You've stolen my disease, gwray. As it turns out there are a number of related words, including nosocomial zoonoses,
xenozoonoses, prionzoonoses, and ichtyozoonoses. See
http://zoonosesonline.org/nosocomial-zoonoses.html
About nosocomial zoonoses, it seems health workers come to the hospital carrying microbic hitchhikers from their pets.
Am I correct about these observations?