According to the Centres for Disease Control and Prevention (CDC), the German cockroach is a known vector for diseases including: 

• Salmonellosis – Salmonella food poisoning causes diarrhea, fever, and abdominal cramps within 12 to 72 hours. Symptoms are generally mild, but can be severe, especially for those with a compromised immune system.
• Staphylococcus infections – This gastrointestinal illness develops soon after food is eaten and usually last about a day. The toxins are heat resistant so are not destroyed by cooking.
• Escherichia coli (E. coli) bacteria normally lives in the intestines of people and animals and some types can cause illness with diarrhea. 
• Typhoid fever – This life-threatening illness is caused by Salmonella Typhi. When a contaminated food is consumed, the bacteria multiply and spread into the bloodstream. 
• Gastroenteritis – inflammation of the stomach and small and large intestines, generally leading to vomiting or diarrhea.
  General diarrhea.

People may become infected with any of these by eating or drinking a contaminated food or beverage. Cockroaches can also trigger asthma and other allergies. 
 
Learn more about Types of Cockroaches.