This hardy roach is difficult to eradicate, as it breeds quickly, hides during the day, and gets into your home through small cracks and holes, or as a stowaway in bags, boxes and other products. Once your home is infested, the German cockroach eats tidbits of garbage, food scraps, pet food or even glue. Roaches can not only spread disease, they are also a common cause of allergies and asthma.