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Mathematical and Statistical Estimation Approaches in Epidemiology pp 343–360Cite as

The Role of Nonlinear Relapse on Contagion Amongst Drinking Communities

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Abstract

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.

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Author information

Authors and Affiliations

  1. Center for Research in Scientific Computation, Box 8212, North Carolina State University, Raleigh, NC 27695-8205, USA

    Ariel Cintrón-Arias

  2. Department of Biological Statistics and Computational Biology, Cornell University, Ithaca, NY 14853-7801, USA

    Fabio Sánchez

  3. Mathematical, Computational, and Modeling Sciences Center, P.O. Box 871904, Arizona State University, Tempe, AZ 85287, USA

    Xiaohong Wang & Carlos Castillo-Chavez

  4. School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287, USA

    Carlos Castillo-Chavez

  5. Department of Mathematics and Statistics, Arizona State University, Tempe, AZ, 85287, USA

    Carlos Castillo-Chavez

  6. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA

    Carlos Castillo-Chavez

  7. Department of Epidemiology and Biostatistics, School of,Rural Public Health, Texas A&M Health Science Center, P.O. Box 1266, College Station, TX 77843-1266, USA

    Dennis M. Gorman

  8. Prevention Research Center, 1995 University Avenue, Suite 450, Berkeley, CA 94704, USA

    Paul J. Gruenewald

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  1. Ariel Cintrón-Arias
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  2. Fabio Sánchez
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  4. Carlos Castillo-Chavez
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  6. Paul J. Gruenewald
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Editor information

Editors and Affiliations

  1. Arizona State University School of Human Evolution & Social Change, Tempe, AZ 85287-2402, USA

    Gerardo Chowell

  2. Los Alamos National Laboratory, Mail Stop B284, Los Alamos, NM 87545, USA

    James M. Hyman  & Luís M. A. Bettencourt  & 

  3. Dept. Mathematics & Statistics, Arizona State University, P.O.Box 871804, Tempe, AZ 85287, USA

    Carlos Castillo-Chavez

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Cintrón-Arias, A., Sánchez, F., Wang, X., Castillo-Chavez, C., Gorman, D.M., Gruenewald, P.J. (2009). The Role of Nonlinear Relapse on Contagion Amongst Drinking Communities. In: Chowell, G., Hyman, J.M., Bettencourt, L.M.A., Castillo-Chavez, C. (eds) Mathematical and Statistical Estimation Approaches in Epidemiology. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2313-1_14

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