Ordinarily, asking about apocalyptic conditions in Zeitoun would relate to the destruction of the city of New Orleans, but asking about this in regards to the portion of the book in which Abdulrahman is imprisoned brings up a different set of issues. The word "apocalypse," which in Merriam-Webster's dictionary is defined as "a sudden and very bad event that causes much fear, loss, or destruction," can best be related to this portion of the book by discussing the ideas of how, after a disaster like Katrina, the ruling powers will often resort to Draconian measures to restore the social order, which is dominated by fear.
In order to placate the fears of the ruling powers after Hurricane Katrina, perfectly legitimate members of society, like Abdulrahman Zeitoun were placed in prisons described like this:
"Chain-link fences, topped by razor wire, had been erected into a long, sixteen-foot-high cage extending about a hundred yards into the lot. Above the cage was a roof, a freestanding shelter like those at gas stations. The barbed wire extended to meet it."
These quickly constructed cages seem to be necessities in post-apocalyptic worlds to suppress any violence or anything that might interfere in the ruling powers' attempt to regain control.
In this real-life case, Abdulrahman, Nassar, and Todd did not evacuate the city when ordered to. These men became non-people. They lost all rights and all ability to communicate with the outside world. American laws, like the right to trial, were abandoned in favor of indefinite internment.
In conclusion, the best way to apply the word "apocalypse" in this book is to discuss the authoritarian treatment of the people remaining in New Orleans as "post-apocalyptic."