Unlike a normal virus where people exchange it at random, here people that are more likely to get the virus also seek out other people that are more likely to get the virus. Normal r-value calculations do not apply because you no longer have homogenous population.
You do not need a lot of these people to keep the virus alive. A person that practices unsafe sex once is more likely to do it more than once, with other people who will do the same. In effect forming a network within general population.
While people who practice safe sex might become collateral damage (like spouses of people who practice unsafe sex or patients at a clinic that used untested blood) they are very unlikely to transmit it further (safe sex practices are very effective at preventing spread of HIV).
Also no need to bring politics to it. Viruses do not care about politics.
This is correct. Over two thirds of HIV cases around 2009 were transferred genitally; over 80% if one includes the intestinal tract (rectal) [1].
> Viruses do not care about politics
But people do, and their behaviour influences how viruses like HIV spread.
[1] http://perspectivesinmedicine.cshlp.org/content/2/11/a006965...