Stability of a binge drinking model with delay

A more realistic binge drinking model with time delay is introduced. Time delay is used to represent the time lag of the immunity against drinking in our model. For the model without the time delay, using Routh-Hurwitz criterion, we obtain that the alcohol-free equilibrium is locally asymptotically stable if [Formula: see text]. We also obtain that the unique alcohol-present equilibrium is locally asymptotically stable if [Formula: see text]. For the model with time delay, the local stability of all the equilibria is derived. Furthermore, regardless of the time delay length, using comparison theorem and iteration technique, we obtain that the alcohol-free equilibrium is globally asymptotically stable under certain conditions. Numerical simulations are also conducted to illustrate and extend our analytic results.