Dynamic modeling of behavior change
Authors:
H. T. Banks, Keri L. Rehm, Karyn L. Sutton, Christine Davis, Lisa Hail, Alexis Kuerbis and Jon Morgenstern
Journal:
Quart. Appl. Math. 72 (2014), 209-251
MSC (2010):
Primary 91E10, 34K29, 62G10
DOI:
https://doi.org/10.1090/S0033-569X-2014-01296-3
Published electronically:
February 10, 2014
MathSciNet review:
3186233
Full-text PDF Free Access
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Abstract: We consider a conceptual and quantitative modeling approach for investigating dynamic behavior change. While the approach is applicable to behavior change in eating disorders, smoking, substance abuse and other behavioral disorders, here we present our novel dynamical systems modeling approach to understand the processes governing an individual’s behavior in the context of problem drinking. Recent advances in technology have resulted in large intensive longitudinal data sets which are particularly well suited for study within such frameworks. However, the lack of previous work in this area (specifically, on the inter- and intra-personal factors governing the drinking behavior of individuals) renders this a daunting and unique challenge. As a result, issues which are typically routine in mathematical modeling require considerable effort such as the determination of key quantities of interest, and the timescale on which to represent them. We discuss the construction of an initial mathematical model for two starkly distinct individuals and make a case for the potential for such efforts to help in understanding the underlying mechanisms responsible for behavior change in problem drinkers.
References
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- R. Scribner, A. S. Ackleh, B. G. Fitzpatrick, G. Jacquez, J. J. Thibodeaux, R. Rommel, and N. Simonsen, A systems approach to college drinking: Development of a deterministic model for testing alcohol control policies, Journal of Studies on Alcohol and Drugs, 70 (2009), 805–821.
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References
- A. S. Ackleh, B. G. Fitzpatrick, S. Scribner, J. J. Thibodeaux, and N. Simonsen, Ecosystem modeling of college drinking: Parameter estimation and comparing models to data, Mathematical and Computer Modelling, 50 (2009), 481–497.
- B. M. Adams, H. T. Banks, M. Davidian, and E. S. Rosenberg, Estimation and prediction with HIV-treatment interruption data, CRSC-TR05-40, NCSU, October, 2005; Bulletin of Mathematical Biology, 69 (2007), 563–584.
- H.T. Banks, M. Davidian, S. Hu, G.M. Kepler and E.S. Rosenberg, Modeling HIV immune response and validation with clinical data, Journal of Biological Dynamics, 2 (2008), 357–385. MR 2467293 (2009k:92118)
- H. T. Banks, M. Davidian, J. R. Samuels, Jr., Karyn L. Sutton, An inverse problem statistical methodology summary, in “Mathematical and Statistical Estimation Approaches in Epidemiology” (eds. Gerardo Chowell, Carlos Castillo-Chavez, James M. Hyman, and Luis Bettencourt), Springer, Berlin, Heidelberg, New York, 2009, pp. 249–302; Center for Research in Scientific Computation Technical Report, CRSC-TR08-01, January, 2008, North Carolina State University.
- H.T. Banks, J.L. Davis, S.L. Ernstberger, S. Hu, E. Artimovich, A.K. Dhar and C.L. Browdy, A comparison of probabilistic and stochastic formulations in modeling growth uncertainty and variability, CRSC-TR08-03, NCSU, February, 2008; J. Biological Dynamics, 3 (2009), 130–148. MR 2573998 (2010k:92133)
- H.T. Banks and B.G. Fitzpatrick, Inverse problems for distributed systems: statistical tests and ANOVA, LCDS/CSS Report 88-16, Brown University, July 1988; Proc. International Symposium on Math. Approaches to Envir. and Ecol. Problems, Springer Lecture Notes in Biomath., 81 (1989), 262–273. MR 1041334
- H.T. Banks and B.G. Fitzpatrick, Statistical methods for model comparison in parameter estimation problems for distributed systems, CAMS Tech. Rep. 89-4, September, 1989, University of Southern California; J. Math. Biol., 28 (1990), 501–527. MR 1069009 (91m:92002)
- H.T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems, Birkhauser, Boston, 1989. MR 1045629 (91b:93085)
- H. T. Banks, K. L. Rehm, K. L. Sutton, C. Davis, L. Hail, A. Kuerbis, and J. Morgenstern, Model formulation of drinking behavior using longitudinal data, Center for Research in Scientific Computation Technical Report, CRSC-TR10-19, December, 2010, North Carolina State University.
