The role of nonlinear relapse on contagion amongst drinking communities

Ariel Cintrón-Arias, Fabio Sánchez, Xiaohong Wang, Carlos Castillo-Chavez, Dennis M. Gorman, Paul J. Gruenewald

Research output: Chapter in Book/Report/Conference proceedingChapter

11 Scopus citations


Relapse, the recurrence of a disorder following a symptomatic remission, is a frequent outcome in substance abuse disorders. Some of our prior results suggested that relapse, in the context of abusive drinking, is likely an unbeatable force as long as recovered individuals continue to interact in the environments that lead to and/or reinforce the persistence of abusive drinking behaviors. Our earlier results were obtained via a deterministic model that ignored differences between individuals, that is, in a rather simple social setting. In this paper, we address the role of relapse on drinking dynamics but use models that incorporate the role of chance, or a high degree of social heterogeneity, or both. Our focus is primarily on situations where relapse rates are high. We first use a Markov chain model to simulate the effect of relapse on drinking dynamics. These simulations reinforce the conclusions obtained before, with the usual caveats that arise when the outcomes of deterministic and stochastic models are compared. However, the simulation results generated from stochastic realizations of an equivalent drinking process in populations living in small world networks, parameterized via a disorder parameter p, show that there is no social structure within this family capable of reducing the impact of high relapse rates on drinking prevalence, even if we drastically limit the interactions between individuals (p ≈ 0). Social structure does not matter when it comes to reducing abusive drinking if treatment and education efforts are ineffective. These results support earlier mathematical work on the dynamics of eating disorders and on the spread of the use of illicit drugs. We conclude that the systematic removal of individuals from high risk environments, or the development of programs that limit access or reduce the residence times in such environments (or both approaches combined) may reduce the levels of alcohol abuse.

Original languageEnglish (US)
Title of host publicationMathematical and Statistical Estimation Approaches in Epidemiology
PublisherSpringer Netherlands
Number of pages18
ISBN (Print)9789048123124
StatePublished - 2009


  • deterministic model
  • drinking behavior
  • drinking dynamics
  • small-world network
  • social influence
  • stochastic model

ASJC Scopus subject areas

  • General Mathematics


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