Short answer: Our desert cockroaches are not known to transmit disease pathogens.
More information: Some cockroach species are known to transfer pathogens, but these are species that are known to live in close association with us.
The fact that some cockroaches live in homes, sewers, kitchens, hospitals, etc. and feed on human foods, feces, and cadavers make it possible for them to vector a variety of human disease-causing organisms, both internally and externally. They have been known to carry viruses, bacteria, fungi and protozoa. At least 18 bacteria that cause human diseases have been found naturally in pest species. The American and German cockroaches are species of medical importance.
