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Hopf bifurcation analysis for a delayed nonlinear-SEIR epidemic model on networks

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  • Barman, Madhab
  • Mishra, Nachiketa

Abstract

Using graph Laplacian diffusion, a delayed Susceptible–Exposed–Infected–Removed (SEIR) epidemic model with a non-linear incidence rate has been considered. This model incorporates a diffusion term that captures population mobility through a network. The local stability analysis for each steady state is demonstrated. Furthermore, we have explored the existence of Hopf bifurcation at the endemic equilibrium and addressed its direction using the Normal Form Theory and Center of Manifold Theorem. To visually illustrate our theoretical findings, we have performed computational experiments on a small-world Watts–Strogatz graph.

Suggested Citation

  • Barman, Madhab & Mishra, Nachiketa, 2024. "Hopf bifurcation analysis for a delayed nonlinear-SEIR epidemic model on networks," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
  • Handle: RePEc:eee:chsofr:v:178:y:2024:i:c:s0960077923012535
    DOI: 10.1016/j.chaos.2023.114351
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    References listed on IDEAS

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    1. Tian, Canrong & Ling, Zhi & Zhang, Lai, 2020. "Delay-driven spatial patterns in a network-organized semiarid vegetation model," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    2. Jin, Yu & Wang, Wendi & Xiao, Shiwu, 2007. "An SIRS model with a nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1482-1497.
    3. Cheng, Xinxin & Wang, Yi & Huang, Gang, 2021. "Global dynamics of a network-based SIQS epidemic model with nonmonotone incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    4. Tipsri, S. & Chinviriyasit, W., 2015. "The effect of time delay on the dynamics of an SEIR model with nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 153-172.
    5. Bao, Xiaomei & Tian, Canrong, 2019. "Delay driven vegetation patterns of a plankton system on a network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 74-88.
    6. Chang, Lili & Jin, Zhen, 2018. "Efficient numerical methods for spatially extended population and epidemic models with time delay," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 138-154.
    7. Lv, Wei & He, Hanfei & Li, Kezan, 2022. "Robust optimal control of a network-based SIVS epidemic model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    8. Yuan, Xinpeng & Xue, Yakui & Liu, Maoxing, 2013. "Analysis of an epidemic model with awareness programs by media on complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 48(C), pages 1-11.
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