Spatiotemporal dynamics in a diffusive eco-epidemiological system with spatial memory and fear effect

This paper proposes and analyzes a novel delayed diffusive model to investigate the complex spatiotemporal dynamics of an eco-epidemiological system. The model is distinguished by its simultaneous integration of four critical ecological mechanisms: a fear effect that suppresses prey reproduction, disease transmission within the prey population, standard diffusion, and a memory-based anti-predator taxis, wherein prey actively avoid predators based on past information. Rigorous mathematical analysis establishes the system’s well-posedness and reveals intricate stability dynamics. We demonstrate that the prey’s anti-predator taxis can trigger a Turing instability, leading to the formation of stationary spatial patterns. Crucially, this destabilizing effect is counteracted by the fear mechanism, which acts as a spatial stabilizer by expanding the parameter domain for homogeneous coexistence. Furthermore, our analysis identifies the time delay in the prey’s response as a potent driver of temporal instability, inducing sustained population oscillations via a Hopf bifurcation. Beyond local bifurcations, we also derive sufficient conditions for the global asymptotic stability of both the infection-free and coexistence equilibria using Lyapunov functional methods. Numerical simulations not only corroborate our analytical predictions but also unveil the emergence of a rich variety of complex spatial structures in two dimensions, including spots, stripes, and mixed-mode patterns. In summary, our findings highlight that the sophisticated interplay between fear, memory, and movement can profoundly alter system stability and generate diverse spatiotemporal heterogeneity, offering significant insights into the mechanisms governing community structure and disease dynamics in natural ecosystems.