well, if some of those doctors are using that needle on a patient with AIDS, anyone who follows on that same needle would probably get it, too.
Actually HIV is the least of one's worries from a reused needle. That will take years to kill you, there are plenty of infections that can come from such a needle that will kill you in days. The bodily fluids that are on a needle are perfect incubation points for bacteria, so if a needle sits after use, it would easily become contaminated with Staphylococcus and lead to a quick and very unpleasant death. The needle is also more likely to be infected with other diseases, that would diminish the immune system and make contracting even more significant ailments more likely (such as AIDS, Marburg, or Ebola).
It should also be noted, that blood screening in Africa is not on par with what is being done in the Western world, so there is also a strong possibility of contaminated blood reaching patients.