Andorian measles was a highly contagious disease known to Federation medicine in the 24th century. It presumably originated from the Andorian people but can apparently infect other species, including Humans.

In 2370 Beverly Crusher told Admiral Adams that the crew of the USS Enterprise-D was suffering an outbreak of Andorian measles and as such half the crew, including Captain Picard were under quarantine. In reality the captain and crew were perfectly healthy and Dr Crusher had made up the outbreak to provide cover for their investigation of a Starfleet conspiracy on Earth. (TNG comic: "An Inconvenient Truth")

It is possible Crusher made up this disease, or exaggerated the precautions she claimed to have put in place. However as a medical expert it's just as likely she based the cover on real science to secure it's believability.