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THE DEMON DRINK

Part of: Mathematical sociology

Published online by Cambridge University Press:  02 November 2017

MARK IAN NELSON Open the ORCID record for MARK IAN NELSON [Opens in a new window] ,
PETER HAGEDOORN  and
ANNETTE L. WORTHY
MARK IAN NELSON*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia email nelsonm@member.ams.org, ph247@uowmail.edu.au, annie@uow.edu.au
PETER HAGEDOORN
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia email nelsonm@member.ams.org, ph247@uowmail.edu.au, annie@uow.edu.au
ANNETTE L. WORTHY
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia email nelsonm@member.ams.org, ph247@uowmail.edu.au, annie@uow.edu.au
*
✉nelsonm@member.ams.org
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Abstract

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We provide a qualitative analysis of a system of nonlinear differential equations that model the spread of alcoholism through a population. Alcoholism is viewed as an infectious disease and the model treats it within a sir framework. The model exhibits two generic types of steady-state diagram. The first of these is qualitatively the same as the steady-state diagram in the standard sir model. The second exhibits a backwards transcritical bifurcation. As a consequence of this, there is a region of bistability in which a population of problem drinkers can be sustained, even when the reproduction number is less than one. We obtain a succinct formula for this scenario when the transition between these two cases occurs.

Keywords

alcohol consumptionbackwards bifurcationbinge drinkingcollege studentsepidemiologyequilibriasocial influencestability

MSC classification

Primary: 92D30: Epidemiology
Secondary: 91D30: Social networks 92D25: Population dynamics (general)
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 2 , October 2017 , pp. 135 - 154
Copyright
© 2017 Australian Mathematical Society 

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