There's definitely a concept here, and I like how the ordinary takes over for a majority of the play experience. It seems you want to keep the character of the apocalypse a mystery, but I do want maybe a little more detail on what kind of "end of the world" is being experienced (like, a zombie/biological one? or alien invasion? or something more fantastical/supernatural?).
I think resting on the idea of "no class. no noise. no people" should take priority before we really kick into the chaos and screaming of this scenario, since that initial part is the most ominous/eerie part of the whole experience.