It seems he chose the simulation parameters without any regard to what the real life numbers are. Anyone who has studied complex systems will tell you this is a big deal. In things like weather simulations, a small change in initial conditions makes for huge differences later on. In something relatively simple like this, it could mean that you are falling on one side of a differential equation or the other.
I mean seriously. Half the folks who often have sex will have AIDS?
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.
There's a lot of formalism surrounding the study of how much parameters matter; the field is called "dynamical systems" and often covers topics like bifurcation theory and chaos theory.
In this particular system, the parameters matter, but not very much for the particular question the author was asking. The system is well-behaved; it doesn't bifurcate or go chaotic. Tweaking the parameters will change whether the final level of infections is 10% or 90%, but the overall conclusion that "sexual conservatives taking more partners increases total infections" remains valid.
The conclusion isn't valid, IMO, because the assumptions are way off, again IMO. I think the "high-activity players" are at least two orders of magnitude more active than he models them, for example (in a conservative society which frowns deeply on premarital sex). Fewer of them, but more connected; and their numbers will go down, drastically, with more liberal attitudes.
Further, one can think of intuitive reasons that the conservatives having more sex might help. e.g. it lowers the chance of an STD going from a high risk person to a high risk person (which would cause it to be spread way more after). I have no idea who that makes right, I'm just saying intuitively one can think of simple reasons it might go either way and so the details definitely do matter.
Modelling systems is hard, this is an interesting attempt but yes the lack of ANY sources for his assumptions and initial conditions means you cannot even begin to draw conclusions from this model. Hell the models I was exposed to at Uni didn't even provide an absolute answer, just a probability.
17% of the US adult population has Herpes. Something like 25% has HPV (the numbers on this are all over the place, but this seems like the most common result of studies).
About one in six Americans (17%) had the genital herpes virus -- called HSV-2 -- during 1999-2004. But that is down from the 21% rate seen in 1988-1994.
But then closes with this, which seems very real world relevant to this thought experiment/theory/whatever you want to call it:
As its name suggests, HSV-2 isn't the only herpes virus out there. HSV-1, the virus that causes cold sores, is much more common. As of 1999-2004, 57.7% of Americans carry the virus -- down slightly from the 62% HSV-1 infection rate seen in 1988-1994.
There's some bad news here: HSV-1 is causing more genital herpes than ever before. About 2% of people with HSV-1 infection -- but not HSV-2 -- have genital herpes.
"Our findings are consistent with previous reports that genital herpes caused by HSV-1 may be increasing in the United States, as in other developed countries," Xu and colleagues note.
The researchers warn that the herpes virus that causes cold sores may one day become a more important cause of genital herpes. One factor: The increase in teen oral sex that's helping stop HSV-2 spread may be increasing genital infections with HSV-1.
Frankly I just wish everyone had frigging herpes so we could all stop worrying about it. And, of course, jack up the r&d necessary to remove it from our lives once and for all.
I mean seriously. Half the folks who often have sex will have AIDS?