Syphilis

Syphilis was a fatal illness. The Europeans brought the disease to the New World when Hernando Cortez brought them there (PROSE: Bullet Time) — therefore in either 1519 (PROSE: The Aztecs, The Left-Handed Hummingbird) or 1520. (TV: The Aztecs) In and around the 1960s, the US government infected "negro populations" with syphilis, and refused to treat them to observe the diseases' effects. (PROSE: Heart of TARDIS)
 * Though no more information is given on the immoral study, this is the real-world .

When smuggling Anji Kapoor out of Leith Hospital, Hannah Baxter used the second excuse that came to mind — the body under the sheet was a prostitute who'd died of syphilis. Her first thought was leprosy. (PROSE: The Domino Effect)

Jared Khan said that "what few brain cells [ Randolph Bellingham ] had left were now being eaten away by opium and syphilis." (PROSE: Birthright) A man who John Watson called "rat-face" had his nose "almost eaten away" by syphilis. (PROSE: All-Consuming Fire)

Behind the scenes
There is a widespread belief in fandom that Dodo Chaplet contracts syphilis in the novels. This view was taken by the long-running podcast, Radio Free Skaro, some of whose hosts vociferously maintained in episode 177 that she "died of syphilis" in Who Killed Kennedy. Even David Bishop, the author of Kennedy, said in his notes to the e-book version of his novel that Dodo contracted "an illness interpreted by some as a form of space herpes".

All that's pretty wide of the mark, however. The idea that she died of syphilis is a common conflation of Who Killed Kennedy, where she's simply killed by, and The Man in the Velvet Mask, where she contracts the genetically-engineered Minski's virus through sexual contact. However, she doesn't die from it, nor was it even possible for her to do so, according to the Doctor. Minski's virus wasn't anything close to a venereal disease and could have been contracted by drinking water or consuming food contaminated by it. Perhaps more to the point, the word syphilis doesn't occur once in either novel.