Dynamical Behavior Analysis Of Two Kinds Of Transmission Models

In this paper,a dynamic model of the coupling effects of individual transmission and media publicity is established based on the characteristics of smoking transmission.Based on animal detection,considering the influence of environmental factors and detection intensity,a stochastic model of animal epidemic detection information is established.The dynamic behavior of the model is studyed by stability,bifurcation theory and stochastic dynamics method.The details are as follows:In the second chapter,a mathematical model reflecting the dynamics of smoking transmission is established,considering two risk factors,individual transmission and media publicity,and the effects of these two factors on the behavior of dynamic model studied.It is found that the system occurs backward bifurcation,meaning that smokers are likely to persist when the smoking transmission thresholdR₀(27)1.In addition,the smoking-free equilibrium point is locally asymptotically stable is found,indicating the importance of smoking at a low level.Finally,whenR₀(29)1,the system has a unique smoking-present and the model is uniformly persistent,suggesting that smoking will persist forever.In the third chapter,a new stochastic model based on animal epidemic detection information,considering the environmental factors and the detection intensity is established.The existence and uniqueness by using the stopping-time and Lyapunov method is proved,and the asymptotic behavior of the solution of the stochastic model near the disease free equilibrium and endemic equilibrium of the corresponding deterministic model is discussed.In the end,the paper summarizes the whole paper,clarifies the practical significance of the study,and provides new ideas for further research.