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" 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.
One of the most common images in post-apocalyptic literature is the mass incarceration of anyone who defies the attempt to restore order. Think about any movie about an apocalypse. Just recently, the AMC show Fear the Walking Dead, had this extraordinary image of survivors locked up underground in cages that looked very similar to those described here in Zeitoun:
"Chain-link fences, topped by razor wife, 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 dissent 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 to 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."