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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:
[1]

Hakan Andersson and Tom Britton, "Stochastic Epidemic Models and their Statistical Analysis,", Lecture Notes in Statistics, 151 (2000). doi: 10.1007/978-1-4612-1158-7.

[2]

Maurice S. Bartlett, Measles periodicity and community size,, Journal of the Royal Statistical Society, 120 (1957), 48. doi: 10.2307/2342553.

[3]

Richard J. Bruan, Robert A. Wilson, Johan A. Pelesko, J. Robert Buchanan and James P. Gleeson, Applications of small-world network theory in alcohol epidemiology,, Journal of Studies on Alcohol and Drugs, 67 (2006), 591.

[4]

Ruth C. Engs and David J. Hanson, Boozing and brawling on campus: A national study of violent problems associated with drinking over the past decade,, Journal of Criminal Justice, 22 (1994), 171. doi: 10.1016/0047-2352(94)90111-2.

[5]

Ruth C. Engs, Beth A. Diebold and David J. Hanson, The drinking patterns and problems of a national sample of college students, 1994,, Journal of Alcohol and Drug Education, 41 (1996), 13.

[6]

Jennifer A. Epstein, Kenneth W. Griffin and Gilbert J. Botvin, A social influence model of alcohol use for inner-city adolescents: Family drinking, perceived drinking norms, and perceived social benefits of drinking,, Journal of Studies on Alcohol and Drugs, 69 (2008), 397.

[7]

Ralph Hingson, Timothy Heeren, Michael Winter and Henry Wechsler, Magnitude of alcohol-related mortality and morbidity among US college students ages 18-24: Changes from 1998 to 2001,, Annual Review of Public Health, 26 (2005), 259.

[8]

Ralph W. Hingson, Wenxing Zha and Elissa R. Weitzman, Magnitude of and trends in alcohol-related mortality and morbidity among US college students ages 18-24, 1998-2005,, Journal of Studies on Alcohol and Drugs Supplement, 16 (2009), 12.

[9]

Thomas G. Kurtz, Strong approximation theorems for density dependent markov chains,, Stochastic Processes and Their Applications, 6 (1978), 223.

[10]

Simeone Marion, Ian B. Hogue, Christian J. Ray and Denise E. Kirschner, A methodology for performing global uncertainity and sensitivity analysis in systems biology,, Journal of Theoretical Biology, 254 (2008), 178. doi: 10.1016/j.jtbi.2008.04.011.

[11]

Anuj Mubayi, "The Role of Environmental Context in the Dynamics and Control Use,", Ph.D thesis, (2008).

[12]

Anuj Mubayi, Priscilla E. Greenwood, Carlos Castillo-Chavez, Paul Gruenewald and Dennis M. Gorman, The impact of relative residence times on the distribution of heavy drinkers in highly distinct environment,, Socio-Economic Planning Sciences, 44 (2010), 45. doi: 10.1016/j.seps.2009.02.002.

[13]

Anuj Mubayi, Christopher Kribs-Zaleta, Maia Martcheva and Carlos Castillo-Chavez, A cost-based comparison of quarantine strategies for new emerging diseases,, Mathematical Biosciences and Engineering, 7 (2010), 689. doi: 10.3934/mbe.2010.7.687.

[14]

Anuj Mubayi, Carlos Castillo-Chavez, Gerardo Chowell, Christopher Kribs-Zaleta, S. Niyamat A. Siddiqui, Narnedra Kumar and Pradeep Das, Transmission dynamics and underreporting of Kala-azar in the Indian state of Bihar,, The Journal of Theoretical Biology, 262 (2010), 177. doi: 10.1016/j.jtbi.2009.09.012.

[15]

Anuj Mubayi, Priscilla Greenwood, Xiaohong Wang, Carlos Castillo-Chavez, Dennis M. Gorman, Paul Gruenewald and Robert F. Saltz, Types of drinkers and drinking settings: An application of a mathematical model,, Addiction, 106 (2011), 749. doi: 10.1111/j.1360-0443.2010.03254.x.

