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2013, 10(5&6): 1281-1300. doi: 10.3934/mbe.2013.10.1281

Influence of environmental factors on college alcohol drinking patterns

1. 

Department of Mathematics, Northeastern Illinois University, 5500 N. St. Louis Ave, Chicago, IL 60625-4699, United States, United States, United States

2. 

Department of Mathematics, University of British Columbia, 1209 Math Annex, Vancouver, BC V6T 1Z2, Canada

3. 

Mathematics Department, University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408, United States

4. 

Department of Mathematics, Northeastern Illinois University, 5500 N. St. Louis Ave, BBH 214A, Chicago, IL 60625-4699, United States

Received  February 2013 Revised  June 2013 Published  August 2013

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.
Citation: Ridouan Bani, Rasheed Hameed, Steve Szymanowski, Priscilla Greenwood, Christopher M. Kribs-Zaleta, Anuj Mubayi. Influence of environmental factors on college alcohol drinking patterns. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1281-1300. doi: 10.3934/mbe.2013.10.1281
References:
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Ph.D thesis, Arizona State University in Tempe, 2008. Google Scholar

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Socio-Economic Planning Sciences, 44 (2010), 45-56. doi: 10.1016/j.seps.2009.02.002.  Google Scholar

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Mathematical Biosciences and Engineering, 7 (2010), 689-719. doi: 10.3934/mbe.2010.7.687.  Google Scholar

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The Journal of Theoretical Biology, 262 (2010), 177-185. doi: 10.1016/j.jtbi.2009.09.012.  Google Scholar

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Addiction, 106 (2011), 749-758. doi: 10.1111/j.1360-0443.2010.03254.x.  Google Scholar

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Mathematical Population Studies, 20 (2013), 27-53. doi: 10.1080/08898480.2013.748588.  Google Scholar

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Journal of Studies on Alcohol and Drugs, 60 (1999), 90. Google Scholar

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Sage Publications, Beverly Hills, 1976. Google Scholar

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Journal of Studies on Alcohol and Drugs, 70 (2009), 805-821. Google Scholar

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show all references

References:
[1]

Lecture Notes in Statistics, 151, Springer-Verlag, New York, 2000. doi: 10.1007/978-1-4612-1158-7.  Google Scholar

[2]

Journal of the Royal Statistical Society, 120 (1957), 48-70. doi: 10.2307/2342553.  Google Scholar

[3]

Journal of Studies on Alcohol and Drugs, 67 (2006), 591-599. Google Scholar

[4]

Journal of Criminal Justice, 22 (1994), 171-180. doi: 10.1016/0047-2352(94)90111-2.  Google Scholar

[5]

Journal of Alcohol and Drug Education, 41 (1996), 13-33. Google Scholar

[6]

Journal of Studies on Alcohol and Drugs, 69 (2008), 397-405. Google Scholar

[7]

Annual Review of Public Health, 26 (2005), 259-279. Google Scholar

[8]

Journal of Studies on Alcohol and Drugs Supplement, 16 (2009), 12-20. Google Scholar

[9]

Stochastic Processes and Their Applications, 6 (1978), 223-240.  Google Scholar

[10]

Journal of Theoretical Biology, 254 (2008), 178-196. doi: 10.1016/j.jtbi.2008.04.011.  Google Scholar

[11]

Ph.D thesis, Arizona State University in Tempe, 2008. Google Scholar

[12]

Socio-Economic Planning Sciences, 44 (2010), 45-56. doi: 10.1016/j.seps.2009.02.002.  Google Scholar

[13]

Mathematical Biosciences and Engineering, 7 (2010), 689-719. doi: 10.3934/mbe.2010.7.687.  Google Scholar

[14]

The Journal of Theoretical Biology, 262 (2010), 177-185. doi: 10.1016/j.jtbi.2009.09.012.  Google Scholar

[15]

Addiction, 106 (2011), 749-758. doi: 10.1111/j.1360-0443.2010.03254.x.  Google Scholar

[16]

Mathematical Population Studies, 20 (2013), 27-53. doi: 10.1080/08898480.2013.748588.  Google Scholar

[17]

Advances in Applied Probability, 28 (1996), 895-932. doi: 10.2307/1428186.  Google Scholar

[18]

Mathematical Biosciences, 179 (2002), 1-19. doi: 10.1016/S0025-5564(02)00098-6.  Google Scholar

[19]

Theoretical Population Biology, 67 (2005), 203-216. Google Scholar

[20]

Disponiblea, (2008). Available from: http://www.maths.uq.edu.au/~pkp/papers/qsds/qsds.pdf. Google Scholar

[21]

Journal of Studies on Alcohol and Drugs, 60 (1999), 90. Google Scholar

[22]

Sage Publications, Beverly Hills, 1976. Google Scholar

[23]

Journal of Studies on Alcohol and Drugs, 70 (2009), 805-821. Google Scholar

[24]

American Journal of Public Health, 85 (1995), 335-340. doi: 10.2105/AJPH.85.3.335.  Google Scholar

[25]

Journal of Studies on Alcohol and Drugs, 68 (2007), 208-219. Google Scholar

[26]

University of California, 2003. Available from: http://www.ucop.edu/sas. Google Scholar

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