The demon drink


  • Mark Ian Nelson
  • Peter Hagedoorn University of Wollongong
  • Annette L. Worthy University of Wollongong



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


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

Author Biographies

Peter Hagedoorn, University of Wollongong

(former honours student) School of Mathematics and Applied Statistics

Annette L. Worthy, University of Wollongong

Associate Professor, Department of Mathematics and Applied Statistics





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