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The Demon Drink

Journal Article


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.

Publication Date


  • 2017

Citation


  • Nelson, M. Ian., Hagedoorn, P. & Worthy, A. L. (2017). The Demon Drink. ANZIAM Journal, 59 (2), 135-154.

Scopus Eid


  • 2-s2.0-85033378420

Number Of Pages


  • 19

Start Page


  • 135

End Page


  • 154

Volume


  • 59

Issue


  • 2

Place Of Publication


  • United Kingdom

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.

Publication Date


  • 2017

Citation


  • Nelson, M. Ian., Hagedoorn, P. & Worthy, A. L. (2017). The Demon Drink. ANZIAM Journal, 59 (2), 135-154.

Scopus Eid


  • 2-s2.0-85033378420

Number Of Pages


  • 19

Start Page


  • 135

End Page


  • 154

Volume


  • 59

Issue


  • 2

Place Of Publication


  • United Kingdom