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Global stability of a network-based SIRS epidemic model with nonmonotone incidence rate

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  • Liu, Lijun
  • Wei, Xiaodan
  • Zhang, Naimin

Abstract

This paper studies the dynamics of a network-based SIRS epidemic model with vaccination and a nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological or inhibitory effect from the behavioral change of the susceptible individuals when the number of infective individuals on heterogeneous networks is getting larger. Using the analytical method, epidemic threshold R0 is obtained. When R0 is less than one, we prove the disease-free equilibrium is globally asymptotically stable and the disease dies out, while R0 is greater than one, there exists a unique endemic equilibrium. By constructing a suitable Lyapunov function, we also prove the endemic equilibrium is globally asymptotically stable if the inhibitory factor α is sufficiently large. Numerical experiments are also given to support the theoretical results. It is shown both theoretically and numerically a larger α can accelerate the extinction of the disease and reduce the level of disease.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:515:y:2019:i:c:p:587-599
    DOI: 10.1016/j.physa.2018.09.152
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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. 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.
    3. Zhu, Guanghu & Chen, Guanrong & Fu, Xinchu, 2017. "Effects of active links on epidemic transmission over social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 614-621.
    4. Wei, Xiaodan & Liu, Lijun & Zhou, Wenshu, 2017. "Global stability and attractivity of a network-based SIS epidemic model with nonmonotone incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 789-798.
    5. 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.
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    Cited by:

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    4. Zhang, Yuexia & Pan, Dawei, 2021. "Layered SIRS model of information spread in complex networks," Applied Mathematics and Computation, Elsevier, vol. 411(C).

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