Two Kinds Of Binge Drinking Models With Time Delay

The drinking behavior of young people's caused widespread public concern.It is well known that alcohol abuse not only harm to personal health,but also lead to a series of negative influence on the society,for example,violence,antisocial and criminal behavior.Long-term drinking almost have harm to the human body each organ,for example,liver cirrhosis,heart disease,pancreatitis.So,it is of great practical significance to study alcoholism transmission mechanism and then take effective measures to prevent and control it.At present,researches on alcoholism mainly based on differential equation to establish mathematical model,then analysis the alcoholism propagation and give out relevant control strategies.Firstly,we research the dynamic behavior of a more realistic drinking model with two stages and time delay;Secondly,we simulate the drinking behavior with relapse and time delay.In chapter 1,we give the definition of alcoholism,introduces the development of alcoholism,research background and significance.In this paper,some preliminary knowledge of need is also given.In chapter 2,a more realistic SAIRS drinking model with two stages and time delay is introduced,we divide alcoholics into light problem alcoholics and heavy problem alcoholics,and consider the recovery to not drink alcohol or moderate drinkers transformation.The main purpose of this paper is to study the effect of time delay spread for alcoholism.The basic reproduction numbers obtained by analyzing,and the stability of two equilibrium is proved.The results show that time delay does not influence,but it can influence the dynamic behavior of the system.In chapter 3,a SIRS class of alcohol models with relapse and time delay are built.Main purpose is to study the effect of recurrence and delay spread on drinking behavior.The basic reproduction numbers obtained by analyzing,and the stability of two equilibrium is proved.We find that the relapse rate has a great influence on drinking behavior,effective control of relapse rates can greatly reduce the number of alcoholics.