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Bifurcations of an epidemic model with non-monotonic incidence rate of saturated mass action

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  • Zhou, Yugui
  • Xiao, Dongmei
  • Li, Yilong

Abstract

In this paper, we study the bifurcations of an epidemic model with non-monotonic incidence rate of saturated mass action, which describes the psychological effects of the community on certain serious diseases when the number of infective is getting larger. By carrying out the bifurcation analysis of the model, we show that there exist some values of the model parameters such that numerous kinds of bifurcation occur for the model, such as Hopf bifurcation, Bogdanov–Takens bifurcation.

Suggested Citation

  • Zhou, Yugui & Xiao, Dongmei & Li, Yilong, 2007. "Bifurcations of an epidemic model with non-monotonic incidence rate of saturated mass action," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1903-1915.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:5:p:1903-1915
    DOI: 10.1016/j.chaos.2006.01.002
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    References listed on IDEAS

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    1. Li, Guihua & Jin, Zhen, 2005. "Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1177-1184.
    2. Li, Guihua & Zhen, Jin, 2005. "Global stability of an SEI epidemic model with general contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 997-1004.
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    Cited by:

    1. Das, Tanuja & Srivastava, Prashant K., 2023. "Effect of a novel generalized incidence rate function in SIR model: Stability switches and bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Liu, Junli & Zhou, Yicang, 2009. "Global stability of an SIRS epidemic model with transport-related infection," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 145-158.
    3. Yingying Zhang & Chentong Li, 2023. "Bifurcation of an SIRS Model with a Modified Nonlinear Incidence Rate," Mathematics, MDPI, vol. 11(13), pages 1-24, June.
    4. Kumar, Anuj & Srivastava, Prashant K. & Gupta, R.P., 2019. "Nonlinear dynamics of infectious diseases via information-induced vaccination and saturated treatment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 77-99.

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