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Global stability of a network-based SIS epidemic model with a saturated treatment function

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  • Wei, Xiaodan
  • Zhao, Xu
  • Zhou, Wenshu

Abstract

We study global stability of a network-based SIS epidemic model with a saturated treatment function. The model was proposed by Huang and Li (2019). They obtained a threshold R0, depending on the network structure and some parameters (except the parameter α used to measure the extent of the effect of the infected being delayed for treatment), and some sufficient conditions on the stability of the equilibria. The aim of the present paper is to conduct a further analysis on the global stability of the equilibria by means of an iterative technique. For the case when R0<1, it is proved that if the disease-free equilibrium is the unique one, then it is globally asymptotically stable. In addition, we give some new conditions guaranteeing that the disease-free equilibrium is the unique one, and show the existence of two endemic equilibria if α is sufficiently large, which verifies partially their numerical observation. For the case when R0>1, it is proved that if the model admits a unique endemic equilibrium, then the unique endemic equilibrium is globally attractive, and is globally asymptotically stable if α is sufficiently large or small. In particular, we present a condition such that the threshold R0 determines the global stability of the disease-free equilibrium and the endemic equilibrium. Numerical experiment is also performed to illustrate our theoretical results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:597:y:2022:i:c:s0378437122002461
    DOI: 10.1016/j.physa.2022.127295
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    References listed on IDEAS

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    1. Yang, Meng & Chen, Guanrong & Fu, Xinchu, 2011. "A modified SIS model with an infective medium on complex networks and its global stability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2408-2413.
    2. 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.
    3. 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.
    4. 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.
    5. Khan, Muhammad Altaf & Khan, Yasir & Islam, Saeed, 2018. "Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 210-227.
    6. Huang, Yi-Jie & Li, Chun-Hsien, 2019. "Backward bifurcation and stability analysis of a network-based SIS epidemic model with saturated treatment function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
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