Some Kinds Of Binge Drinking Models In The Complex Networks

Various problems caused by alcohol addiction have become increasingly serious,recently, which cause a general concern of the community. According to the results of an investigation on the public health of Chinese and their drinking in 2007, there were approximately 84.1% men and 29.3% women drinking, in which the proportion of heavy drinkers accounts for 16.1% and 2.5%, respectively. In China, about 114100 people die of alcohol poisoning and 2.737 million people get disabled each year,accounting for 1.3% and 3% of the total morbidity, respectively. Excessive drinking not only harms personal health, but also induces serious consequences for the family and society. Therefore, the analysis of alcohol problems and the attempt to seek measures of controlling alcohol addiction are necessary. Nowadays more and more researchers investigate the drinking behavior through building mathematical models.Firstly, we research the dynamic properties of the binge drinking model with the impact of media in the scale-free networks; Secondly, we add the population factor to our model, and simulate the drinking behavior with the nonlinear infectivity in the weighted networks.In chapter 1, we introduce the background, the development situation and the common theoretical tools of the drinking model. The theoretical basis of building models, and some relevant preliminaries are proposed in the paper.In chapter 2, we develop a binge drinking model with the complex network structure and media coverage. We research the effect of media coverage on the drinking behavior, calculate the basic reproduction number R0, prove the stability of the alcohol free equilibrium and the uniqueness of the alcohol present equilibrium. Furthermore, we verify the corresponding theoretical results by numerical simulations.The results show that media coverage does not influence R0, but it is an effective measure of controlling the drinking spread.In chapter 3, a class of alcohol models with the population dynamics factor are built in the scale-free networks. Firstly, we establish a drinking model with the linear infectivity in the unweighted scale-free networks and analyze the models’ dynamic properties; Secondly, binge drinking models with the nonlinear infectivity are researched in the fixed and adaptive weighted networks, respectively. In addition,we calculate the basic reproduction number, and mimic the drinking behavior by using numerical simulations. We find that the drinking behavior in the fixed weighted network is the most easily to break out and the infectivity exponent has a greater effect on the drinking threshold than the weight exponent.