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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 720818, 16 pages
http://dx.doi.org/10.1155/2013/720818
Research Article

Network Firewall Dynamics and the Subsaturation Stabilization of HIV

1Department of Math and Computer Science, John Jay College (CUNY), New York, NY 10019, USA
2Department of Anthropology, John Jay College (CUNY), New York, NY 10019, USA
3Social Networks Research Group, John Jay College (CUNY), New York, NY 10019, USA
4Department of Sociology, CUNY Graduate Center, New York, NY 10016, USA
5Institute for AIDS Research at National Development and Research Institutes, Inc., New York, NY 10010, USA
6Center for Drug Use and HIV Research, New York, NY 10003, USA

Received 29 December 2012; Revised 20 March 2013; Accepted 25 March 2013

Academic Editor: Carlo Piccardi

Copyright © 2013 Bilal Khan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In 2001, Friedman et al. conjectured the existence of a “firewall effect” in which individuals who are infected with HIV, but remain in a state of low infectiousness, serve to prevent the virus from spreading. To evaluate this historical conjecture, we develop a new graph-theoretic measure that quantifies the extent to which Friedman’s firewall hypothesis (FH) holds in a risk network. We compute this new measure across simulated trajectories of a stochastic discrete dynamical system that models a social network of 25,000 individuals engaging in risk acts over a period of 15 years. The model’s parameters are based on analyses of data collected in prior studies of the real-world risk networks of people who inject drugs (PWID) in New York City. Analysis of system trajectories reveals the structural mechanisms by which individuals with mature HIV infections tend to partition the network into homogeneous clusters (with respect to infection status) and how uninfected clusters remain relatively stable (with respect to infection status) over long stretches of time. We confirm the spontaneous emergence of network firewalls in the system and reveal their structural role in the nonspreading of HIV.