[16]

Anuj Mubayi and Priscilla E. Greenwood, Contextual interventions for controlling alcohol drinking,, Mathematical Population Studies, 20 (2013), 27. doi: 10.1080/08898480.2013.748588.

[17]

Ingemar Nåsell, The quasi-stationary distribution of the closed endemic SIS model,, Advances in Applied Probability, 28 (1996), 895. doi: 10.2307/1428186.

[18]

Ingemar Nåsell, Stochastic models of some endemic infections,, Mathematical Biosciences, 179 (2002), 1. doi: 10.1016/S0025-5564(02)00098-6.

[19]

Ingemar Nåsell, A new look at the critical community size for childhood infections,, Theoretical Population Biology, 67 (2005), 203.

[20]

Phil K. Pollet, Quasi-stationary distributions: A bibliography,, Disponiblea, (2008).

[21]

Brian M. Quigley and Lorraine Collins, The modeling of alcohol consumption: A meta-analytic review,, Journal of Studies on Alcohol and Drugs, 60 (1999).

[22]

Rudolph J. Rummel, "Social Behavior and Interaction in Conflict and War. Vol. 2,", Sage Publications, (1976).

[23]

Richard A. Scribner, Azmy S. Ackleh, Ben G. Fitzpatrick, Geoffrey Jacquez, Jeremy J. Thibodeaux, Robert Rommel and Neal 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.

[24]

Richard A. Scribner, David P. MacKinnon and James H. Dwyer, The risk of assaultive violence and alcohol availability in Los Angeles county,, American Journal of Public Health, 85 (1995), 335. doi: 10.2105/AJPH.85.3.335.

[25]

Traci L. Toomey, Kathleen M. Lenk and Alexander C. Wagenaar, Environmental policies to reduce college drinking: Options and research findings,, Journal of Studies on Alcohol and Drugs, 68 (2007), 208.

[26]

, "UC Information Digest 2003, A Reference Guide on Student Access and Performance at the University of California,", University of California, (2003).

show all references

References:
[1]

Hakan Andersson and Tom Britton, "Stochastic Epidemic Models and their Statistical Analysis,", Lecture Notes in Statistics, 151 (2000). doi: 10.1007/978-1-4612-1158-7.

[2]

Maurice S. Bartlett, Measles periodicity and community size,, Journal of the Royal Statistical Society, 120 (1957), 48. doi: 10.2307/2342553.

[3]

Richard J. Bruan, Robert A. Wilson, Johan A. Pelesko, J. Robert Buchanan and James P. Gleeson, Applications of small-world network theory in alcohol epidemiology,, Journal of Studies on Alcohol and Drugs, 67 (2006), 591.

[4]

Ruth C. Engs and David J. Hanson, Boozing and brawling on campus: A national study of violent problems associated with drinking over the past decade,, Journal of Criminal Justice, 22 (1994), 171. doi: 10.1016/0047-2352(94)90111-2.

[5]

Ruth C. Engs, Beth A. Diebold and David J. Hanson, The drinking patterns and problems of a national sample of college students, 1994,, Journal of Alcohol and Drug Education, 41 (1996), 13.

[6]

Jennifer A. Epstein, Kenneth W. Griffin and Gilbert J. Botvin, A social influence model of alcohol use for inner-city adolescents: Family drinking, perceived drinking norms, and perceived social benefits of drinking,, Journal of Studies on Alcohol and Drugs, 69 (2008), 397.

[7]

Ralph Hingson, Timothy Heeren, Michael Winter and Henry Wechsler, Magnitude of alcohol-related mortality and morbidity among US college students ages 18-24: Changes from 1998 to 2001,, Annual Review of Public Health, 26 (2005), 259.

[8]

Ralph W. Hingson, Wenxing Zha and Elissa R. Weitzman, Magnitude of and trends in alcohol-related mortality and morbidity among US college students ages 18-24, 1998-2005,, Journal of Studies on Alcohol and Drugs Supplement, 16 (2009), 12.

