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.
As part of a recent study of the dynamics of the retail market for methamphetamine use in New York City, we used network sampling methods to estimate the size of the total networked population. This process involved sampling from respondents’ list of co-use contacts, which in turn became the basis for capture-recapture estimation. Recapture sampling was based on links to other respondents derived from demographic and “telefunken” matching procedures–the latter being an anonymized version of telephone number matching. This paper describes the matching process used to discover the links between the solicited contacts and project respondents, the capture-recapture calculation, the estimation of “false matches”, and the development of confidence intervals for the final population estimates. A final population of 12,229 was estimated, with a range of 8235 – 23,750. The techniques described here have the special virtue of deriving an estimate for a hidden population while retaining respondent anonymity and the anonymity of network alters, but likely require larger sample size than the 132 persons interviewed to attain acceptable confidence levels for the estimate.
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