My comment, which the site couldn't accept, was that there should be plenty of gas in underground tanks for the needs of one guy - provided it stays fresh. He could pump it out with a gas-powered pump, manually, or with an electric pump run by gas-powered generator. There should be plenty of bottled water around, and if the water system is powered by gravity it too should last for quite a while with only one user. After a while, the rivers would even become drinkable. He can get all the generators, pumps, and other supplies he needs. And we do see him growing and shooting his own food. There's nothing like disease, pollution, or radiation that's contaminating things.
A better question would be why he chose to stay isolated on Manhattan Island with thousands of hungry zombies around. Why not relocate to, say, Liberty Island and be safe? BTW, how did those zombies continue to function without anything to eat?
I heard there's a prequel coming out, so maybe we'll get a few answers.