Manisha Yadav
Department of Mathematics, Faculty of Applied and Basic Sciences, SGT University, Gurugram, 122505, Haryana, India.

Pradeep Malik
Department of Mathematics, Faculty of Applied and Basic Sciences, SGT University, Gurugram, 122505, Haryana, India.

Ashish Tiwari
Department of Mathematics, Faculty of Applied and Basic Sciences, SGT University, Gurugram, 122505, Haryana, India.

DOI https://doi.org/10.33889/IJMEMS.2025.10.5.060

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Abstract

This research paper comprehensively examines a discretized three-dimensional predator-prey model with disease and prey refuge. The model incorporates vital dynamics such as predation, infection, prey population growth, and refuge population growth to capture the intricate interactions among predators, prey, and refuge in ecological systems. The study investigates the long-term behaviour of predator, prey, and refuge populations through equilibrium analysis, stability analysis, and numerical simulations. Equilibrium points are identified, and their stability properties are assessed, providing insights into the system’s critical points. The condition for Neimark-Sacker bifurcation is discussed. Numerical simulations validate the theoretical analysis, providing a deeper understanding of the model’s dynamics. Moreover, fractional calculus methods are employed to enhance the modeling and analysis of the system.

Keywords- Three-dimensional discrete model, Stability, Prey refuge, Neimark-Sacker Bifurcation.

Citation

Yadav, M., Malik, P., & Tiwari, A. (2025). Epidemics and Predator-Prey Interactions: A Three-dimensional Discrete Model Perspective. International Journal of Mathematical, Engineering and Management Sciences, 10(5), 1248-1265. https://doi.org/10.33889/IJMEMS.2025.10.5.060.