Minski's virus was a virus transmitted through ingestion or sexual activity. It was created by Deputy Minski, son of the Marquis de Sade and ruler of France in an alternate timeline. He thought he would be able to eventually infect the whole world with it.
The virus itself was comprised of tiny "maggots" — in reality, as the First Doctor established, "engineered machines with organic components". They were programmed to "feed on nervous tissue and cerebral material". The virus was not itself deadly, but it could be passed directly between humans and to one's children. Minski could use the virus to control people's actions. Because of the ease with which the virus spread, it was theoretically possible that Minski could have used the virus to control the world. The Doctor thwarted Minski's plans, however, by reverting history to its proper course and eliminating the timeline in which Minski developed the virus.
Prior to the righting of the timeline, however, Dodo Chaplet lost her virginity to Dalville and thereby likely contracted the virus. The tiny machines that comprised the virus lived on in her, probably for the rest of her life. She likely passed them on to other sexual partners. However, since there was no threat of Minski or anyone else using the virus within her, it was essentially a "souvenir" of her first sexual encounter. In fact, she claimed to have wanted to keep the virus inside her, since it would be the only tangible proof that the alternate timeline and her first lover ever existed. (PROSE: The Man in the Velvet Mask)
Behind the scenes Edit
As is pointed out at the Doctor Who Reference Guide entry for The Man in the Velvet Mask, many fans confuse this virus for a venereal disease, claiming, for instance, that "Dodo died of syphilis." However, she didn't die in the story, nor was Minski's virus any sort of venereal disease.