[9]

Thomas G. Kurtz, Strong approximation theorems for density dependent markov chains,, Stochastic Processes and Their Applications, 6 (1978), 223.

[10]

Simeone Marion, Ian B. Hogue, Christian J. Ray and Denise E. Kirschner, A methodology for performing global uncertainity and sensitivity analysis in systems biology,, Journal of Theoretical Biology, 254 (2008), 178. doi: 10.1016/j.jtbi.2008.04.011.

[11]

Anuj Mubayi, "The Role of Environmental Context in the Dynamics and Control Use,", Ph.D thesis, (2008).

[12]

Anuj Mubayi, Priscilla E. Greenwood, Carlos Castillo-Chavez, Paul Gruenewald and Dennis M. Gorman, The impact of relative residence times on the distribution of heavy drinkers in highly distinct environment,, Socio-Economic Planning Sciences, 44 (2010), 45. doi: 10.1016/j.seps.2009.02.002.

[13]

Anuj Mubayi, Christopher Kribs-Zaleta, Maia Martcheva and Carlos Castillo-Chavez, A cost-based comparison of quarantine strategies for new emerging diseases,, Mathematical Biosciences and Engineering, 7 (2010), 689. doi: 10.3934/mbe.2010.7.687.

[14]

Anuj Mubayi, Carlos Castillo-Chavez, Gerardo Chowell, Christopher Kribs-Zaleta, S. Niyamat A. Siddiqui, Narnedra Kumar and Pradeep Das, Transmission dynamics and underreporting of Kala-azar in the Indian state of Bihar,, The Journal of Theoretical Biology, 262 (2010), 177. doi: 10.1016/j.jtbi.2009.09.012.

[15]

Anuj Mubayi, Priscilla Greenwood, Xiaohong Wang, Carlos Castillo-Chavez, Dennis M. Gorman, Paul Gruenewald and Robert F. Saltz, Types of drinkers and drinking settings: An application of a mathematical model,, Addiction, 106 (2011), 749. doi: 10.1111/j.1360-0443.2010.03254.x.

[16]

Anuj Mubayi and Priscilla E. Greenwood, Contextual interventions for controlling alcohol drinking,, Mathematical Population Studies, 20 (2013), 27. doi: 10.1080/08898480.2013.748588.

[17]

Ingemar Nåsell, The quasi-stationary distribution of the closed endemic SIS model,, Advances in Applied Probability, 28 (1996), 895. doi: 10.2307/1428186.

[18]

Ingemar Nåsell, Stochastic models of some endemic infections,, Mathematical Biosciences, 179 (2002), 1. doi: 10.1016/S0025-5564(02)00098-6.

[19]

Ingemar Nåsell, A new look at the critical community size for childhood infections,, Theoretical Population Biology, 67 (2005), 203.

[20]

Phil K. Pollet, Quasi-stationary distributions: A bibliography,, Disponiblea, (2008).

[21]

Brian M. Quigley and Lorraine Collins, The modeling of alcohol consumption: A meta-analytic review,, Journal of Studies on Alcohol and Drugs, 60 (1999).

[22]

Rudolph J. Rummel, "Social Behavior and Interaction in Conflict and War. Vol. 2,", Sage Publications, (1976).

[23]

Richard A. Scribner, Azmy S. Ackleh, Ben G. Fitzpatrick, Geoffrey Jacquez, Jeremy J. Thibodeaux, Robert Rommel and Neal 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.

[24]

Richard A. Scribner, David P. MacKinnon and James H. Dwyer, The risk of assaultive violence and alcohol availability in Los Angeles county,, American Journal of Public Health, 85 (1995), 335. doi: 10.2105/AJPH.85.3.335.

[25]

Traci L. Toomey, Kathleen M. Lenk and Alexander C. Wagenaar, Environmental policies to reduce college drinking: Options and research findings,, Journal of Studies on Alcohol and Drugs, 68 (2007), 208.

[26]

, "UC Information Digest 2003, A Reference Guide on Student Access and Performance at the University of California,", University of California, (2003).

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