An assessment of preferential attachment as a mechanism for human sexual network formation

  • Jones J
  • Handcock M
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Abstract

Recent research into the properties of human sexual-contact networks has
suggested that the degree distribution of the contact graph exhibits
power-law scaling. One notable property of this power-law scaling is
that the epidemic threshold for the population disappears when the
scaling exponent p is in the range 2 < rho fundamental significance for the control of sexually transmitted
diseases (STDs) such as HIV/AIDS since it implies that an STD can
persist regardless of its transmissibility. A stochastic process, known
as preferential attachment, that yields one form of power-law scaling
has been suggested to underlie the scaling of sexual degree
distributions. The limiting distribution of this preferential attachment
process is the Yule distribution, which we fit using maximum likelihood
to local network data from samples of three populations: (i) the Rakai
district, Uganda; (ii) Sweden. and (iii) the USA. For all local networks
but one, our interval estimates of the scaling parameters are in the
range where epidemic thresholds exist. The estimate of the exponent for
male networks in the USA is close to 3, but the preferential attachment
model is a very poor fit to these data. We conclude that the epidemic
thresholds implied by this model exist in both single-sex and two-sex
epidemic model formulations. A strong conclusion that we derive from
these results is that public health interventions aimed at reducing the
transmissibility of STD pathogens, such as implementing condom use or
high-activity anti-retroviral therapy, have the potential to bring a
population below the epidemic transition, even in populations exhibiting
large degrees of behavioural heterogeneity.

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Authors

  • J H Jones

  • M S Handcock

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