Title: Spatio-temporal patterns using Holling type-IV in a predator-based disease with immune prey

Authors: Atish Kumar Sethy; Jyotiska Datta

Addresses: Department of Mathematics, Central University of Odisha, Koraput – 763004, Odisha, India ' Department of Mathematics, Central University of Odisha, Koraput – 763004, Odisha, India

Abstract: Eco-epidemiological models provide an effective framework for examining how population interactions and disease transmission shape ecological outcomes. This work investigates a reaction-diffusion predator-prey system based on the Rosenzweig-MacArthur model with a Holling type-IV functional response, where predators are divided into susceptible and infected classes. Analytical results establish positivity conditions and characterise both local stability and diffusion-driven instability using the Routh-Hurwitz criterion. Numerical simulations display diverse dynamics, including limit cycles, travelling waves, spiral structures, and irregular spatio-temporal activity. The study shows that disease-free systems can produce classical Turing patterns under suitable diffusion settings, whereas the presence of infection disrupts these stationary patterns and leads to wave-like or chaotic behaviour. Bifurcation analysis further reveals transitions from stable equilibria to Hopf oscillations and complex regimes, highlighting the strong influence of disease parameters on coexistence and spatial structure. These findings offer new perspectives on ecological stability, resilience, and disease spread in natural predator-prey communities.

Keywords: prey-predator; infected predators; diffusive instability; Hopf bifurcation; phase portrait; spatio-temporal chaos.

DOI: 10.1504/IJDSDE.2025.151444

International Journal of Dynamical Systems and Differential Equations, 2025 Vol.14 No.6, pp.469 - 487

Received: 28 Nov 2024
Accepted: 04 Oct 2025
Published online: 30 Jan 2026 *

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