JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (7): 70-81.doi: 10.6040/j.issn.1671-9352.0.2025.191

• Mathematical Biology • Previous Articles    

Study on astochastic SIR model with noise interference in higher-order networks

LI Siyu, GUO Xiang, LIU Maoxing*   

  1. School of Science, Beijing University of Civil Engineering and Architecture, Beijing 102616, China
  • Published:2026-07-01

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Abstract: To explore how random noise affects the spread of infectious diseases in higher-order networks, this study develops a stochastic SIR epidemic model rooted in simplicial complexes. Firstly, the model constructs a social network of node connections using simplicial complexes, leverages mean field theory to model the temporal evolution of network nodes, and integrates white noise perturbations into the transmission dynamics. Then, through dynamic analysis, the disease outbreak threshold is deduced, establishing the existence and uniqueness of the systems global positive solution under specific conditions, alongside proving disease extinction and asymptotic oscillations of the solution. Finally, simulations on two real-world networks confirm the role of noise intensity in disease spread. Critically, networks with differing topological properties exert distinct influences on transmission: higher average degrees of simplices expedite disease propagation.

Key words: simplicial complex, white noise, outbreak threshold, Lyapunov method

CLC Number: 

  • O175
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