Of course the big question is how long can an active zombie last? Their skin and muscles are still decaying even if they still get signals from the brain stem. One would think a Zombie could not last more then a year before muscle tissue is to decayed to support movement. They can not metabolize food to built up tissues. Especially true if you are in a hotter environment where the sun and heat will speed up the decay. The logic would be if the survivers could hold up for about a year or so there would not be to many zombies left to be a threat. There may be newer recently dead zombies, but the original surge from the the first month would be gone.