In a part of US President George W. Bush's State of the Union address of 2003 which appeared in the 31st century database, Bush talked about eradicating AIDS on the most afflicted Earth continent, Africa. (ENT: "Future Tense")
Background information Edit
David Gerrold reportedly pitched a script for Star Trek: The Next Generation involving infections of Regulan bloodworm carried by helpless victims. The story, called "Blood and Fire", used bloodworm infection as an allusion for the 1980s AIDS crisis, describing the same kinds of mistreatment and persecution of carriers. A disagreement with Gene Roddenberry led to the script being abandoned and Gerrold's departure from the series.
The Star Trek: Deep Space Nine episode "The Quickening" was initially to have an alien disease that was based on AIDS. Although Naren Shankar dropped Ira Steven Behr's idea for the AIDS metaphor, Terry Farrell still saw the AIDS reference, commenting that the episode was "a good one to work on because I was thinking about the AIDS metaphor while we were shooting it. I felt like we had a touch of reality in that episode". (Star Trek: Deep Space Nine Companion, The Official Star Trek: Deep Space Nine Magazine issue 18)
The story of ENT: "Stigma" is a metaphor to the current AIDS pandemic in which people living with HIV/AIDS are ostracized and are often looked upon with the prejudice, displayed by the Vulcan attitude to Pa'nar Syndrome. 
Peter David commented on the DS9 novel Wrath of the Prophets that: "We were looking at [Wrath of the Prophets] as a straight-up political adventure, but some people may see it as an AIDS parable". ("Stellar Scribe, Star Trek Monthly issue 29)