If it were me I wouldn't bother with completely eliminating zombies for any time period. When selecting which city to play in it says the population, so have that many npcs spawn at world creation. Give the players the ability to select A% of them alive and healthy, B% alive and infected, C% start as zombies at game setup. For the suggested "You were at home watching TV when an emergency broadcast came on, informing you that the zombie infection has reached Kentucky, it will be days until it hits your town, and that it is advised that you don't panic and stay in your homes." staring broadcast set it like A=80, B=15, C=5. Then as people die more zombies will raise up. To ensure your living npcs don't actually win again the zombie horde and ruin your fun of surviving it, have npcs always flee from zombies once they're knocked down to the ground instead of finishing them off.