- H. T. Banks, K. L. Rehm, K. L. Sutton, C. Davis, L. Hail, A. Kuerbis, and J. Morgenstern, Dynamic modeling of behavior change in problem drinkers, Center for Research in Scientific Computation Technical Report, CRSC-TR11-08, August, 2011, North Carolina State University.
- H.T. Banks and H.T. Tran, Mathematical and Experimental Modeling of Physical and Biological Processes, CRC Press, Boca Raton, 2009. MR 2488750 (2010f:93024)
- S. T. Chermack, F. C. Blow, E. S. L. Gomberg, S. A. Mudd, and E. M. Hill, Older adult controlled drinkers and abstainers, Journal of Substance Abuse, 8 (1996), 453–462.
- A. Cintron-Arias, F. Sanchez, S. Wang, X. C. Castillo-Chavez, D. M. Gorman, and P. J. Gruenewald, The role of nonlinear relapse on contagion amongst drinking communities, In: Mathematical and Statistical Estimation Approaches in Epidemiology (eds. G. Chowell, J. M. Hyman, L. M. A. Bettencourt, and C. Castillo Chavez), Springer, New York, 2009, 343–360.
- M. Davidian and D.M. Giltinan, Nonlinear Models for Repeated Measurement Data, Chapman and Hall, London, 2000.
- M. Field and W.M. Cox, Attentional bias in addictive behaviors: A review of its development, causes, and consequences, Drug and Alcohol Dependence, 97 (2008), 1–20.
- B. Frey, and L. J. Lau, Towards a mathematical model of government behaviour, Zeitschrift fur Nationalokonomie, 28 (1968), 355–380.
- D. M. Gorman, P. J. Gruenewald, P. J Hanlon, I. Mezic, L. A. Waller, C. Castillo-Chavez, E. Bradley, and J. Mezic, Implications of systems dynamic models and control theory for environmental approaches to the prevention of alcohol- and other drug use-related problems, Substance Use and Misuse, 39 (2004), 1713–1750.
- K. A. Gregoire, and D. J. Schultz, Substance-abusing child welfare parents: Treatment and child placement outcomes, Child Welfare, 80 (2001), 433–452.
- S. Grossberg, Adaptive resonance in development, perception and cognition, In: Proceedings of the Symposium in Applied Mathematics of AMS and SIAM (ed. S. Grossberg), American Mathematical Society, Philadelphia, PA, 1980, 107–156. MR 657411 (84k:92010a)
- S. Grossberg, Psychophysiological substrates of schedule interactions and behavioral contrast, In: Proceedings of the Symposium in Applied Mathematics of AMS and SIAM (ed. S. Grossberg), American Mathematical Society, Philadelphia, PA, 1980, 157–186. MR 657412 (84k:92010b)
- R. V. Hogg, and E. A. Tanis, A Brief Course in Mathematical Statistics, Pearson Education, Boston San Francisco New York, 2008.
- I. T. Jolliffe, Principal Component Analysis, 2nd ed., Springer-Verlag, New York, 2002. MR 2036084 (2004k:62010)
- M. P. King, and J. A. Tucker, Behavior change patterns and strategies distinguishing moderation drinking and abstinence during the natural resolution of alcohol problems without treatment, Psychology of Addictive Behaviors, 14 (2000), 48–55.
- D. C. Lay, Linear Algebra and its Applications, 3rd ed., Pearson Education, Boston, San Francisco, New York, 2003.
