Lox, re your "As more people become infected, more people will be at risk, so the rate of increase will also increase."
If this were happening we would be seeing an exponential increase.
That is not what the figures show.
We see a slow, linear increase of around 200 per year.

That makes hetero acquired HIV an incredibly rare disease and likely to remain a rare disease for at least a century.
That accords well with WHO appraisal I provided yesterday.

It is only contradicted by that multi-polymath expert on everything Royston.
I doubt WHO and UNAIDS are tearing up their reports on his account though.