IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v197y2022icp45-90.html
   My bibliography  Save this article

Dynamical complexity of a delay-induced eco-epidemic model with Beddington–DeAngelis incidence rate

Author

Listed:
  • Dutta, Protyusha
  • Sahoo, Debgopal
  • Mondal, Sudeshna
  • Samanta, Guruprasad

Abstract

Present article has proposed a general eco-epidemic model with disease in predator population subject to Beddington–DeAngelis type incidence rate with the significance of fear in prey individuals and also analyzed the impact of external food supply to the sound predator. As an additional factor in representing the interplay amongst the predator and prey species, the Holling type-II functional response in the context of intra-specific competition within the prey species is taken into consideration. The model dynamics is studied by employing discrete time-delay in prey and gestation delay in predator in order to generate more authentic and natural dynamics. Positivity, uniform boundedness, and uniform persistence of the solutions for the model system have been explained analytically. Furthermore, the extinction criteria of the predator population have been explored and also illustrated by numerical simulations. For the non-delayed model, the existence and stability conditions of all conceivable critical points are investigated associated with the model parameters. The basic fundamental bifurcation assessments of the model reveal the formation of local bifurcations (Hopf-bifurcation and transcritical bifurcation) and provide the parametric region for occurrence of Bautin bifurcation and Gavrilov–Guckenheimer bifurcation. It is also reported that the provision of supplementary food to the sound predator may enable to remove the infection more promptly. Afterward, the stability dynamics of the coexistence state for different configurations of the delay factors have been scrutinized, as well as the delay parameters may produce oscillations via Hopf-bifurcation if they exceed some threshold value. But, when the gestation delay has been incorporated only in infected predators, no critical point can be obtained at which the Hopf-bifurcation takes place for the considered parameter values. Most of the theoretical discoveries have been certified through several numerical experiments constructed with the application of MATLAB and MATCONT.

Suggested Citation

  • Dutta, Protyusha & Sahoo, Debgopal & Mondal, Sudeshna & Samanta, Guruprasad, 2022. "Dynamical complexity of a delay-induced eco-epidemic model with Beddington–DeAngelis incidence rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 45-90.
  • Handle: RePEc:eee:matcom:v:197:y:2022:i:c:p:45-90
    DOI: 10.1016/j.matcom.2022.02.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422000556
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2022.02.002?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. Chunjin Wei & Lansun Chen, 2008. "A Delayed Epidemic Model with Pulse Vaccination," Discrete Dynamics in Nature and Society, Hindawi, vol. 2008, pages 1-12, March.
    2. Xu, Rui & Ma, Zhien, 2009. "Stability of a delayed SIRS epidemic model with a nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2319-2325.
    3. Das, Bijoy Kumar & Sahoo, Debgopal & Samanta, G.P., 2022. "Impact of fear in a delay-induced predator–prey system with intraspecific competition within predator species," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 134-156.
    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. Nirapada Santra & Sudeshna Mondal & Guruprasad Samanta, 2022. "Complex Dynamics of a Predator–Prey Interaction with Fear Effect in Deterministic and Fluctuating Environments," Mathematics, MDPI, vol. 10(20), pages 1-38, October.

    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. Bansal, Komal & Mathur, Trilok & Agarwal, Shivi, 2023. "Fractional-order crime propagation model with non-linear transmission rate," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Lahrouz, A. & El Mahjour, H. & Settati, A. & Bernoussi, A., 2018. "Dynamics and optimal control of a non-linear epidemic model with relapse and cure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 299-317.
    3. Bi, Zhimin & Liu, Shutang & Ouyang, Miao, 2022. "Spatial dynamics of a fractional predator-prey system with time delay and Allee effect," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    4. Tipsri, S. & Chinviriyasit, W., 2015. "The effect of time delay on the dynamics of an SEIR model with nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 153-172.
    5. Keshri, Neha & Mishra, Bimal Kumar, 2014. "Two time-delay dynamic model on the transmission of malicious signals in wireless sensor network," Chaos, Solitons & Fractals, Elsevier, vol. 68(C), pages 151-158.
    6. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Asymptotic behavior of a stochastic delayed SEIR epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 870-882.
    7. Saha, Sangeeta & Sahoo, Debgopal & Samanta, Guruprasad, 2023. "Role of predation efficiency in prey–predator dynamics incorporating switching effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 299-323.
    8. Samanta, G.P., 2014. "Analysis of a delayed epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 74-85.
    9. Wang, Jinling & Jiang, Haijun & Hu, Cheng & Yu, Zhiyong & Li, Jiarong, 2021. "Stability and Hopf bifurcation analysis of multi-lingual rumor spreading model with nonlinear inhibition mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    10. Haoming Shi & Fei Xu & Jinfu Cheng & Victor Shi, 2023. "Exploring the Evolution of the Food Chain under Environmental Pollution with Mathematical Modeling and Numerical Simulation," Sustainability, MDPI, vol. 15(13), pages 1-17, June.
    11. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Periodic solution for a stochastic nonautonomous SIR epidemic model with logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 816-826.
    12. Xu, Changyong & Li, Xiaoyue, 2018. "The threshold of a stochastic delayed SIRS epidemic model with temporary immunity and vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 227-234.
    13. Nirapada Santra & Sudeshna Mondal & Guruprasad Samanta, 2022. "Complex Dynamics of a Predator–Prey Interaction with Fear Effect in Deterministic and Fluctuating Environments," Mathematics, MDPI, vol. 10(20), pages 1-38, October.
    14. Sajan, & Dubey, Balram & Sasmal, Sourav Kumar, 2022. "Chaotic dynamics of a plankton-fish system with fear and its carry over effects in the presence of a discrete delay," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    15. Yanhui Wei & Liang’an Huo & Hongguang He, 2022. "Research on Rumor-Spreading Model with Holling Type III Functional Response," Mathematics, MDPI, vol. 10(4), pages 1-13, February.

    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:matcom:v:197:y:2022:i:c:p:45-90. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.