IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v127y2019icp55-69.html
   My bibliography  Save this article

Dynamics of a time-delayed SIR epidemic model with logistic growth and saturated treatment

Author

Listed:
  • Avila-Vales, Eric
  • Pérez, Ángel G.C.

Abstract

In this paper, we incorporate a nonlinear incidence rate and a logistic growth rate into a SIR epidemic model for a vector-borne disease with incubation time delay and Holling type II saturated treatment. We compute the basic reproduction number and show that it completely determines the local stability of the disease-free equilibrium. Sufficient conditions for the existence of backward bifurcation and Hopf bifurcation are also established. Furthermore, we determine the direction and stability of the Hopf bifurcation around the endemic equilibrium by means of the center manifold theory. Our study reveals that the model admits a Bogdanov–Takens bifurcation when the time delay and the maximal disease transmission rate are varied. Numerical simulations are presented to illustrate the dynamics of the model and to study the effects caused by varying the treatment rate and delay parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:127:y:2019:i:c:p:55-69
    DOI: 10.1016/j.chaos.2019.06.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007791930236X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.06.024?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Muhammad Ozair & Abid Ali Lashari & Il Hyo Jung & Kazeem Oare Okosun, 2012. "Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-21, November.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Gupta, R.P. & Kumar, Arun, 2022. "Endemic bubble and multiple cusps generated by saturated treatment of an SIR model through Hopf and Bogdanov–Takens bifurcations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 1-21.
    3. Sabbar, Yassine & Din, Anwarud & Kiouach, Driss, 2023. "Influence of fractal–fractional differentiation and independent quadratic Lévy jumps on the dynamics of a general epidemic model with vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    4. Kumari, Sangeeta & Upadhyay, Ranjit Kumar, 2021. "Exploring the behavior of malware propagation on mobile wireless sensor networks: Stability and control analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 246-269.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ángel G. C. Pérez & Eric Avila-Vales & Gerardo Emilio García-Almeida, 2019. "Bifurcation Analysis of an SIR Model with Logistic Growth, Nonlinear Incidence, and Saturated Treatment," Complexity, Hindawi, vol. 2019, pages 1-21, July.
    2. 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).
    3. Liu, Li & Luo, Xiaofeng & Chang, Lili, 2017. "Vaccination strategies of an SIR pair approximation model with demographics on complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 282-290.
    4. Cai, Li-Ming & Li, Xue-Zhi & Li, Zhaoqiang, 2013. "Dynamical behavior of an epidemic model for a vector-borne disease with direct transmission," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 54-64.
    5. 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).
    6. 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).
    7. Pang, Liuyong & Zhao, Zhong & Song, Xinyu, 2016. "Cost-effectiveness analysis of optimal strategy for tumor treatment," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 293-301.
    8. 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).
    9. 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.
    10. 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).
    11. 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.
    12. 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.
    13. Kumari, Sangeeta & Upadhyay, Ranjit Kumar, 2021. "Exploring the behavior of malware propagation on mobile wireless sensor networks: Stability and control analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 246-269.
    14. Upadhyay, Ranjit Kumar & Singh, Prerna, 2020. "Modeling and control of computer virus attack on a targeted network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    15. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:127:y:2019:i:c:p:55-69. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.