Document Type

Article

Publication Date

1-1-2018

Publication Source

Proceedings of the 2017 Undergraduate Mathematics Day

Inclusive pages

1-10

Abstract

In this paper, we study how media awareness campaigns influence the spread and persistence of drinking behavior in a community. Here, we present a compartmental population model with an additional differential equation to describe the dynamics of media awareness campaigns in combating problem drinking ([10], [12], [21]). Our model indicates a basic reproductive number, R0, where there exists an asymptotically stable drinking-free equilibrium if R0 < 1, and a unique endemic state, which appears to be stable when R0 > 1. We found that the following two components affect the basic reproductive number: the strength of peer influence of problem drinkers on susceptibles and the average overall time spent in the problem drinking environment. Furthermore, we conclude that the existence of media awareness programs and effective treatment options does not eliminate a drinking culture in the community, it only temporarily alleviate the issue. To support our findings, we present analytical and numerical approaches.

Keywords

Alcoholism, Media Campaigns, SIR dynamic

Disciplines

Mathematics

Comments

This paper was presented Saturday, Nov. 11, 2017, as part of Undergraduate Mathematics Day at the University of Dayton. Launched in 2003, Undergraduate Mathematics Day is held in odd-numbered years and alternates with the Biennial Alumni Career Seminar. The conference coincides with the annual Schraut Memorial Lecture, named Kenneth “Doc” Schraut, a mathematics faculty member from 1940 to 1978 and department chair from 1954 to 1970.

The 2017 invited lecturer was Joseph Gallian, the Morse Alumni Distinguished University Professor of Teaching at the University of Minnesota Duluth and a past president of the Mathematical Association of America. He presented the lecture “Breaking Driver’s License Codes.”

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