Ergodic stationary distribution of a stochastic rumor propagation model with general incidence function

作     者：张宇槐 朱建军 Yuhuai Zhang;Jianjun Zhu

作者机构：College of Economics and ManagementNanjing University of Aeronautics and AstronauticsNanjing 211106China 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2022年第31卷第6期

页      面：145-154页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 0811[工学-控制科学与工程] 

基　　金：supported by the Funding for Outstanding Doctoral Dissertation in NUAA(Grant No.BCXJ18-09) the National Natural Science Foundation of China(Grant No.72071106) Postgraduate Research&Practice Innovation Program of Jiangsu Province,China(Grant No.KYCX180234)。 

主　　题：rumor propagation model general incidence function It?’s formula ergodic stationary distribution 

摘      要：In daily lives,when emergencies occur,rumors will spread widely on the internet.However,it is quite difficult for the netizens to distinguish the truth of the information.The main reasons are the uncertainty of netizens’behavior and attitude,which make the transmission rates of these information among social network groups be not fixed.In this paper,we propose a stochastic rumor propagation model with general incidence function.The model can be described by a stochastic differential equation.Applying the Khasminskii method via a suitable construction of Lyapunov function,we first prove the existence of a unique solution for the stochastic model with probability one.Then we show the existence of a unique ergodic stationary distribution of the rumor model,which exhibits the ergodicity.We also provide some numerical simulations to support our theoretical results.The numerical results give us some possible methods to control rumor propagation.Firstly,increasing noise intensity can effectively reduce rumor propagation when R_(0)1That is,after rumors spread widely on social network platforms,government intervention and authoritative media coverage will interfere with netizens’opinions,thus reducing the degree of rumor propagation.Secondly,speed up the rumor refutation,intensify efforts to refute rumors,and improve the scientific quality of netizen(i.e.,increase the value ofβand decrease the value ofαandγ),which can effectively curb the rumor propagation.