The model itself is broken. It is doubtful the population is bimodal, divided between people who are nymphomaniacs, and people who will be satisfied once they find "the one". I just don't believe that people don't have affairs, or that prostitution doesn't exist.
It is more plausible that the number sexual partners follows a Pareto distribution. It is likewise plausible that the economist sought to flatten the Pareto curve, even if this may result in the area under the curve increasing somewhat. Would it work? Maybe not. But this counterexample just reflects badly upon us. Programmers are the new physicists of this era.
My model didn't follow a bimodal distribution; it followed a uniform distribution. I got the same results. A Pareto distribution would be interesting to try.
Your model has two different kinds of players, not one. There are players with a target activity rate of 0.1 and a players with a target activity rate of 0.01. Randomizing the activity rate over that will not produce a uniform distribution of activity.
If you really want to take the economist up to task, you should find his paper, code his model and parameters exactly, see if you reproduce his hypothesis over a number of trial runs (for all we know, he may not have run a sim at all, given the NYTimes' shoddy reporting).
No, the OP's model has two different kinds of players. I'm not the OP; the OP wrote a simulation in Python following the bimodal distribution you described; I wrote a completely different simulation in Ruby following a uniform distribution several months ago when I first read the story in question: http://news.ycombinator.com/item?id=1749324
My model does have a number of flaws (a uniform distribution is still not very good; there's no gender distinction; the transmission rate per encounter is artificially high; people only stay with their partners for a random-yet-uniform amount of time) but I'm not sure to what extent these matter.
Perhaps the parent could find a lower bound on the percentage of people with AIDS whereupon more sex does equal safer sex. That would certainly answer the parent's question.
