Jenner showed what happens when someone infected dies--part of the brain reanimates and they're a zombie. For muscles to work, some sustenance is required, so they eat living tissue. It appears they prefer human, but are willing to eat non-humans (Rick's horse in Atlanta).
But what happens when they run out? What will keep their muscles sustained? And why aren't their bodies continuing to rot away? (I know, "then there's no show.") Basically, given time, shouldn't they just rot away to nothing and the problem is solved?
I did like the old man's belief, that this is a plague to rebalance things on Earth. Seems reasonable and kinda better than a man-created problem.