Stability and optimal control for delayed rumor-spreading model with nonlinear incidence over heterogeneous networks

doi:10.1088/1674-1056/acb490

Abstract On the multilingual online social networks of global information sharing, the wanton spread of rumors has an enormous negative impact on people's lives. Thus, it is essential to explore the rumor-spreading rules in multilingual environment and formulate corresponding control strategies to reduce the harm caused by rumor propagation. In this paper, considering the multilingual environment and intervention mechanism in the rumor-spreading process, an improved ignorants-spreaders-1-spreaders-2-removers (I2SR) rumor-spreading model with time delay and the nonlinear incidence is established in heterogeneous networks. Firstly, based on the mean-field equations corresponding to the model, the basic reproduction number is derived to ensure the existence of rumor-spreading equilibrium. Secondly, by applying Lyapunov stability theory and graph theory, the global stability of rumor-spreading equilibrium is analyzed in detail. In particular, aiming at the lowest control cost, the optimal control scheme is designed to optimize the intervention mechanism, and the optimal control conditions are derived using the Pontryagin's minimum principle. Finally, some illustrative examples are provided to verify the effectiveness of the theoretical results. The results show that optimizing the intervention mechanism can effectively reduce the densities of spreaders-1 and spreaders-2 within the expected time, which provides guiding insights for public opinion managers to control rumors.

Keywords: rumor propagation heterogeneous network nonlinear incidence optimal control

Received: 25 September 2022
Revised: 16 December 2022
Accepted manuscript online: 19 January 2023

PACS:	87.23.Ge	(Dynamics of social systems)
	05.45.-a	(Nonlinear dynamics and chaos)
	02.30.Ks	(Delay and functional equations)
	02.30.Yy	(Control theory)

Fund: Project supported by the National Natural Science Foundation of People's Republic of China (Grant Nos. U1703262 and 62163035), the Special Project for Local Science and Technology Development Guided by the Central Government (Grant No. ZYYD2022A05), and Xinjiang Key Laboratory of Applied Mathematics (Grant No. XJDX1401).

Corresponding Authors: Haijun Jiang
E-mail: jianghaijunxju@163.com

Cite this article:

Xupeng Luo(罗续鹏), Haijun Jiang(蒋海军), Shanshan Chen(陈珊珊), and Jiarong Li(李佳容) Stability and optimal control for delayed rumor-spreading model with nonlinear incidence over heterogeneous networks 2023 Chin. Phys. B 32 058702

[1] Peterson W A and Gist N P 1951 Am. J. Sociol. 57 159
[2] Doerr B, Fouz M and Friedrich T 2012 Commun. ACM 55 70
[3] Vosoughi S, Roy D and Aral S 2018 Science 359 1146
[4] Wen S, Jiang J J, Xiang Y, Yu S, Zhou W and Jia W J 2014 IEEE Trans. Parallel Distrib. Syst. 25 3306
[5] Shalbafan M and Khademoreza N 2020 Am. J. Drug Alcohol Ab. 46 1
[6] Daley D J and Kendall D G 1964 Nature 204 1118
[7] Daley D J and Kendall D G 1965 IMA J. Appl. Math. 1 42
[8] Maki D P and Thomson M 1973 Mathematical Models and Applications (Prentice-Hall: Englewood Cliffs)
[9] Zhao Z J, Liu Y M and Wang K X 2016 Phys. A 443 263
[10] Li T T and Guo Y M 2021 Qual. Theor. Dyn. Syst. 20 84
[11] Tian Y and Ding X J 2019 Appl. Math. Comput. 363 124599
[12] Huo L A, Wang L and Zhao X M 2019 Phys. A 517 551
[13] Zhang Y H and Zhu J J 2022 Chin. Phys. B 31 060202
[14] Huo L A and Dong Y F 2022 Chin. Phys. B 31 030202
[15] Pastor-Satorras R and Vespignani A 2001 Phys. Rev. Lett. 86 3200
[16] Tanaka G, Morino K and Aihara K 2012 Sci. Rep. 2 232
[17] Watts D J and Strogatz S H 1998 Nature 393 440
[18] Zanette D H 2001 Phys. Rev. E 64 050901
[19] Barabási A L and Albert R 1999 Science 286 509
[20] Moreno Y, Nekovee M and Pacheco A F 2004 Phys. Rev. E 69 066130
[21] Zhu L H and Zhao H Y 2017 Int. J. Syst. Sci. 48 2064
[22] He Z B, Cai Z P, Yu J G, Wang X M, Sun Y C and Li Y S 2017 IEEE Trans. Veh. Technol. 66 2789
[23] Cao X Y, Chen Y, Jiang C X and Ray Liu K J 2016 IEEE Trans. Signal Inform. Process Netw. 2 595
[24] Li T T and Guo Y M 2022 Chaos Soliton. Fract. 156 111825
[25] Laarabi H, Labriji E, Rachik M and Kaddar A 2012 Nonlinear Anal. Modell. Control 17 448
[26] Zhang C M and Huang H T 2016 Phys. A 451 251
[27] Cheng Y Y, Huo L A and Zhao L J 2021 Inform. Sci. 564 237
[28] Zhong X J, Yang Y K, Miao R Q, Peng Y Q and Liu G Y 2022 Chin. Phys. B 31 040205
[29] Wang J L, Jiang H J, Ma T L and Hu C 2019 Chaos Soliton. Fract. 126 148
[30] Li J R, Jiang H J, Mei X H, Hu C and Zhang G L 2020 Inform. Sci. 536 391
[31] Yang S, Jiang H J, Hu C, Yu J and Li J R 2022 Adv. Differ. Equ. 2020 628
[32] Yu S Z, Yu Z Y, Jiang H J, Mei X H and Li J R 2020 Nonlinear Dyn. 100 2933
[33] Yu S Z, Yu Z Y, Jiang H J and Li J R 2021 Chaos Soliton. Fract. 145 110806
[34] Chen S S, Jiang H J, Li L and Li J R 2020 Chaos Soliton. Fract. 140 110206
[35] Xiao D M and Ruan S G 2007 Math. Biosci. 208 419
[36] Li C H 2015 Phys. A 427 234
[37] Zhu L H and Guan G 2019 Phys. A 533 121953
[38] Pastor-Satorras R and Vespignani A 2002 Phys. Rev. E 65 036104
[39] Huang S Y 2005 Int. J. Biomath. 9 1650009
[40] Chen F D 2005 J. Comput. Appl. Math. 180 33
[41] Guo H B, Li M and Shuai Z S 2006 Can. Appl. Math. Q. 14 259
[42] LaSalle J P 1976 The Stability of Dynamical Systems (Philadelphia: Woodhead) pp. 39-43
[43] Fleming W and Rishel R 1975 Deterministic and Stochastic Optimal Control (Berlin: Springer-Verlag) pp. 20-59
[44] Zhang H F and Fu X C 2009 Nonlinear Anal. 70 3273

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Stability and optimal control for delayed rumor-spreading model with nonlinear incidence over heterogeneous networks

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