New Mathematical Model for HIV
Byon May 19, 2011 01:51 PM
By Ethan Knudson '11
Uganda 1993: Sociologist and statistician Martina Morris '80 had just presented her sophisticated mathematical model on the spread of HIV to a conference attended by African elders.
In the back, a man raised his hand and asked, "Can your models account for having more than one partner at a time?"
When Morris admitted they didn't, the man walked out.
Talking to Reed students this spring, Morris explained how this incident launched her on an academic journey to construct a realistic model of AIDS transmission. Along the way she would meet Obama's grandmother, go head to head with a dominant epidemiological theory, and develop an intervention strategy based not on drugs but instead on a simple change in behavior...
Traditional transmission models rely on differential equations that assume every sex act occurs independently. Your likelihood of becoming infected is calculated as a function of the rate of transmission, the number of partners over a period of time, and the length of time you are sexually active.
The traditional model assumes that "every time you have sex you close your eyes and pick someone from the population," Morris says. "That makes no sense."
In order to produce the infection rates observed in Uganda and other parts of southern Africa under the traditional model, each individual would have to have at least two partners and engage in seven sex acts a week--an assumption that she contends is patently absurd.
Using network analysis, Morris developed a model that brings the couple back into the picture. Most individuals do not simply walk into a dark room and pick out a random stranger; instead they typically maintain relationships with specific partners over various lengths of time. Those in HIV-negative couples can only transmit the disease to one another if one of them picks it up from outside the partnership.
When people maintain multiple partnerships at the same time--a phenomenon Morris dubs "concurrency"--they are more likely not only to contract the disease (since they have more partners) but also to transmit it. Serial monogamists, on the other hand, tend to slow infection rates down.
A high degree of concurrency enables rapid transmission of the disease across populations, but Morris's work demonstrates that small downward shifts in concurrency can dramatically reduce transmission. If the mean number of concurrent sexual partners drops from 1.86 to 1.65, the percentage of the population exposed to the disease plunges from 64% to 2%.
Unfortunately, her work has not always been well-received by the epidemiological establishment. Many AIDS researchers continue to rely on flawed studies contending the concurrency has no effect on rates of HIV prevalence, and prefer to employ the traditional model.
However, Morris and her collaborators have designed an intervention strategy, "Know Your Network," to make communities aware of the effect of concurrent sexual behavior. When testing the intervention in Kenya, a man told Morris that "This is the medicine we've been waiting for."
Now she just has to deliver it.