Cockroaches can carry a wide range of diseases, as a wide reservoir of bacteria, like salmonella and staphylococcus, and virus, like polio virus, can survive in their digestive system for months to years after being ingested into their body. Cockroaches are known to consume just about anything, from food droppings on the floor to feces. The reservoir of bacteria can even be passed through the cockroaches in their droppings.
The diseases that are carried by the cockroaches are transmitted to human being when cockroaches vomit or defecate on food that later gets consumed. On top of spreading diseases, cockroaches have also been associated with allergies.