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Stability and bifurcation analysis of an SIR epidemic model with logistic growth and saturated treatment

Author

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  • Li, Jinhui
  • Teng, Zhidong
  • Wang, Guangqing
  • Zhang, Long
  • Hu, Cheng

Abstract

In this paper, we introduce the saturated treatment and logistic growth rate into an SIR epidemic model with bilinear incidence. The treatment function is assumed to be a continuously differential function which describes the effect of delayed treatment when the medical condition is limited and the number of infected individuals is large enough. Sufficient conditions for the existence and local stability of the disease-free and positive equilibria are established. And the existence of the stable limit cycles also is obtained. Moreover, by using the theory of bifurcations, it is shown that the model exhibits backward bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcations. Finally, the numerical examples are given to illustrate the theoretical results and obtain some additional interesting phenomena, involving double stable periodic solutions and stable limit cycles.

Suggested Citation

  • Li, Jinhui & Teng, Zhidong & Wang, Guangqing & Zhang, Long & Hu, Cheng, 2017. "Stability and bifurcation analysis of an SIR epidemic model with logistic growth and saturated treatment," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 63-71.
    • Handle: RePEc:eee:chsofr:v:99:y:2017:i:c:p:63-71
    DOI: 10.1016/j.chaos.2017.03.047
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    Citations

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    Cited by:

    1. Nudee, K. & Chinviriyasit, S. & Chinviriyasit, W., 2019. "The effect of backward bifurcation in controlling measles transmission by vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 400-412.
    2. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2020. "Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    3. repec:hin:complx:9876013 is not listed on IDEAS
    4. 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).
    5. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    6. Xinyu Liu & Yuting Ding, 2022. "Stability and Numerical Simulations of a New SVIR Model with Two Delays on COVID-19 Booster Vaccination," Mathematics, MDPI, vol. 10(10), pages 1-27, May.
    7. 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.
    8. Zheng, Qianqian & Shen, Jianwei & Pandey, Vikas & Guan, Linan & Guo, Yantao, 2023. "Turing instability in a network-organized epidemic model with delay," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    9. Saha, Pritam & Mondal, Bapin & Ghosh, Uttam, 2023. "Dynamical behaviors of an epidemic model with partial immunity having nonlinear incidence and saturated treatment in deterministic and stochastic environments," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    10. Han, Bingtao & Jiang, Daqing & Zhou, Baoquan & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SIRSI epidemic model with saturation incidence rate and logistic growth," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    11. Avila-Vales, Eric & Pérez, Ángel G.C., 2019. "Dynamics of a time-delayed SIR epidemic model with logistic growth and saturated treatment," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 55-69.

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