Infestations pop up fairly often, so if you're legitimately playing the game, you should be able to knock out all 15 in a matter of time. They are random side quests, where you have to clear out a house or area of 10-15 zombies and 1-2 special zombies. The best way to clear them is to use a vehicle and simply run everything over.
If you simply want to get this over with, the fastest way that I found requires you to start a new game in the base game. Start a new game and play through the base storyline as quickly as possible. You'll have a few cutscenes, you'll need to do the scouting mission, go investigate the gunshots (you can skip searching the cabins), go back to the station, and finally, make your way to the church. When you get to the church, go through all of the dialogue and such, and you'll then get another scouting mission. Scouting will reveal one infestation on the map, and you'll find another while driving towards it (or very close by it).
That's two infestations in 10-15 minutes, now exit the game, start a new one, and repeat.
If you don't want to start a new game and erase your progress, you can simply idle in any of the modes and infestations will randomly pop up as side missions, but this will take longer.