Elliot Page.
Nice! Never heard of this before, I'll check it out!
Using my boomer brain I can kind of see this being viewed as an allegory for the treatment of vietnam vets in the US
The movie "the cure" is about there being a, well, cure for zombification. Except they do remember everything they did as a zombie. It's not bad