Study on stability and information sharing sensitivity in blockchain diffusion dynamics with the fractional-order delayed SEIR model

Peng Wan; Shujian Ma; Yuaoran Liu; Jiangwen Ju; Sumei Pan; Jun Wang; Minyi Xu; Peng Wan; Shujian Ma; Yuaoran Liu; Jiangwen Ju; Sumei Pan; Jun Wang; Minyi Xu

doi:10.3934/math.2026174

AIMS Mathematics

2026, Volume 11, Issue 2: 4335-4368. doi: 10.3934/math.2026174

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Study on stability and information sharing sensitivity in blockchain diffusion dynamics with the fractional-order delayed SEIR model

1.
School of Mathematical and Physical Sciences, Nanjing Tech University, Nanjing, 211816, China
2.
Institute of Block Chain and Complex Systems, Nanjing Tech University, Nanjing, 211816, China
3.
Institute of Finance and Technology, University College London, 66-72 Gower Street, London WC1E 6EA, United Kingdom
4.
School of Economics and Management, Nanjing Tech University, Nanjing, 211816, China
5.
Nanjing Vocational Institute of Railway Technology, Nanjing, 210031, China

Received: 11 November 2025 Revised: 02 February 2026 Accepted: 04 February 2026 Published: 12 February 2026
MSC : 91G45, 34D20, 34K37

In this study, we tackled the issue of insufficient information sharing among small and medium-sized enterprises (SMEs) in supply chain finance (SCF). Blockchain technology (BCT), with its tamper-proof and decentralized nature, offers a viable solution. The adoption of BCT can be viewed as a diffusion process, which we modeled by extending the classic SEIR epidemic framework with Caputo fractional-order derivatives and time-delay effects. We also introduced a nonlinear index to measure potential adopters' sensitivity to information sharing and examined its influence on diffusion speed and adoption scale. Theoretical analysis showed that when the basic reproduction number exceeds one, a unique endemic equilibrium emerges. Moreover, the interplay between time delays and fractional-order memory effects can trigger Hopf bifurcation, leading to oscillatory adoption patterns. Numerical simulations revealed a negative correlation between the fractional order and critical time delay. Importantly, while greater sensitivity to information sharing generally accelerates diffusion and enlarges the final adoption scale under certain conditions, exceeding an optimal threshold may reduce diffusion efficiency. These results suggest that although enhanced information sharing fosters blockchain adoption, it must be carefully managed to avoid adverse outcomes. This study offers theoretical insights and practical guidance for optimizing blockchain promotion strategies in SCF.
- supply chain finance,
- blockchain technology diffusion,
- fractional-order delayed SEIR model,
- information sharing sensitivity,
- stability analysis
Citation: Peng Wan, Shujian Ma, Yuaoran Liu, Jiangwen Ju, Sumei Pan, Jun Wang, Minyi Xu. Study on stability and information sharing sensitivity in blockchain diffusion dynamics with the fractional-order delayed SEIR model[J]. AIMS Mathematics, 2026, 11(2): 4335-4368. doi: 10.3934/math.2026174

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Abstract

In this study, we tackled the issue of insufficient information sharing among small and medium-sized enterprises (SMEs) in supply chain finance (SCF). Blockchain technology (BCT), with its tamper-proof and decentralized nature, offers a viable solution. The adoption of BCT can be viewed as a diffusion process, which we modeled by extending the classic SEIR epidemic framework with Caputo fractional-order derivatives and time-delay effects. We also introduced a nonlinear index to measure potential adopters' sensitivity to information sharing and examined its influence on diffusion speed and adoption scale. Theoretical analysis showed that when the basic reproduction number exceeds one, a unique endemic equilibrium emerges. Moreover, the interplay between time delays and fractional-order memory effects can trigger Hopf bifurcation, leading to oscillatory adoption patterns. Numerical simulations revealed a negative correlation between the fractional order and critical time delay. Importantly, while greater sensitivity to information sharing generally accelerates diffusion and enlarges the final adoption scale under certain conditions, exceeding an optimal threshold may reduce diffusion efficiency. These results suggest that although enhanced information sharing fosters blockchain adoption, it must be carefully managed to avoid adverse outcomes. This study offers theoretical insights and practical guidance for optimizing blockchain promotion strategies in SCF.

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