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Chin. Phys. B, 2022, Vol. 31(6): 060202    DOI: 10.1088/1674-1056/ac48fa
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Ergodic stationary distribution of a stochastic rumor propagation model with general incidence function

Yuhuai Zhang(张宇槐) and Jianjun Zhu(朱建军)
College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
Abstract  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 $\widehat{\mathcal{R}}$0>1. That 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 of β and decrease the value of α and γ), which can effectively curb the rumor propagation.
Keywords:  rumor propagation model      general incidence function      Itô's formula      ergodic stationary distribution  
Received:  19 August 2021      Revised:  29 December 2021      Accepted manuscript online:  07 January 2022
PACS:  02.50.Ey (Stochastic processes)  
  02.50.Fz (Stochastic analysis)  
  05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)  
  87.10.Mn (Stochastic modeling)  
Fund: Project supported by the Funding for Outstanding Doctoral Dissertation in NUAA (Grant No. BCXJ18-09), the National Natural Science Foundation of China (Grant No. 72071106), and Postgraduate Research & Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX18 0234).
Corresponding Authors:  Yuhuai Zhang, Jianjun Zhu     E-mail:;

Cite this article: 

Yuhuai Zhang(张宇槐) and Jianjun Zhu(朱建军) Ergodic stationary distribution of a stochastic rumor propagation model with general incidence function 2022 Chin. Phys. B 31 060202

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