Social Networks and AIDS

I don't usually follow up on a post with another post explaining it, but these are very difficult questions, and I want to share a thought I have.

Talking about the Surgeon General's comment I mentioned that a disease like AIDS moves along a social network. By that I mean a particular thing, there is a science of social networks, related to graph theory in mathematics but applied to sociology and usually practiced by physicists, go figure. Generally, you imagine a graph, where each person is a node, say a little circle, and there are lines connecting various ones of them. Not every node is connected to every other, you typically have dense regions -- clusters -- with sparse connections between them.

You've heard it said that everyone in the world is connected by seven or less steps to everyone else -- the "six degrees of separation" effect. Well, now you're talking about social networks. Who's connected to who, what links you'd follow to get from you to Kevin Bacon. More to the point, you've probably heard it said that when you have sex with somebody, you're having sex with everybody they ever had sex with, and so on, moving out through the social network.

Some diseases are just distributed randomly in the population. Somebody gets the flu, they cough and sneeze, the virus goes into the air, and people nearby are exposed to it. There is some probability of them actually getting sick, but there is no requirement that they actually know the person they caught it from. Some proportion are sick, and that is a parameter of the population; some have recovered already, some have not caught the disease yet, some have died ... these are just parameters that can be entered into a formula or model to make predictions.

On the train-ride home I started thinking about this. After seeing some of the comments on that last post, I realized that some people don't have this concept. So I Googled [AIDS epidemic "social network"]. The first hit was about drug users, so I clicked on the second one.

It's a pdf file of a scientific paper by a lady named E. Ann Stanley, published in a journal called Connections, which is put out by ISNSA, the International Network for Social Network Analysis. She used to work at Los Alamos National Laboratory, then at Iowa State University, and now she lists her affiliation as "Bend, Oregon." I don't know her, but I do know a couple of people who have co-authored with her, and I see that her publications look very good. She was involved in some of the early modeling of the AIDS epidemic, even back into the Eighties.

This 2006 paper is really just a kind of introduction to social networks, drawing upon other more technical papers that the author and others have published. It's called Social Networks and Mathematical Modeling.

This blog is not the place for technical mathematical papers, but let me copy and paste a few paragraphs from this one for you, because it's right on the money.

Mathematical modeling studies have shown that the AIDS epidemic is very sensitive to the human behaviors that spread HIV, including: the amount of risky behavior; the manner in which that risky behavior is distributed in the population; and the social network structures within which people practice those risky behaviors. In fact, these models have shown that if we do not understand all three of these factors, then we cannot hope to predict and control the spread of HIV and other sexually transmitted diseases(Hyman and Stanley, 1988, 1994; Stanley, et al., 1991).

One of the earliest indications that this was so occurred in the mid-1980's. At that time, the US Centers for Disease Control was predicting that the AIDS epidemic was already dying out. They predicted this based upon the fact that the epidemic was growing more slowly than exponentially. With infections that are transmitted via casual contacts, such as measles or the common cold, case data which grow less than exponentially does indeed indicate that an outbreak is peaking and will soon be on the decline. Early mathematical models of the AIDS epidemic also demonstrated exponential growth, followed by slowing towards a peak and then decline (Anderson, et al., 1986)

See, they were thinking it was like the flu, and the only thing you had to know was how many people have it. But AIDS is different. Every contagion event occurs intimately between two people, the disease passes from node to node through the network; you don't catch it from doorknobs, you catch it from somebody you know. And the population-level effects of these two kinds of processes look different.

Excuse me, but I love this stuff.

She continues:

However, while these early models did account for both sexual activity levels and the distribution of those activity levels in the population at risk, they did not account for social network structure. Instead, they assumed random mixing. Simply adding the fact that people who are high risk tend to associate more often with others of high risk, and similarly for those of low risk, to our model, along with data on the distribution of partner acquisition rates from various studies in homosexual populations, showed that the epidemic should be growing cubically in time. Reanalysis of the CDC data showed that this was indeed the case (Hyman and Stanley, 1988, Colgate, et al., 1989)

So the traditional epidemiologists were predicting that the epidemic was dying down, but these guys' model predicted that it was actually growing. Remember, AIDS has a long incubation rate, and people are infectious before they have symptoms, so there can be hidden propagation going on.

When she says "the distribution of partner acquisition rates" she means they look at how many people have lots of partners, how many have kind of a lot, how many have only a few, etc. That histogram will look different for different populations, I'd be sure, and it's an important thing to put into a predictive model. You'd also know how many of the Highs know other Highs, how many Highs the Lows know and vice versa, and so on.

This modeling effort showed that the epidemic was decidedly not dying out. This had important policy implications, since many were saying that, since the epidemic was dying out, it would go away on its own, and it wasn't worth spending a lot of money to control it.
Another important feature of the epidemic that biased mixing models captured was the fact that it was primarily the highest risk individuals who were infected first, followed by the next-highest risk individuals, and so on, whereas the random mixing models had most of their early infections in the large low risk groups.

See how cool this stuff is? If it's the flu, then anybody who rides a bus or train is going to be exposed to it: the "random mixing model." In the "biased mixing model," their model, there is more structure to the spread of the disease.

Modeling HIV spread in age and sex- structured populations pointed out another way in which network structures affect the spread of sexually transmitted diseases. Since female partners tend to be younger than their male partners, women tend to become infected at younger ages than men, with the difference in age being societally-determined, and similar to the difference in age at marriage. But more than that, the way that society is structured, ie the network patterns and norms, strongly influences the speed and pattern of spread. Such questions as who goes to brothels, how many wives and concubines men have, and who gets to have multiple female partners, all affect the spread of disease via sex (Stanley, et al., 1991). Collection and analysis of network data have highlighted some of these factors, showing that clustering of heavily interacting individuals into local risk-taking networks, is an important factor in the spread of disease (Rothenberg et al., 2005 and 2005).

Some of this paper is just instructional and technical and not too relevant to this discussion.

The point is this. As soon as I posted that last comment we had a guy in the comments asserting that the epidemic targets gays because they're promiscuous. That's not what this model says. This model says that you catch the disease from somebody you know, and gay people know each other. And guess what: when you ostracise a subpopulation they tend to cluster together more densely, provide the context for something like this kind of epidemic to happen.

Neat little paper -- not too hard, either. I say, click on the link and see how you like that way of looking at contagion. (It applies to beliefs and attitudes, too.)