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Mathematical Biosciences and Engineering (MBE)
 

Influence of environmental factors on college alcohol drinking patterns

Pages: 1281 - 1300, Volume 10, Issue 5/6, October/December 2013      doi:10.3934/mbe.2013.10.1281

 
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Ridouan Bani - Department of Mathematics, Northeastern Illinois University, 5500 N. St. Louis Ave, Chicago, IL 60625-4699, United States (email)
Rasheed Hameed - Department of Mathematics, Northeastern Illinois University, 5500 N. St. Louis Ave, Chicago, IL 60625-4699, United States (email)
Steve Szymanowski - Department of Mathematics, Northeastern Illinois University, 5500 N. St. Louis Ave, Chicago, IL 60625-4699, United States (email)
Priscilla Greenwood - Department of Mathematics, University of British Columbia, 1209 Math Annex, Vancouver, BC V6T 1Z2, Canada (email)
Christopher M. Kribs-Zaleta - Mathematics Department, University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408, United States (email)
Anuj Mubayi - Department of Mathematics, Northeastern Illinois University, 5500 N. St. Louis Ave, BBH 214A, Chicago, IL 60625-4699, United States (email)

Abstract: Alcohol abuse is a major problem, especially among students on and around college campuses. We use the mathematical framework of [16] and study the role of environmental factors on the long term dynamics of an alcohol drinking population. Sensitivity and uncertainty analyses are carried out on the relevant functions (for example, on the drinking reproduction number and the extinction time of moderate and heavy drinking because of interventions) to understand the impact of environmental interventions on the distributions of drinkers. The reproduction number helps determine whether or not the high-risk alcohol drinking behavior will spread and become persistent in the population, whereas extinction time of high-risk drinking measures the effectiveness of control programs. We found that the reproduction number is most sensitive to social interactions, while the time to extinction of high-risk drinkers is significantly sensitive to the intervention programs that reduce initiation, and the college drop-out rate. The results also suggest that in a population, higher rates of intervention programs in low-risk environments (more than intervention rates in high-risk environments) are needed to reduce heavy drinking in the population.

Keywords:  Alcohol drinking, social interactions, drinking environments, time to extinction, critical community size, alcohol intervention programs.
Mathematics Subject Classification:  Primary: 60H10, 91E99; Secondary: 37H10.

Received: February 2013;      Accepted: June 2013;      Available Online: August 2013.

 References