Modeling And Analysis Of Dynamics In Drinking Addiction

This dissertation focuses on dynamics of alcohol addiction.Based on compartmental models in epidemiology,two classes of alcohol addiction dynamical models are established.Using the fundamental theory of differential equations,dynamical systems,we analysize the dynamics of the models,some sufficient conditions for the stability of the equalibria and the uniform persistence are obtained.Moreover,some numerical examples are given to illustrate effectiveness of the derived theoretical results.In the first chapter,background and research situation of alcohol addiction dynamics are introduced.Some relevant preliminary knowledge and theoretical tools needed in the paper are given.Also,we present our main research work in the dissertation.The second chapter,referring to modeling method of epidemic dynamics,we divide the copulation into four groups: the occasional drink,heavy drinking,participates in the treatment and recovery class.Considering the possibility of the recoveries return to the new drinkers,a class of corresponding dynamic model is established.By analyzing the dynamics of the model,basic reproduction number and its sensitivity as well as some sufficient condition ensuring the stability of the equilibrium,uniform persistence are obtained.Finally,some numerical simulations are given to verify the effectiveness of our results.In the third chapter,considering the infectiousness of the alcoholic on the susceptible drinkers,we use the compartmental models method to establish a class of dynamic model with abstinence and the dynamics of the model is studied.Some sufficient conditions for stability of the free addiction equilibration and persistence are obtained.The theoretical results are compared with numerical simulation and the effectiveness of the results is verified.