Actually I've been researching about that. Apparently it happened in the 年 2047. If あなた take the timeline of Finn and Jake which is 3043 and then take away 996 as mentioned in the episode "Simon and Marcie" あなた get 2047. It's probably like World War I または II.The War ended when the キノコ Bomb was dropped. And only few people survived. And the apocalyptic thing, actually I bet the so-called "zombies" might have been caused によって the bomb, the chemicals, または maybe a disease または something. I'm not sure which happened first though :) Wait, actually I think it's because of the chemicals and wastes mostly. Because when Shoko from the episode "The Vault" she fell in the river and was mutated.