The demon drink
Nelson, Mark Ian ; Hagedoorn, Peter ; Worthy, Annette L.
ANZIAM Journal, Tome 59 (2018), / Harvested from Australian Mathematical Society
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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. doi:10.1017/S1446181117000347

Publié le : 2018-01-01
DOI : https://doi.org/10.21914/anziamj.v59i0.10721 
@article{10721,
     title = {The demon drink},
     journal = {ANZIAM Journal},
     volume = {59},
     year = {2018},
     doi = {10.21914/anziamj.v59i0.10721},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/10721}
}

Nelson, Mark Ian; Hagedoorn, Peter; Worthy, Annette L. The demon drink. ANZIAM Journal, Tome 59 (2018) . doi : 10.21914/anziamj.v59i0.10721. http://gdmltest.u-ga.fr/item/10721/