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Global stability for a binge drinking model with two stages. (English) Zbl 1253.91157

Summary: A more realistic two-stage model for binge drinking problem is introduced, where the youths with alcohol problems are divided into those who admit the problem and those who do not admit it. We also consider the direct transfer from the class of susceptible individuals towards the class of admitting drinkers. Mathematical analyses establish that the global dynamics of the model are determined by the basic reproduction number, \(R_0\). The alcohol-free equilibrium is globally asymptotically stable, and the alcohol problems are eliminated from the population if \(R_0 < 1\). A unique alcohol-present equilibrium is globally asymptotically stable if \(R_0 > 1\). Numerical simulations are also conducted in the analytic results.

MSC:

91D30 Social networks; opinion dynamics
37N40 Dynamical systems in optimization and economics
91B74 Economic models of real-world systems (e.g., electricity markets, etc.)
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