They're arguing for "increased sexual activity by conservatives" which obviously means they're arguing for increase in total number of sexual encounters over the entire population.
In effect they say that disease would spread more slowly in a graph with less highly connected hubs and more balanced number of connections per node. This is quite unsurprising.
The point about prostitutes was just a thought experiment, and it looks rather far from reality. The second thought experiment about Joan hooking up with Maxwell seems much more realistic, but I don't see why Maxwell wouldn't hook up with someone else the same day. Actually, the more promiscuous side usually takes the initiative, so I'd say it is quite likely that if not for Joan, some other poor girl would get AIDS anyway.
Or to put it another way; to reduce the outliers who take a disproportionately high number of lovers. It is logical that this would hamper the "global" spread of disease.
This particular theory is saying that the way to do that is to reduce the opposite form of outlier - the sexual conservative.