Memory Effects in Eco-Epidemiology: A Dynamical Systems Approach to Fear-Disease-Harvesting Interactions - Afiyah, Siti Nurul; Fatmawati; Windarto; Akanni, John O. (Statistics, Optimization & Information Computing, 2025)
This research proposes a novel fractional-order eco-epidemiological model to investigate predator-prey interactions under the combined effects of fear-induced behavioral changes, disease transmission in predators, and controlled harvesting. Unlike classical integer-order models, our approach employs Caputo fractional derivatives to incorporate memory effects and hereditary traits in ecological processes, offering a more realistic representation of long-term dynamics. We establish the existence, uniqueness, and boundedness of solutions, and analyze the stability of all equilibrium points, including the coexistence state where prey, susceptible predators, and infected predators persist. Numerical simulations demonstrate that: (1) fear effects significantly reduce prey extinction risk by dampening predation rates, (2) harvesting intensity critically influences system stability, with excessive harvesting driving predator extinction, and (3) fractional-order dynamics reveal memory-dependent transitions not observable in traditional models. These findings provide actionable insights for ecosystem management, particularly in designing harvesting policies that balance biodiversity conservation and disease control. The model’s framework is adaptable to empirical data, bridging theoretical ecology and practical conservation strategies.