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Firewalls and sub-saturation stabilization of HIV prevalence
Khan, Dombrowski, Saad, McLean, Friedman

Friedman et al’s 2001 conjecture of a “firewall effect” asserts that individuals with mature HIV infections may act as barriers or ”firewalls” to further HIV propagation among networks of people who inject drugs. Towards the evaluation of this effect, we provide a formalization of what we call the “firewall hypothesis” that allows us to more clearly test for situations where Friedman’s firewall conjecture holds. Using the MABUSE platform, we apply this test across 15+ year simulations of up to 25,000 individuals whose structure is drawn from documented IDU networks in New York City from the early 1990s. In simulations of more than 1000 nodes, we find that in a majority of cases and for a range of parameter settings, the firewall effect holds. In these cases, nodes with mature HIV+ status can be seen to divide the network into clusters of uninfected nodes which themselves remain relatively stable in their infection status over long stretches of simulation time. In a discussion of local structures, these firewall nodes are shown to play an important role in the nonspreading of HIV, despite the presence of high numbers of uninfected nodes and the ongoing reappearance of new, high infectiousness outbreaks.

Modeling Dynamic Risk Networks
We describe a general framework for stochastic actor-based modeling of real-world dynamic risk networks. The models capture heterogeneity in the types of individuals, their interconnecting risk relationships, and the pathogens flowing between them. Dynamism is supported through arrival and departure processes, continuous restructuring of risk relationships, and changes to the pathogen over its lifetime. Whenever possible, the system is regulated through constraints on the local agency of individual nodes, risk relationships, and pathogen flows, rather than by system-wide specifications. We illustrate the application of the framework by applying it to a case study of HIV prevalence in injecting drug user (IDU) networks in New York City.
Khan, Dombrowski, Saad

A Re-examination of Connectivity Trends via Exponential Random Graph Modeling in Two IDU Risk Networks

Kirk Dombrowski
Bilal Khan
Katherine McLean
Ric Curtis
Travis Wendel
Evan Misshula
Samuel Friedman

Abstract: Patterns of risk in injecting drug user (IDU) networks—including co-use, equipment sharing, and sex in the context of drug use—have been a key focus of network approaches to HIV and other disease transmission histories. New network modeling techniques allow for a re-examination of these patterns with greater statistical accuracy and the comparative weighting of model elements. This paper describes the results of a re-examination of network data from the SFHR and P90 data sets using Exponential Random Graph Modeling (ERGM). ERGM allows researchers to produce “regression-like” models to describe connection tendencies that consider both personal attributes (such as age, gender, race/ethnicity, and injection history) and network structural factors (such as transitivity—the tendency of an individual to form a network tie with the partner of a current partner). Similar to ordinary statistical modeling, ERGM network models provide model coefficients that demonstrate the relative weighting of such factors as they contribute to the formation of the networks in question, along with error estimation statistics. Cross-network comparison of the relative importance of model coefficients is also possible. These findings contribute to a more clear understanding of the “logic” of network connectivity among IDU networks.

Keywords: Injector Networks, ERGM, HIV Transmission, Network Modeling

This project was supported by NIH/NIDA Challenge Grant 1RC1DA028476-01/02 awarded to the CUNY Research Foundation and John Jay College, CUNY. Initial funding for a pilot version of this project was provided by the NSF Office of Behavioral, Social, and Economic Sciences, Anthropology Program Grant BCS-0752680.