I wasnt very impressed by this game so far. I found 3 zombies right outside my starting safe house. They never once tried to attack me. I was also unable to kill even 1 of them in my 50 moves. Kinda boring game.
Logged off zombies won't attack you. Also attacking with a low chance to hit attack kinda sucks. The more skills that increase chance to attack you buy (like pistol training, etc) the better your hit % will be.
It's not for everyone though, and the 50ap/day limit does suck.