Asymptotic Behavior Of Two Types Of Stochastic Rumor Models

There are always some stochastic disturbance in the propagation process of rumors,which influences the propagation trend of rumors.Therefore,it is of great significance to study the rumor model under stochastic disturbance to control the propagation of rumor.Based on this,this paper mainly studies the asymptotic behavior of two kinds of rumor models under stochastic disturbance.Chapter 1 introduces the research trends of stochastic rumor model and gives the main research content of this paper.Chapter 2 establishes a kind of stochastic rumor model(?) First,the existence and uniqueness of the global positive solution of the model is proved by the stopping time.Then,by constructing Lyapunov function,we study the pth moment exponential stability and almost surely exponential stability of the rumor free equilibrium of the model.In addition,we analyze the oscillation behavior and the stochastically persistence of the model.Finally,the theoretical results are verified by numerical simulation.The results in this paper generalize and improve the corresponding results in the existing literature.Chapter 3 discusses a stochastic rumor model with latency period(?)Firstly,we construct a suitable Lyapunov function to prove the existence of global positive solutions.Then,by using Ito’s formula and constructing Lyapunov function,we study the pth moment exponential stability and almost surely exponential stability of the rumor free equilibrium of the model.In addition,we analyze the oscillation behavior and the stochas-tically persistence of the model.Finally,the theoretical results are verified by numerical simulation.The results in this paper generalize and improve the corresponding results in the existing literature.Chapter 4 summarizes the results of this paper and gives the direction of future research.