Yeah, but that's not the only reason. There's a whole bunch of crap contributing to the problem:
1. Idiot missionaries teach that birth control is not what "God wants." This is a huge problem in ALL developing countries. Fucking christians spreading the "be fruitful and multiple" need to STFU, period, I don't care what country they're in.
2. Say what you will, female promiscuity is not the problem (it almost never is, most societies have been contaminated by paternal religious dogma that condems female sexuality). Africa is one of the few countries that still has areas performing female circumcision, in fact. Meanwhile, men are raised thinking they have the right to anything they want, including any (or as many) woman. Women have no status, no value, no rights.
3. Rape is more likely to transmit the virus than consensual relations because there is more likely to be trauma involved.
4. It's an appallingly poor country. A lot of medical supplies are reused, including needles and syringes.