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Stability analysis of an SIS epidemic model with feedback mechanism on networks

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  • Zhang, Jiancheng
  • Sun, Jitao

Abstract

In this paper, an epidemic model with feedback mechanism on networks is investigated. We obtain the basic reproductive number R0, and analyze the stability behaviors of disease-free equilibrium E0 and endemic equilibrium E∗. When R0<1, the disease-free equilibrium is globally asymptotically stable, and when R0>1, the endemic equilibrium is asymptotically stable. Although the feedback mechanism cannot change the basic reproductive number R0 as we prove, it should be indicated that it can weaken the spreading of diseases and reduce the endemic level. Finally, the results of the stability and the effectiveness of the feedback mechanism are illustrated by some numerical simulations.

Suggested Citation

  • Zhang, Jiancheng & Sun, Jitao, 2014. "Stability analysis of an SIS epidemic model with feedback mechanism on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 24-32.
    • Handle: RePEc:eee:phsmap:v:394:y:2014:i:c:p:24-32
    DOI: 10.1016/j.physa.2013.09.058
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    Citations

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    Cited by:

    1. Liu, Qiming & Li, Hua, 2019. "Global dynamics analysis of an SEIR epidemic model with discrete delay on complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 289-296.
    2. Li, Jingjing & Zhang, Yumei & Man, Jiayu & Zhou, Yun & Wu, Xiaojun, 2017. "SISL and SIRL: Two knowledge dissemination models with leader nodes on cooperative learning networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 740-749.
    3. Li, Chun-Hsien, 2015. "Dynamics of a network-based SIS epidemic model with nonmonotone incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 234-243.
    4. Wang, Haiying & Wang, Jun & Ding, Liting & Wei, Wei, 2017. "Knowledge transmission model with consideration of self-learning mechanism in complex networks," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 83-92.
    5. Wei, Xiaodan & Xu, Gaochao & Zhou, Wenshu, 2018. "Global stability of endemic equilibrium for a SIQRS epidemic model on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 203-214.
    6. Huo, Jingjing & Zhao, Hongyong, 2016. "Dynamical analysis of a fractional SIR model with birth and death on heterogeneous complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 41-56.
    7. Jia, Nan & Ding, Li & Liu, Yu-Jing & Hu, Ping, 2018. "Global stability and optimal control of epidemic spreading on multiplex networks with nonlinear mutual interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 93-105.
    8. Wei, Xiaodan & Xu, Gaochao & Liu, Lijun & Zhou, Wenshu, 2017. "Global stability of endemic equilibrium of an epidemic model with birth and death on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 78-84.
    9. Qu, Leilei & Gao, Xubin & Kang, Baolin & He, Mingfeng & Pan, Qiuhui, 2019. "Population dynamics models based on the transmission mechanism of MCR-1," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 310-323.
    10. Wei, Xiaodan & Zhao, Xu & Zhou, Wenshu, 2022. "Global stability of a network-based SIS epidemic model with a saturated treatment function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    11. Li, Tao & Liu, Xiongding & Wu, Jie & Wan, Chen & Guan, Zhi-Hong & Wang, Yuanmei, 2016. "An epidemic spreading model on adaptive scale-free networks with feedback mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 649-656.
    12. Liu, Lijun & Wei, Xiaodan & Zhang, Naimin, 2019. "Global stability of a network-based SIRS epidemic model with nonmonotone incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 587-599.
    13. Wang, Jinling & Jiang, Haijun & Hu, Cheng & Yu, Zhiyong & Li, Jiarong, 2021. "Stability and Hopf bifurcation analysis of multi-lingual rumor spreading model with nonlinear inhibition mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    14. Zhu, Linhe & Liu, Wenshan & Zhang, Zhengdi, 2020. "Delay differential equations modeling of rumor propagation in both homogeneous and heterogeneous networks with a forced silence function," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    15. Nian, Fuzhong & Liu, Jinshuo, 2021. "Feedback driven message spreading on network," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    16. Li, Hong-Li & Zhang, Long & Teng, Zhidong & Jiang, Yao-Lin & Muhammadhaji, Ahmadjan, 2018. "Global stability of an SI epidemic model with feedback controls in a patchy environment," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 372-384.

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