Modeling peer influence effects on the spread of high-risk alcohol consumption behavior

Alcohol dependence is among the main healthy risky behavior due to the high relevance of negative health and social effect. We study a mathematical model, given by nonlinear ordinary differential equations, describing the spread of high–risk alcohol consumption behavior within a community of individuals. We describe the peer-influence effects on alcohol addiction by assuming that susceptibles become heavy drinkers through the mechanism of imitation. We show that the model may exhibit the phenomenon of backward bifurcation. This means that alcohol problems may persist in the population even if the basic reproduction number is less than one. Nonlinear stability analysis of equilibria is also provided.