I read a book on the mathematics of networks this weekend. The book used AIDS to illustrate some of the workings of networks. These ideas could be helpful in slowing and preventing AIDS epidemics.
There is one type of networks, "Scale Free Networks", that have some very interesting properties. The Internet is a scale free network. Most nodes on the network have a small number of connections (1 - 2). The ramp up of connection counts is not statistically even. There is a cluster of nodes, a hub, with about 10 connections and there is a cluster of nodes with about 100 connections and there is a cluster of nodes with about 1000 connections.
If a virus is unleashed the network favors infecting the largest hubs quickly. A hub with a 1000 connections has many more opportunities to get infected than does a hub with 10 connections. Once the hub with 1000 nodes gets infected it immediately infects many other nodes. This explains why well-designed viruses can spread so quickly and are difficult to stop. The priority is protecting the very biggest hubs.
The early research is showing that a societies sexual web follows the structure of scale-free networks. Most people have a few sexual partners over their lifetime. There is a cluster/hub around 10 - 12, another around 200 and another around 2000. The sexual webs, for the societies studied so far, are scale-free networks.
Mathematical modeling has demonstrated that randomly protecting nodes in a scale-free network does very little to contain an epidemic. All actions to protect or isolate the most connected nodes dampen the epidemic, usually enough for it peter out the way most flu outbreaks do.
If this research holds up to scrutiny, it will have significant impact on strategies for managing AIDS epidemics. First, it will mean developing a way to identify the high order nodes (sexual permissions). Altering the behavior of these people is how to have the most impact on the spread of the virus. If treatment is scarce and difficult to deliver, the priority is to treat these high order nodes. If there is a vaccination, vaccinating these people will dampen the epidemic, while random vaccination will have very little impact.
This will lead to some very difficult policy decisions that will not sit well with anyone political leaning. Identifying and treating the most promiscuous members of society and giving them special treatment that is not available to everyone will take a strong political will aimed at getting the job done rather than simply doing something about the problem.
Paul |
