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Bifurcation and chaos in a delayed eco-epidemic model induced by prey configuration

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  • Gupta, Ashvini
  • Dubey, Balram

Abstract

The present study assumes that infectious disease among prey classifies them as susceptible (S) and infected (I) prey. When strong (susceptible) prey forms a herd to defend against the predator, it can reverse their role. This paper focuses on spotlighting the impact of disease, generalized herd shape, predator mortality due to prey group, the attack rate for healthy prey, and time delay. These factors crucially govern the system’s dynamics like Hopf-bifurcation, transcritical bifurcation, and chaos. The sketch of the maximum Lyapunov exponent confirms the chaotic nature. Extensive theoretical and numerical analysis reveals the existence and stability of steady-states in the presence or absence of delay. This study finds out that disease spread in prey can enhance the chances of predator survival. Furthermore, sensitivity analysis demonstrates the influence of some epidemic and ecological parameters on the reproduction numbers of the proposed eco-epidemic system.

Suggested Citation

  • Gupta, Ashvini & Dubey, Balram, 2022. "Bifurcation and chaos in a delayed eco-epidemic model induced by prey configuration," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p1:s096007792200964x
    DOI: 10.1016/j.chaos.2022.112785
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    References listed on IDEAS

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    1. Djilali, Salih, 2019. "Impact of prey herd shape on the predator-prey interaction," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 139-148.
    2. Bulai, Iulia Martina & Venturino, Ezio, 2017. "Shape effects on herd behavior in ecological interacting population models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 40-55.
    3. Alzahrani, Abdullah K. & Alshomrani, Ali Saleh & Pal, Nikhil & Samanta, Sudip, 2018. "Study of an eco-epidemiological model with Z-type control," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 197-208.
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    1. Li, Danyang & Liu, Hua & Zhang, Haotian & Wei, Yumei, 2023. "Influence of multiple delays mechanisms on predator–prey model with Allee effect," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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