Additional factors once a person has been infected with the virus that leads to quicker death is not only lack of medicine (cost), but also widespread malnutrition in poorer population, which means weaker bodies and immune system. Some experts say that many sick in hospitals are generally weak and might or might not have AIDS. Even the tests are too expensive and difficult to administer in those rural areas, so they assume everybody who’s in bad shape has AIDS, but can’t confirm it.
In a book on the effect of the black plague in Europe, a sidenote was a tentative conclusion that a difference in genome in Europeans was the result of surviving the plague by being resistant due to a genetic mutation. The modern Africans don’t have that mutation, and that might be the explanation for higher rates of transmission for certain strains of AIDS in Africa vs. Europe, even accounting for all the enviromental factors mentioned above, that the old genetic mutation also confers resistance to some (not all) strains of AIDS to Europeans.
This was couched in very careful terms and with cautions of “needs more research” to avoid the impression that the Africans can’t be helped because they will get AIDS anyway or other misguided interpretations people with an agenda might twist from this.
As for the belief about curing AIDS by raping little girls - charity organisations are regularly reporting about this, esp. in South Africa. Some years ago, a prominent South African politican, a minister for sth. or other, publically announced that the whole information campaign about AIDS was a conspiracy from Whites/Europeans/the US/CIA to suppress the South Africans, and that sleeping with a virgin could cure it. Raping little schoolgirls is the only way to be sure of virgin status for many of the men who believe that. (The charities involved in the information campaigns were upset, of course, but the damage was done).