<p>The aim of this work is to propose and analyze a generalized epidemiological model for alcohol problems. This model is constructed by combining a recognized ordinary differential equation (ODE) model for alcohol problems with nonlinear incidence rates. Using the Lyapunov stability theory, global asymptotic stability (GAS) of a unique alcohol-free equilibrium point is established, whereas, the GAS of a unique alcohol-present (alcoholism) equilibrium point is investigated based on the Poincaré-Bendixon theorem and the Bendixson-Dulac criterion. As an important consequence, global dynamics of the alcohol model under consideration is fully determined, which provides an improvement to a previous stability analysis of the original ODE model. Additionally, the theoretical findings are supported by a set of illustrative numerical experiments.</p>