THE DEMON DRINK

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...

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Bibliographic Details
Published in:The ANZIAM journal 2017-10, Vol.59 (2), p.135-154
Main Authors: NELSON, MARK IAN, HAGEDOORN, PETER, WORTHY, ANNETTE L.
Format: Article
Language:English
Subjects:
Alcoholism
Beer
Disease
Epidemiology
Peer relationships
Voters
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Summary: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.
ISSN:1446-1811
1446-8735
DOI:10.1017/S1446181117000347