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Modeling Alcohol Abuse Patterns in Hispanic-American Populations Using an SIR Model

Lora, Marissa Rose
http://rave.ohiolink.edu/etdc/view?acc_num=akron1302641058

Abstract Details

2011, Master of Science, University of Akron, Applied Mathematics.
SIR (Susceptible-Infected-Recovered) models may be used to examine the dynamics of socially based phenomena, such as alcohol abuse, by assuming such issues are a product of social contact and interaction. Recent studies have shown that there is an increase in the prevalence of abusive drinking behavior in the Hispanic-Immigrant population due to the increase in interaction with the U.S. population. By altering the governing differential equations of the SIR model, it is possible to model the increase in alcohol abuse in the Hispanic population. The Sanchez et al. model is analyzed by seeking steady state solutions and performing a linear stability analysis. We find that the base state is stable if the rate at which individuals enter the drinking sub-population is less than the rate at which individuals leave the drinking sub-population. For the bifurcating solution, the upper branch is stable and the lower branch is unstable. If the population lies on the upper branch, then there exists a finite population of abusive drinkers in the population. Finally, the effect of the standard population on the Hispanic population is examined through various examples. The standard population may have a great impact on the Hispanic population if the rate at which Hispanics come into contact with individuals from the standard population is large enough.
Curtis Clemons, Dr. (Advisor)
Gerald Young, Dr. (Advisor)
Robert Peralta, Dr. (Committee Member)
J. Patrick Wilber, Dr. (Committee Member)
74 p.
Mathematics
acculturation; SIR; epidemiology; alcohol abuse; Hispanic

Recommended Citations

Citations

  • Lora, M. R. (2011). Modeling Alcohol Abuse Patterns in Hispanic-American Populations Using an SIR Model [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302641058

    APA Style (7th edition)

  • Lora, Marissa. Modeling Alcohol Abuse Patterns in Hispanic-American Populations Using an SIR Model. 2011. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1302641058.

    MLA Style (8th edition)

  • Lora, Marissa. "Modeling Alcohol Abuse Patterns in Hispanic-American Populations Using an SIR Model." Master's thesis, University of Akron, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302641058

    Chicago Manual of Style (17th edition)

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© 2011, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.