You can have proof but also a problem with interpretation, mistake, and assumption.
Aids in Africa is far more complicated than just saying, Aids in Africa.
How that practice is going to be seen. What are the cultural practices. What does this virus look like. How does it behave. Retrovirus: that very rapid ability to mutate. It is RNA that matters here not DNA. The microbe is changing in a lot of ways. People just can’t catch it, let alone keep up with it. Vaccine can protect certain warrants but cannot change how that will have to be changed. How much of this is how society interprets disease rather than just the biological function of it.
Practices that make it difficult to stop the spread: prostitution, rape, impossible negotiation, poverty, government unwillingness to use Western Medicine (ATZ), ethnic warfare in an ugly way, pressure to have kids, widow re-marry, pressure from society to have kids and terms of worth reflected back into society with how many kids are produced.