- G. A. Marlatt, M. E. Larimer, J. S. Baer, and L. A. Quigley, Harm reduction for alcohol problems: Moving beyond the controlled drinking controversy, Behavior Therapy, 24 (1993), 461–503.
- C. D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, Philadelphia, PA, 2000. MR 1777382
- E. E. McCollum, T. S. Nelson, R. A. Lewis, and T. S. Trepper, Partner relationship quality and drug use as predictors of women’s substance abuse treatment outcome, American Journal of Drug and Alcohol Abuse, 31 (2005), 111–127.
- B. S. McCrady, To have but one true friend: Implications for practice of research of alcohol use disorders and social networks, Psychology of Addictive Behaviors, 18 (2004), 113–121.
- T. B. Moyers, T. Martin, J. K. Manuel, S. M. Hendrickson, and W. R. Miller, Assessing competence in the use of motivational interviewing, Journal of Substance Abuse Treatment, 28 (2005), 19–26.
- A. Mubayi, P. E. Greenwood, C. Castillo-Chavez, P. J. Gruenewald, and D. M. Gorman, The impact of relative residence times on the distribution of heavy drinkers in highly distinct environments, Socio-Economic Planning Sciences, 44 (2010), 45–56.
- A. Mubayi, The role of environmental context in the dynamics and control of alcohol use, Arizona State University, December 2008. MR 2712620
- National Institute of Alcohol Abuse and Alcoholism, NIAAA council approves definition of binge drinking, NIAAA Newsletter, 3 (2004), 3.
- J. Rasul, R. Rommel, G. M. Jacquez, B. G. Fitzpatrick, A. S. Ackleh, N. Simonsen, and R. Scribner, Heavy episodic drinking on college campuses: Does changing the legal drinking age make a difference?, Journal of Studies on Alcohol and Drugs, to appear.
- R. J. Rummel, Applied Factor Analysis, Northwestern Univ., Evanston, 1970.
- F. Sanchez, X. Wang, C. Castillo-Chavez, D. M. Gorman, and P. J. Gruenewald, Drinking as an epidemic – a simple mathematical model, In: Therapist’s Guide to Evidence-Based Relapse Prevention (eds. K. Witkiewitz, G. A. Marlatt), Academic Press, New York, 2007, 353–368.
- SAS Support, Principal Component Analysis, 1998, 1–56.
- R. Scribner, A. S. Ackleh, B. G. Fitzpatrick, G. Jacquez, J. J. Thibodeaux, R. Rommel, and N. Simonsen, A systems approach to college drinking: Development of a deterministic model for testing alcohol control policies, Journal of Studies on Alcohol and Drugs, 70 (2009), 805–821.
- S. L. A. Straussner, Gender and substance abuse, In: Gender & addictions (eds. S. L. A. Straussner, and E. Zelvin), Jason Aronson Inc., Northvale, NJ, 1997, 3–28.
- TELESAGE, Smart Q 5.2 automated telephone survey software, Chapel Hill, NC, 2005.
- P. van Geert, A dynamic systems model of cognitive and language growth, Psychological Review, 98 (1991), 3–53.
- P. van Geert, A dynamic systems model of basic developmental mechanisms: Piaget, Vygotsky, and beyond, Psychological Review, 105 (1998), 634–677.
- S. J. Wilson, M. A. Sayette, and J. Fiez, Prefrontal responses to drug cues: a neurocognitive analysis, Nature Neuroscience, 7 (2004), 211–214.
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Additional Information
Jon Morgenstern
Address at time of publication:
Center for Research in Scientific Computation, Center for Quantitative Science in Biomedicine, North Carolina State University, Raleigh, North Carolina 27695-8212;
Substance Abuse Services, Department of Psychiatry, Columbia University Medical Center, 180 Fort Washington Avenue HP-240, New York, New York 10032
Keywords:
Mathematical psychology,
inverse problems,
delay differential equations,
behavior change,
model comparison
Received by editor(s):
October 25, 2011
Published electronically:
February 10, 2014
Article copyright:
© Copyright 2014
Brown University
The copyright for this article reverts to public domain 28 years after publication.
