Abstract

Alcohol consumption is a problem of both social and health interest since consumption at an early age increases the probability of developing alcohol dependence, along with a series of risks associated with diseases, violence, and injuries. In young people, the first episode and recurrence of alcohol consumption usually occur in the form of binge drinking, in which peers assume a protective or risky role. Mathematical modeling of binge drinking has frequently been performed based on interactions with other consumption patterns, defined in terms of quantity and frequency, without considering that the periodicity of excessive (or compulsive) alcohol consumption is associated with specific social contexts, such as parties, where mainly social drinkers adopt this pattern. Our objective is to analyze the influence exerted by social drinkers on their peers who adopt excessive alcohol consumption, as well as the recurrence and persistence of harmful consumption. We formulate a mathematical model described by a Filippov system, where the “contagion” dynamic is based on two transfer sequences according to the workweek and weekend. Our findings establish that depending on the parameter values of the model, four asymptotic periodic dynamics can arise. In addition to this, the existence of a trade-off between protective and risk factors is evidenced, allowing evaluation of the effect of social variables on binge drinking prevalence.