Martina Morris, a Professor of Sociology and Statistics at the University of Washington, studies the transmission of sexually transmitted diseases like HIV using network analysis, including random graph models. A really interesting story, called “Breaking the Chain” about some of the history of her involvement in the study of these networks was published in Reed magazine. In the story she relates a defining moment that took place in Uganda in 1993.
From the story in Reed:
Fresh out of grad school, she was giving a talk to a group of African academics and public health workers on her dissertation, which explored how age differences between sexual partners might be related to the spread of the HIV virus. As she described the mathematical model she used in her research, a man in the audience abruptly stood up. “Can your model handle people having more than one partner at a time?” he asked.
Her research, developed over time into a sophisticated model, now suggests that that minor variations in sexual concurrence can lead to vast increases in overall transmission of HIV.
At the upcoming June 17 – 21, 2013 AIM workshop “Exponential random network models,” Martina will join fellow organizers Sourav Chatterjee, Persi Diaconis, and Susan Holmes, to study these and related problems and with the goal of bringing social scientists and statisticians who study exponential random graph models into contact with an emerging group of mathematicians who use a variety of new tools, including graph limit theory and tools from statistical mechanics such as spin glasses.
Here is an excerpt from the Morris website explaining in more detail the limitations of models of transmission. The goal is that random graph models will estimate the network parameters and simulate evolving networks.
“Because infectious diseases are transmitted from person to person, our understanding of disease transmission and prevention are rooted in a theory of population transmission dynamics. The epidemiology of sexually transmitted diseases (STD) like HIV – how quickly they spread and who gets infected – is driven by the network of person-to-person contacts. Early epidemiological studies and mathematical models of this process provided a number of insights that led to changes in STD control strategies during the 1980s. With the advent of HIV, however, new challenges have emerged. Like other incurable infections, HIV has the potential to spread very broadly in a population under the right circumstances. This makes the “core group” concept from the 1980s somewhat less effective for HIV prevention. Much work has been done during the last 15 years to identify which aspects of the partnership network structure matter for the spread of HIV, and to collect data on partnership networks in many populations. Simulation studies have played a crucial role in this effort, by identifying the type of network structures that have large impacts on transmission dynamics. The confluence of data, theory, and methods has created a clear agenda for quantifying the influence of networks on HIV transmission risks. While many of the pieces of the emerging research program are now in place, there is a wide gulf between the network data and the current simulation modeling frameworks. Simulations typically create network effects indirectly, by varying parameters of some convenient function to produce a change in simulated networks. The observable network measures are thus outcomes of the model, rather than inputs. While this strategy has been very useful for orienting initial research, it has hamstrung our ability to evaluate the empirical transmission risk in observed networks.”