More Sex is Safer Sex (1996)
slate.msn.com
slate.msn.com
"What we really want is to minimize the number of infections resulting from any given number of sexual encounters; the flip side of this observation is that it is desirable to maximize the number of (consensual) sexual encounters leading up to any given number of infections."
He's saying that there's this ratio, infections per sexual encounter, that they want to minimize. And the easiest way to minimize this is to increase the denominator. If you have a universe with a skewed (self-selected) distribution, then as you add more people to a category, you'll increasingly get more marginal people. In this case, it's people who have fewer sexual partners and hence are less likely to carry AIDS, resulting in a reduced chance of infection.
Whether this is the metric you care about is debatable. If you're a public health official, you probably care about the absolute number of infections, not the number per sexual encounter, and so this only helps if it brings the probability low enough that the disease can't sustain itself.
Similarly, if you're a married guy who just wants a faithful and devoted wife and kids, you don't care about the chance of infection per sexual encounter, you care about the absolute chance of infection within your life time. This is minimized by not having sex with anyone, or, failing that, having sex with someone who only has sex with you.
Only people who regularly have sex with lots of partners would benefit from this - for them, the metric is chance of infection per sexual encounter (since they'll be having lots of sexual encounters anyway), so why shouldn't they?
Perhaps they made the assumption that the total number of sexual encounters over the entire population is roughly constant. With this assumption the distinction would not matter.
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.
On that note, I know a lot of people in the public health field and not one works for a government. Virtually all of them are indirectly paid by the Bill and Melinda Gates Foundation, through one circuitous path or another.
Even if the sexual contact network is not a hub oriented "small-world network" and more like our highway system -- that doesn't seem to mean that diseases will stay isolated in one area, just it might not spread quite as quickly or pervasively.
And it will to zero forever once you get infected.
But its the likelihood of infection overall that I am concerned with. The more sex you have, the likelier it is that you will have an infective encounter earlier.
the fact remains that if people never have sex, they will never get infected. If they only have sex with one person in their life, and that person follows the same rule, no one will be infected either.
But that's not reality. so we should follow some simple rules, which can be found at http://evensafersex.com
Fair enough-- if you could change the distribution, that would probably slow down the epidemic. But, counter intuitively, it would also increase the number ultimately infected.
This is something network-theorists have spent a lot of time on. See for example: http://rspb.royalsocietypublishing.org/content/274/1628/2925...
One of the mistakes the article makes is in the statement that, if "conservative" girls went out twice as often, the chances of an HIV transfer are decreased because the guy has twice as many potential partners who are HIV-negative. What's missing is the recognition that, if the guy is already HIV positive, he now has twice as many potential partners who he can pass the infection on to.
The changed network could either slow down or speed up the spread of HIV, depending on various specific details (how many men have HIV, how many women have HIV, how many connections to non-carriers do the men have vs the women, and so on.)
As you correctly note, even if this particular change slows down the rate of infection in the present, it may ultimately increase the total number of infections. It may even slow the infection rate for a few years and then suddenly speed it up as some particular critical threshold is reached.
Like I said, I have no clue if this is correct or complete crap, never done anything related to disease and how they spread.
links:
http://en.wikipedia.org/wiki/Small-world_networks
http://en.wikipedia.org/wiki/Degrees_of_separation
http://en.wikipedia.org/wiki/Watts_and_Strogatz_model
http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_m...
Thanks for the links, this article made me want to go back and look into this stuff more. Relevant to my current work also.
1. It would be pretty simple to write a computer simulation to test this, no? Would anyone care to do so?
2. I don't know enough about the AIDS situation in Africa to say whether it is empirical evidence for or against this paper. Is anyone else more familiar with this?
I'm on it. Results in a later reply.
Don't just take my word for it, run my code: http://github.com/philwelch/SexSim
If anyone's interested, let me know and I can work up a blog post and improve my code. (Also, if my code is wrong, let me know or send me a patch.)
EDIT: I have a bug which may invalidate my results. Stand by for fix.
EDIT 2: No, results still valid. Possible fix pushed.
And your simulation is a lot more interesting than anything found in that article.
I may want to play with adding condoms to the simulation, though. My transmission rate is based upon the HIV transmission rate for unprotected anal sex, which is pretty clearly an upper bound--that's why especially slutty or outgoing populations get >50% infection rates after 20 years seeding from 1% infection rate. You also see the odd run where you just have a 1% infection rate after 20 years--probably cases where the randomly seeded HIV+ individual is especially shy and has a low sex drive.
Also, it would have been a lot more interesting if I could have generated random values along different distributions, or...well, lots of things would have helped.
assumption: woman don't want to have sex, men do.
conclusion: it is better for men if women are more promiscuous.