According to the Chicago Tribune, the fall of the Taliban coincided with a rise in AIDS. There was an increase in the use of needle drugs as Afghanistan started producing its own heroin, and the refugees returning from Pakistan and Iran sometimes brought it with them. On AIDS under the Taliban:
Although there were cases of HIV before in Afghanistan—the first was registered in 1989, from a blood transfusion outside the country—only a handful were identified. The Taliban health minister insisted in 1998 there was no AIDS in Afghanistan, because it was against Islam.
I am skeptical of this - while the conditions for an increase in infections seem to have arisen after the fall of the Taliban, that doesn't mean that there wasn't a problem with it before. In the words of the wise Donald Rumsfeld, absence of evidence is not evidence of absence. Just because the Taliban regime was not reporting cases of AIDS and treating it does not mean it didn't exist. From what I know of the Taliban they were not known for their stellar public health initiatives.
When I was in Yemen I had the opportunity to hear the staff of a women's health organization talk about the work that they were doing in Yemen. They discussed the work they were doing to curb AIDS infection using all the right language about education and changing habits and clean needles (of course without saying anything about sex), and then said, the people who are getting AIDS are not pure Yemenis. They are from elsewhere. The foreign members of the audience immediately got upset, thinking that the women were lying to them. The moderator stepped in and said, listen, in a conservative culture you cannot just talk about people having AIDS. There are certain things we cannot discuss. An article like this reminds me of that discussion. There is a rise in AIDS now that the Taliban fell, but part of that 'rise' is just the fact that people know what it is now and can diagnose it instead of just dying from whichever disease takes hold of their weak immune system.