title: Applications of small-world network theory in alcohol epidemiology.
abstract: OBJECTIVE
  This study develops a mathematical model of alcohol abuse in structured populations, such as communities and college campuses. The study employs a network model that has the capacity to incorporate a variety of forms of connectivity membership besides personal acquaintance, such as geographic proximity and common organizations. The model also incorporates a resilience dimension that indicates the susceptibility of each individual in a network to alcohol abuse. The model has the capacity to simulate the effect of moving alcohol abusers into networks of nonabusers, either as the result of treatment or membership in self-help organizations.
  
  
  METHODS
  The study employs a small-world model. A cubic equation for each person (vertex on a graph) governs the evolution of an individual's state between 0 and 1 with regard to alcohol dependence, with 1 indicating absolute certainty of alcohol dependence. The simulations are dependent on initial conditions, the structure of the network, and the resilience distribution of the network. The simulations incorporate multiple realizations of social networks, showing the effect of different network structures.
  
  
  RESULTS
  The model suggests that the prevalence of alcohol abuse can be minimized by treating a relatively small percentage of the study population. In the small populations that we studied, the critical point was 10% or less of the study population, but we emphasize that this is within the limitations and assumptions of this model.
  
  
  CONCLUSIONS
  The use of a simple model that incorporates the influence of the social network neighbors in structured populations shows promise for helping to inform treatment and prevention policy.
authors.affiliation: Department of Mathematical Sciences, University of Delaware, 501 Ewing Hall, Newark, Delaware 19716-2553, USA. braun@math.udel.edu
authors.forename: Richard J
authors.initials: RJ
authors.lastname: Braun
authors.forename: Robert A
authors.initials: RA
authors.lastname: Wilson
authors.forename: John A
authors.initials: JA
authors.lastname: Pelesko
authors.forename: J Robert
authors.initials: JR
authors.lastname: Buchanan
authors.forename: James P
authors.initials: JP
authors.lastname: Gleeson
mesh_terms: D000436:Alcoholics Anonymous; D000437:Alcoholism / Q000453:epidemiology* / Q000523:psychology / Q000628:therapy; D006801:Humans; D007398:Interpersonal Relations; D008960:Models, Psychological; D008962:Models, Theoretical; D015995:Prevalence; D012944:Social Support