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Sexual Network Scaling and Epidemic Thresholds

Jamie Jones

The structure of sexual contact networks plays a central role in the epidemic behavior of sexually-transmitted diseases (STDs). One specific aspect of network structure that has received a great deal of attention is the network degree distribution. Recent work has argued that the underlying degree distribution in human sexual contact networks could permit the spread and maintenance of an STD regardless of the transmissibility of the pathogen, complicating STD eradication. In this talk, we will develop several candidate stochastic models for the degree distribution of a sexual network. The general categories of stochastic model include: (1) Poisson models, (2) preferential attachment models, and (3) bi-relationship models. We present the results of Maximum Likelihood fits of the different models using data from three large sexual behavior surveys: The Rakai Sexual Network Study, Uganda; The Swedish Survey of Sexual Behaviour; and the National Health and Social Life Survey, USA. Using a standard degree-based epidemic model, we calculate the epidemic thresholds under the different models. We use likelihood-based model selection procedures to compare the fits of the different models to the three data sets. The results indicate that in all three populations lower epidemic thresholds exist, suggesting that public health interventions aimed at reducing transmissibility (e.g., promotion of condom use, or HAART) could be effective in reducing STD prevalence. Curiously, the results also indicate that upper thresholds do not exist either, implying that an STD epidemic would be impossible on the inferred network structure, regardless of its transmissibility. This result in particular highlights the weakness of degree-based models for sexual networks and STD epidemics thereon. We conclude the talk with a discussion of dependency-model alternatives to the standard degree-based models.