Stability, Hopf Bifurcation and Optimal Control of Multilingual Rumor-Spreading Model with Isolation Mechanism

Shuzhen Yu (), Zhiyong Yu and Haijun Jiang
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Shuzhen Yu: School of Mathematics Science, Xinjiang Normal University, Urumqi 830017, China
Zhiyong Yu: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
Haijun Jiang: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China

Mathematics, 2022, vol. 10, issue 23, 1-29

Abstract: The propagation of rumors on online social networks (OSNs) brings an awful lot of trouble to people’s life and society. Aiming at combating rumors spreading on OSNs, two novel rumor-propagation models without and with time delays are proposed, which combine with the influence of the immune mechanism, isolation mechanism and network structure. Firstly, we analyze the existence of rumor equilibria and obtain some existence conditions of backward bifurcation. Secondly, the local stabilities of rumor-free and rumor equilibria are proved by using the Jacobian matrix method, and some critical conditions for the existence of Hopf bifurcation are acquired by selecting critical parameters and delays as bifurcation parameters. Furthermore, an optimal control method is proposed, which can prevent the spread of rumors within an expected time period and minimize the cost of control. Finally, some numerical simulations are provided to verify the effectiveness of the proposed theoretical results.

Keywords: stability; rumor spreading; online social networks; Hopf bifurcation; optimal control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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