Sorry, I don't have any more details than that. I guess I'll have to think of them.
It's alright. - It would just be useful to have the context.
What type of game? (Survival, resource-management, linear story, etc.)
Endless gameplay or a set story?
From what perspective? (First-person, third-person, single person, multiple people, specific characters, etc.)
Linear or branching story? - Mandatory or optional dialogue?
What kind of apocalypse? - War? Scientific? Mythological?
What is the situation of people?
How do they live? What do they have left?
What state-of-mind are the people in and what is their conflict?
From that basis, a story could form. - Good luck!