Dynamic Analysis Of A Stochastic Rumor Propagation Model

Based on the classical rumors model,this paper proposes three different types of rumors propagation models to study the spread of rumors by considering the mechanisms of noise and time lag.We mainly study the existence,extinction,boundedness and balance points of rumors propagation model solutions,and through numerical simulation examples to verify the validity of the results.The main content of the article is divided into the following aspects:The first part is a stochastic rumor propagation model with white noise.Based on it,we select the appropriate Lyapunov functionals,by using Ito formulas,strong laws of num-bers,Chebyshev inequalities,and other basic.theoretical knowledge of stochastic differential equations.The existence,persistence and extinction of positive solutions of the rumors are es-tablished.Compared with the corresponding deterministic models,the threshold affected by the white noise is smaller than the basic reproduction number R0 of the deterministic system system.The second part is a rumor propagation model with time delayed.First,the existence of the global solution is obtained.Secondly,the sufficient conditions for the extinction of the rumor are established.Finally,the boundedness of solution is proved and some simulations are given to verify our results.The third part is a rumor propagation model with Levy noise.In this part,the asymptotic behaviors around the rumor free equilibrium and rumor epidemic equilibrium are obtained.And simulations verify our results.