IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v321y2018icp372-384.html
   My bibliography  Save this article

Global stability of an SI epidemic model with feedback controls in a patchy environment

Author

Listed:
  • Li, Hong-Li
  • Zhang, Long
  • Teng, Zhidong
  • Jiang, Yao-Lin
  • Muhammadhaji, Ahmadjan

Abstract

In this paper, we investigate an SI epidemic model with feedback controls in a patchy environment where individuals in each patch can disperse among n(n ≥ 2) patches. We derive the basic reproduction number R0 and prove that the disease-free equilibrium is globally asymptotically stable if R0 ≤ 1. In the case of R0 > 1, we derive sufficient conditions under which the endemic equilibrium is unique and globally asymptotically stable. Our proof of global stability utilizes the method of global Lyapunov functions and results from graph theory. Numerical simulations are carried out to support our theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:372-384
    DOI: 10.1016/j.amc.2017.10.057
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630031730766X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.10.057?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Xie, Youxiang & Wang, Linjun & Deng, Qicheng & Wu, Zhengjia, 2017. "The dynamics of an impulsive predator–prey model with communicable disease in the prey species only," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 320-335.
    3. Xu, Rui, 2012. "Global dynamics of an SEIS epidemiological model with time delay describing a latent period," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 90-102.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mohan, Nishith & Kumari, Nitu, 2021. "Positive steady states of a SI epidemic model with cross diffusion," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Wang, Mengyao & Pan, Qiuhui & He, Mingfeng, 2020. "The effect of individual attitude on cooperation in social dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    3. Pan Tang & Shiwen Qian & Lei Shi & Longxing Qi & Tingting Li, 2023. "The Influence of Migration to Regions with Different Coverages of Health Education on Schistosomiasis," Mathematics, MDPI, vol. 11(12), pages 1-27, June.
    4. Xie, Yingkang & Wang, Zhen & Lu, Junwei & Li, Yuxia, 2020. "Stability analysis and control strategies for a new SIS epidemic model in heterogeneous networks," Applied Mathematics and Computation, Elsevier, vol. 383(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. 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.
    3. Kerr, Gilbert & González-Parra, Gilberto & Sherman, Michele, 2022. "A new method based on the Laplace transform and Fourier series for solving linear neutral delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    4. Nian, Fuzhong & Hu, Chasheng & Yao, Shuanglong & Wang, Longjing & Wang, Xingyuan, 2018. "An immunization based on node activity," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 228-233.
    5. 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).
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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).
    11. Huang, He & Chen, Yahong & Ma, Yefeng, 2021. "Modeling the competitive diffusions of rumor and knowledge and the impacts on epidemic spreading," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    12. 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.
    13. 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.
    14. 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.
    15. Kerr, Gilbert & González-Parra, Gilberto, 2022. "Accuracy of the Laplace transform method for linear neutral delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 308-326.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Nian, Fuzhong & Liu, Jinshuo, 2021. "Feedback driven message spreading on network," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:372-384. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.