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

doi:10.1088/1674-1056/ac48fa

中国物理B ›› 2022, Vol. 31 ›› Issue (6): 60202-060202.doi: 10.1088/1674-1056/ac48fa

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

收稿日期:2021-08-19 修回日期:2021-12-29 接受日期:2022-01-07 出版日期:2022-05-17 发布日期:2022-05-26
通讯作者: Yuhuai Zhang, Jianjun Zhu E-mail:zyhmath@yeah.net;zhujianjun@nuaa.edu.cn
基金资助:
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).

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

Received:2021-08-19 Revised:2021-12-29 Accepted:2022-01-07 Online:2022-05-17 Published:2022-05-26
Contact: Yuhuai Zhang, Jianjun Zhu E-mail:zyhmath@yeah.net;zhujianjun@nuaa.edu.cn
Supported by:
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).

摘要/Abstract

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 $\widehat{\mathcal{R}}$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.

关键词: rumor propagation model, general incidence function, Itô's formula, ergodic stationary distribution

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.

Key words: rumor propagation model, general incidence function, Itô's formula, ergodic stationary distribution

中图分类号: (Stochastic processes)

02.50.Ey

02.50.Fz (Stochastic analysis) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 87.10.Mn (Stochastic modeling)

Yuhuai Zhang(张宇槐) and Jianjun Zhu(朱建军). Ergodic stationary distribution of a stochastic rumor propagation model with general incidence function[J]. 中国物理B, 2022, 31(6): 60202-060202.

Yuhuai Zhang(张宇槐) and Jianjun Zhu(朱建军). Ergodic stationary distribution of a stochastic rumor propagation model with general incidence function[J]. Chin. Phys. B, 2022, 31(6): 60202-060202.

参考文献

[1] Al-Tuwairqi S, Arabia S, Al-Sheikh S and Al-Amoudi R 2015 Open Access Libr. J. 02 1
[2] Anderson R M and May R M 1978 J. Anim. Ecol. 47 219
[3] Bai Z G and Zhou Y C 2012 Nonlinear Anal. Real World Appl. 13 1060
[4] Capasso V and Serio G 1978 Math. Biosci. 42 43
[5] Daley D J and Kendal D G 1964 Nature 204 1118
[6] Daley D J and Kendal D G 1965 IMA J. Appl. Math. 1 42
[7] Dauhoo M Z, Juggurnath D and Adam N R B 2016 Math. Soc. Sci. 82 85
[8] Dong S, Fan F H and Huang Y C 2018 Phys. A 492 10
[9] Gao X Y, Cai Y L, Rao F, Fu S M and Wang W M 2018 Comput. Math. Appl. 75 424
[10] Grabowski A, Kruszwska N and Kosinki R A 2008 Phys. Rev. E 78 066110
[11] Higham D J 2001 SIAM Rev. 43 525
[12] Huo L A, Dong Y F and Lin T T 2021 Chin. Phys. B 30 080201
[13] Iribarren J L and More E 2009 Phys. Rev. Lett. 103 038702
[14] Jain A, Dhar J and Gupta V 2019 Phys. A 519 227
[15] Jia F J and Lv G Y 2018 Phys. A 490 613
[16] Jia F J, Lv G Y, Wang S F and Zou G A 2018 J. Stat. Mech. 2018 023502
[17] Kaddar A 2010 Nonlinear Anal. Model. Control. 15 299
[18] Kawachi K 2008 Nonlinear Anal. Real World Appl. 9 1989
[19] Kermack W O and McKendrick A G 1927 Proc. Royal Soc. Lond. Series A 115 700
[20] Khan M A, Khan Y, Khan T W and Islam S 2017 Int. J. Biomath. 10 1750096
[21] Khasminskii R 2012 Stochastic Stability of Differential Equations, 2nd edn. (Berlin: Springer)
[22] Li J R, Jiang H J, Yu Z Y and Hu C 2019 Appl. Math. Comput. 359 374
[23] Lind P G, Da Silva L R, Andrade Jr J J and Herrmann H J 2007 Phys. Rev. E 76 036117
[24] Liu W M, Hethcote H W and Levin S A 1987 J. Math. Biol. 25 359
[25] Liu W M, Levin S A and Iwasa Y 1986 J. Math. Biol. 23 187
[26] Maki D P and Thomson M 1973 Mathematical Models and Applications, with Emphasis on Social, Life, and Management Sciences (New Jersey: Prentice-Hall)
[27] Mao X 1997 Stochastic Differential Equations and Their Applications (Chichester: Horwood)
[28] Qian Z, Tang S T, Zhang X and Zheng Z M 2015 Phys. A 429 95
[29] Strang G 1988 Linear Algebra and Its Application (Singapore: Thomson Learning)
[30] Wang W D and Ruan S G 2004 J. Math. Anal. Appl. 291 775
[31] Xiao Y N and Tang S Y 2010 Nonlinear Anal. Real World Appl. 11 4154
[32] Xu R and Ma Z E 2009 Chaos Solitons Fractals 41 2319
[33] Zan Y J 2018 Chaos Solitons Fractals 110 191
[34] Zanette D H 2001 Phys. Rev. E 64 050901
[35] Zanette D H 2002 Phys. Rev. E 65 041908
[36] Zhu C and Yin G 2007 SIAM J. Control Optim. 46 1155
[37] Zhu L and Wang Y G 2017 Phys. A 469 750
[38] Zhang Y, Chen S H and Gao S J 2016 Adv. Differ. Equ-NY 2016 1
[39] Zhang Y H and Zhu J J 2018 Phys. A 503 862

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

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

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