Dynamic analysis and control of online information dissemination model considering information beneficiaries

Xuechao Zhang; Yuhan Hu; Shichang Lu; Haomiao Guo; Xiaoyan Wei; Jun li; Xuechao Zhang; Yuhan Hu; Shichang Lu; Haomiao Guo; Xiaoyan Wei; Jun li

doi:10.3934/math.2025229

AIMS Mathematics

2025, Volume 10, Issue 3: 4992-5020. doi: 10.3934/math.2025229

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Research article

Dynamic analysis and control of online information dissemination model considering information beneficiaries

1.
School of Business Administration, Liaoning Technical University, Huludao, Liaoning, China
2.
School of Science, University of Science and Technology Liaoning, Anshan, Liaoning, China
3.
School of Economics and Law, University of Science and Technology Liaoning, Anshan, Liaoning, China

Received: 19 December 2024 Revised: 20 February 2025 Accepted: 27 February 2025 Published: 06 March 2025
MSC : 34D20, 49J15, 37D35

With the rapid rise and widespread adoption of social media, theoretical research on the dynamics of online information dissemination has become increasingly important. Therefore, we developed a new model of information diffusion that took into account the influence of information recipients on the diffusion of information. First, initially, the basic reproduction number of the model was calculated. Then, we analyzed the existence and stability of the equilibrium point. Next, based on the principle of Pontryagin's maximum principle, a control strategy was derived to effectively enhance the propagation of information. Numerical simulations verified the results of theoretical analysis. The results showed that increasing the proportion of propagators and the probability of beneficiaries transitioning into propagators significantly accelerated the speed and extent of information diffusion.
- information spreading,
- information beneficiaries,
- basic reproduction number,
- differential equation,
- stability analysis
Citation: Xuechao Zhang, Yuhan Hu, Shichang Lu, Haomiao Guo, Xiaoyan Wei, Jun li. Dynamic analysis and control of online information dissemination model considering information beneficiaries[J]. AIMS Mathematics, 2025, 10(3): 4992-5020. doi: 10.3934/math.2025229

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Abstract

With the rapid rise and widespread adoption of social media, theoretical research on the dynamics of online information dissemination has become increasingly important. Therefore, we developed a new model of information diffusion that took into account the influence of information recipients on the diffusion of information. First, initially, the basic reproduction number of the model was calculated. Then, we analyzed the existence and stability of the equilibrium point. Next, based on the principle of Pontryagin's maximum principle, a control strategy was derived to effectively enhance the propagation of information. Numerical simulations verified the results of theoretical analysis. The results showed that increasing the proportion of propagators and the probability of beneficiaries transitioning into propagators significantly accelerated the speed and extent of information diffusion.

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