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Dynamics of simplicial SEIRS epidemic model: global asymptotic stability and neural Lyapunov functions

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Abstract

The transmission of infectious diseases on a particular network is ubiquitous in the physical world. Here, we investigate the transmission mechanism of infectious diseases with an incubation period using a networked compartment model that contains simplicial interactions, a typical high-order structure. We establish a simplicial SEIRS model and find that the proportion of infected individuals in equilibrium increases due to the many-body connections, regardless of the type of connections used. We analyze the dynamics of the established model, including existence and local asymptotic stability, and highlight differences from existing models. Significantly, we demonstrate global asymptotic stability using the neural Lyapunov function, a machine learning technique, with both numerical simulations and rigorous analytical arguments. We believe that our model owns the potential to provide valuable insights into transmission mechanisms of infectious diseases on high-order network structures, and that our approach and theory of using neural Lyapunov functions to validate model asymptotic stability can significantly advance investigations on complex dynamics of infectious disease.

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Acknowledgements

W. Yang is supported by the STCSM (Grant Nos. 21511100200, 22ZR1407300 and 22dz1200502). W. Lin is supported by the STCSM (Grant Nos. 22JC1401402, 22JC1402500 and 2021SHZDZX0103), the IPSMEC (Grant No. 2023ZKZD04), and the NSFC (Grant No. 11925103).

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Author notes

  1. Yukun Zou and Xiaoxiao Peng have contributed equally to this work.

Authors and Affiliations

  1. Research Institute of Intelligent Complex Systems, Fudan University, 220 Handan Road, Shanghai, 200433, China

    Yukun Zou, Xiaoxiao Peng, Wei Yang, Jingdong Zhang & Wei Lin

  2. Shanghai Center for Mathematical Sciences and School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai, 200433, China

    Xiaoxiao Peng, Wei Yang, Jingdong Zhang & Wei Lin

  3. Shanghai Artificial Intelligence Laboratory, Shanghai, 200232, China

    Wei Yang & Wei Lin

  4. Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, 220 Handan Road, Shanghai, 200433, China

    Yukun Zou & Wei Lin

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  1. Yukun Zou
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Correspondence to Wei Yang.

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Zou, Y., Peng, X., Yang, W. et al. Dynamics of simplicial SEIRS epidemic model: global asymptotic stability and neural Lyapunov functions. J. Math. Biol. 89, 12 (2024). https://doi.org/10.1007/s00285-024-02119-3

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