Does anybody else wonder how long this type of thing could go on? Eventually all the zombies would deteriorate to the point of not being a threat, and the population is so small that it doesn't seem possible to repopulate, so to speak, the amount of zombies. Most survivors know that you have to "kill" those that die, and the number of people who would die on their own is slim to none, so eventually, wouldn't all the zombies just sort of disappear?
Interesting question...
One possible outcome could be as was described in Max Brook's book, "World War Z". In the book, everything east of the Rockies was given up to the zombies. But there were still groups that survived, much like Rick's group and the former group at Woodbury.
West of the Rockies survivors were much more aggressive at cleansing the land of the walking dead.
Why the Rockies as a dividing point? It was found that the zombies had very difficult time navigating through/over that range of mountains.
Eventually the area of the Rockies became zombie-free.
And then the great sweep happened. Units/groups began working their way east, in as much of a straight line as possible. Progress was slow and deliberate.
As these groups came across hordes or herds, they would retreat a short distance and then form a "square", just like infantry use to do in order to defend themselves against cavalry. The group would then use dogs to go out and lead the zombies back to the formed square– then the fun would begin.
The use of a .50 cal machine gun was mentioned earlier, if you had 4 set up as part of a square, it would keep the walking dead from working their way around you. If you only have one .50 cal, then they would start to pile up in front, and the zombies behind would start going left & right. With one .50 cal you're going to have to constantly swing the gun from one extreme to another.