Study On The Dynamic Properties Of The Mathematical Models Of Quitting Smoking

Smoking behavior is often communicable,that is,a person's smoking behavior will affect the surrounding population.In this paper,three kinds of differential equation models are established to study the propagation mode of smoking behavior,and to provide theoretical basis and quantitative basis for controlling smoking behavior through theoretical analysis and numerical simulations.Specifically,we study different models of quitting smoking,focusing on the threshold of whether smoking behavior is popular-basic reproduction number.By using Routh-Hurwitz criterion,Lyapunov function,LaSalle invariant principle,second additive compound matrix and algebraic method etc.,the global dynamics of the models are discussed.Based on the partial rank correlation coefficients(PRCC s),the influence of some parameters in the models on smokers' transmission is analyzed.According to numerical simulations,the influence of parameters on the models and the stability of the equilibria are shown intuitively.On the other hand,the epidemic trend of the disease is given under different parameters.Finally,we give the strategies to control the spread of smoking behavior.In the first chapter,we introduce the research background,development history and commonly used theoretical tools of infectious disease dynamics.In addition,the background of the research models in this paper is described in detail,and some preparatory knowledge required for this study is given.In the second chapter,a kind of quitting smoking model with nonlinear incidence is discussed.The theoretical analysis and numerical simulations provide the basis for controlling the spread of smoking behavior.In the third chapter,a kind of quitting smoking dynamics model with the Beddington-DeAngelis function is discussed.The dynamics of the model is analyzed,and the numerical simulations show the theoretical analysis results intuitively.In the fourth chapter,we discuss a kind of quitting smoking dynamics model with human behavior.Through theoretical analysis,the local and global dynamics of the model and the specific influence of human behavior on the propagation of smokers are obtained.The numerical simulations show the theoretical analysis results directly.The advantages of this paper compared with other similar articles are summarized in the fifth chapter.