The "Gradual Apocalypse" has also something else for it: you don't know when it is over !
So if people believe it is still happening, they will be paranoid, will have strange behaviour or believes about what needs to be done to preserve them.
Of course, you will also have all the associated behaviours like finding scapegoat, blaming this religion/race/deviant behaviour for the apocalypse, religious zealots of all kind.
Also, having as background huge city with only a few hundred people living in can be quite creepy - for reference the first 20 minutes of "I am Legend", where almost no words is heard, except Will Smith talking to himself.
The cause of a accelerated death rate can be a new disease (classic), the Red Plague, can be huge swarms of insects (like cricket) flying apparently randomly and leaving behind them a desert, without any lifeform left, plant or animal, can be radiation or contamination of air/water/some type of food.
Looking forward which spin you want to give.