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Modeling a delay-driven eco-epidemiological system with fear and migration under ratio-dependent predation

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  • Barman, Kahuwa Kuwali
  • Kashyap, Ankur Jyoti
  • Sarmah, Hemanta Kumar

Abstract

This study investigates an eco-epidemiological predator–prey model that incorporates fear-driven behavioral changes in susceptible prey along with migration in both prey and predator populations. Predation on infected prey is modeled through a ratio-dependent functional response, and a transmission delay is introduced to represent the non-instantaneous nature of infection, adding novelty to the framework. We examine the local and global stability of the non-delayed system, and analyze the occurrence of transcritical and Hopf bifurcations. The results show that fear effects and susceptible prey migration may destabilize the system, whereas a higher conversion rate of infected prey biomass promotes stable coexistence. Delay-induced bifurcation analysis further reveals that increasing the transmission delay destabilizes the interior equilibrium, and numerical simulations support these analytical findings.

Suggested Citation

  • Barman, Kahuwa Kuwali & Kashyap, Ankur Jyoti & Sarmah, Hemanta Kumar, 2026. "Modeling a delay-driven eco-epidemiological system with fear and migration under ratio-dependent predation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 245(C), pages 114-142.
    • Handle: RePEc:eee:matcom:v:245:y:2026:i:c:p:114-142
    DOI: 10.1016/j.matcom.2026.01.002
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    References listed on IDEAS

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    1. Panday, Pijush & Samanta, Sudip & Pal, Nikhil & Chattopadhyay, Joydev, 2020. "Delay induced multiple stability switch and chaos in a predator–prey model with fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 134-158.
    2. Assane Savadogo & Boureima Sangaré & Wendkouni Ouedraogo & Rosanna Manzo, 2024. "A Complex Dynamic of an Eco-Epidemiological Mathematical Model with Migration," Abstract and Applied Analysis, Hindawi, vol. 2024, pages 1-23, March.
    3. Samrat Chatterjee & J. Chattopadhyay, 2007. "Role of migratory bird population in a simple eco-epidemiological model," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 13(1), pages 99-114, February.
    4. Sun, Gui-Quan & Jin, Zhen & Liu, Quan-Xing & Li, Li, 2008. "Dynamical complexity of a spatial predator–prey model with migration," Ecological Modelling, Elsevier, vol. 219(1), pages 248-255.
    5. Wang, Fatao & Yang, Ruizhi & Zhang, Xin, 2024. "Turing patterns in a predator–prey model with double Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 170-191.
    6. Assane Savadogo & Boureima Sangaré & Wendkouni Ouedraogo, 2024. "A Complex Dynamic of an Eco‐Epidemiological Mathematical Model with Migration," Abstract and Applied Analysis, John Wiley & Sons, vol. 2024(1).
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