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

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  • 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
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    References listed on IDEAS

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    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.
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    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).

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