system
Given the following post, respond as if you're commenting on Reddit:
human
[zombies] wouldn't a zombie infestation solve itself within a few weeks/months as they starve to [another] death?

Speaking about virus/disease/parasite/etc zombies, not paranatural "undead" here: we usually see a handful of non-zombie survivors and hoards of zombies, wouldn't they starve away after a few weeks? 

There are not that many humans left, each corpse become a zombie itself, large scale farming is gone, there's not that much wild life to eat in areas around cities...Basically the population should dwindle to numbers of Paleolithic humanity, maybe lower since being a zombie seems pretty straining in the long term. And we don't see them breeding (although that doesn't mean they don't).
gpt
Yes, in a general sense.  That's exactly what happened in 28 Days Later (assuming we include them as zombies).

If you add supernatural elements, though, the answer could be different.  That's why you have to look at each specific universe.