Higher-order dynamics and optimal control of SEIR rumor propagation models in homogeneous and heterogeneous networks

Tong Jiang; Xijian Lv; Dongmei Fan; Qiang Li; Junxian Yang; Tong Jiang; Xijian Lv; Dongmei Fan; Qiang Li; Junxian Yang

doi:10.3934/mmc.2026006

Mathematical Modelling and Control

2026, Volume 6, Issue 1: 72-87. doi: 10.3934/mmc.2026006

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Research article

Higher-order dynamics and optimal control of SEIR rumor propagation models in homogeneous and heterogeneous networks

1.
School of Information and Artificial Intelligence, Anhui Agricultural University, Hefei 230036, China
2.
School of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, China

Received: 11 September 2025 Revised: 10 October 2025 Accepted: 17 November 2025 Published: 03 March 2026

Higher-order interactions play a critical role in driving the rapid propagation of rumors. We propose a susceptible–exposed–infected–removed (SEIR) model that incorporates group interactions as higher-order terms. Detailed analysis reveals the emergence of bistability in both homogeneous and heterogeneous networks and shows that the bistable region expands as group interactions intensify. By utilizing group interactions as the bifurcation parameter, we derive explicit bifurcation conditions for both network types. For heterogeneous networks, we establish global stability criteria and propose an effective control strategy. Numerical simulations demonstrate the significant influence of group interactions on the bistable region. This study advances the theoretical understanding of rumor propagation dynamics and provides a practical strategy for controlling rumor propagation.
- simplicial complexes,
- rumor propagation,
- higher-order dynamics,
- optimal control
Citation: Tong Jiang, Xijian Lv, Dongmei Fan, Qiang Li, Junxian Yang. Higher-order dynamics and optimal control of SEIR rumor propagation models in homogeneous and heterogeneous networks[J]. Mathematical Modelling and Control, 2026, 6(1): 72-87. doi: 10.3934/mmc.2026006

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Abstract

Higher-order interactions play a critical role in driving the rapid propagation of rumors. We propose a susceptible–exposed–infected–removed (SEIR) model that incorporates group interactions as higher-order terms. Detailed analysis reveals the emergence of bistability in both homogeneous and heterogeneous networks and shows that the bistable region expands as group interactions intensify. By utilizing group interactions as the bifurcation parameter, we derive explicit bifurcation conditions for both network types. For heterogeneous networks, we establish global stability criteria and propose an effective control strategy. Numerical simulations demonstrate the significant influence of group interactions on the bistable region. This study advances the theoretical understanding of rumor propagation dynamics and provides a practical strategy for controlling rumor propagation.

References

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