Abstract
A binge drinking model with the impact of media in the scale-free network is proposed. The basic reproduction number R_0 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 R_{0} but it is an effective measure in reducing alcohol problems.
Highlights
It is well known that excessive drinking is harm to personal health, and induce serious consequences for the family and society
Our results show that media coverage does not change the value of R0 but it is an effective measure in reducing alcohol problems
The organization of this paper is as follows: In “The model formulation” section, we propose a binge drinking model with the influence of media coverage in the scale-free network
Summary
It is well known that excessive drinking is harm to personal health, and induce serious consequences for the family and society. Huo and Wang (2014) developed a nonlinear binge drinking model with the effect of awareness programs, they assumed that the cumulative density of media increased at a rate proportional to the number of heavy drinkers. Their results showed that media coverage was an effective method in reducing alcohol problems. By using the mean-field theory and numerical simulation, they showed that both local and contact awareness can raise the epidemic thresholds while the global awareness cannot Their results showed that individual behaviors in the presence of an infectious disease had a.
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