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Modelling drinking with information
Author(s) -
Giacobbe Andrea,
Mulone Giuseppe,
Straughan Brian,
Wang Wendi
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4312
Subject(s) - mathematics , population , dynamical systems theory , variable (mathematics) , dynamics (music) , qualitative analysis , dynamical system (definition) , mathematical analysis , qualitative research , psychology , demography , pedagogy , social science , physics , quantum mechanics , sociology
In this article, we propose a mathematical model that describes the dynamics of a population divided into susceptible drinkers, moderate drinkers, and heavy drinkers subject to an external influence. The external influence is modelled using a supplementary dynamical variable that is not a group of individuals but that enters the equations affecting the choices of the population classes. The system we define can be investigated using two simplified systems (one of which is a real subsystem), which model the populations of susceptible and moderate drinkers or susceptible and heavy drinkers independently. The dynamics of these two subsystems can be described exhaustively. The full system is too rich in possible scenarios, but its qualitative behaviour is connected to that of the two simplified systems. We make a complete description only in one particular case by means of numerical simulations. Copyright © 2017 John Wiley & Sons, Ltd.