Study Of Alcohol Models With Birth And Death Rates On Complex Networks

Wine has always been an object of concern.Since it appeared in people's lives as a drink,various problems caused by alcoholism have been increasing.So,many biological researchers have developed differential equation models to find ways to reduce alcohol abuse.In this paper,based on the dynamics of network infectious diseases,two kinds of drinking models are established.In Chapter 1,the background and present situation of the drinking model are described and the preparation knowledge related to this thesis is given.In Chapter 2,first,a novel SAITS alcoholism model on unweighted networks is introduced,in which alcoholics are divided into light problem alcoholics and heavy problem alcoholics.Susceptible individuals can enter into the compartment of heavy problem alcoholics directly by contacting with light problem alcoholics or heavy problem alcoholics and the heavy problem alcoholics who receive treatment can relapse into the compartment of heavy problem alcoholics are also considered.The dynamics of our model on unweighted networks,including the basic reproduction number,existence and stability of equilibria are studied.Second,the models with fixed weighted and adaptive weighted networks are introduced and investigated.Finally,numerical simulation verified theory results.In Chapter 3,first,a SAITS alcoholism with birth and death rates is introduced.Similarly chapter 2,the basis reproduction number,existence and stability of equilibria are studied.Second,the model with nonlinear infectivity are introduced and investigated.Finally,numerical simulation verified related conclusions.