Impact of media coverage on the drinking dynamics in the scale-free network

Abstract

A binge drinking model with the impact of media in the scale-free network is proposed. The basic reproduction number (Formula presented.) is derived by the next generation matrix method. Stability of the alcohol free equilibrium is proved by the comparison theorem. Existence and uniqueness of the alcohol present equilibrium is also obtained. Furthermore, the permanence of the system and the influence of media coverage on the drinking dynamics are studied, and the difference between our model on heterogeneous and homogeneous networks is also discussed. Numerical simulations are presented to illustrate our theoretical results. Our results show that media coverage does not change the value of (Formula presented.) but it is an effective measure in reducing alcohol problems.