City of Broken Magic (Chronicles of Amicae, 1) [Bolender, Mirah]

Five hundred years ago, magi created a weapon they couldn't control. An infestation that ate magic--and anything else it came into contact with. Enemies and allies were equally filling.

Only an elite team of non-magical humans, known as sweepers, can defuse and dispose of infestations before they spread. Most die before they finish training.

Laura, a new team member, has stayed alive longer than most. Now, she's the last--and only--sweeper standing between the city and a massive infestation.