I'm thinking of writing a zombie play next. But my zombie play will be very different from most movies about zombies. And probably most plays about zombies too, but I've only seen one play about zombies, because there are not many of them, which stands to reason because if there's anything sillier than a movie about zombies it's a play about zombies.
Zombies are so much less threatening than human beings that your script has to be incredibly contrived to make zombies scary - you have to make sure that the humans are vastly outnumbered and/or isolated and/or incapacitated and/or kind of stupid. Because all the zombies I've ever seen portrayed are slow, stupid and easy to kill. Under normal circumstances any reasonably well-funded small-town police force would be able to take out a battalion of zombies with very little trouble, and no police casualties.
And it isn't just that the living, unlike the undead, are responsible for the Holocaust or nuclear weapons - it's because the living are so unpredictable. The living have the element of surprise in their favor. Zombies are entirely predictable. It's just silly to have zombies be a big scary threat in anything, unless you don't mind far-fetched plot contrivances.
So in my play there is a zombie invasion, but the biggest problem is how to dispose of all the zombie carcasses in the most sanitary yet environmentally friendly way.