Yes they can carry and spread disease. After they walk through garbage or sewers, they then walk over and excrete on your food or where you prepare your food. They carry bacteria that is known for causing food poisoning. Cockroaches will also regurgitate material that was previously eaten which may also contain dangerous bacteria. It is believed that cockroaches help spread Typhoid Fever, Dysentery, Cholera, and Tape Worm. People with Asthma may also have a negative reaction to their droppings and body parts. Naturally you will want to learn how to kill them off. Home remedies don’t often work. To find effective ways to rid your location, contact a professional.