The demon drink

Mark Ian Nelson, Peter Hagedoorn, Annette L. Worthy

Abstract


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.

doi:10.1017/S1446181117000347

Keywords


alcohol consumption, backwards bifurcation, binge drinking, college students, epidemiology, equilibria, social influence, stability.



DOI: http://dx.doi.org/10.21914/anziamj.v59i0.10721



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.