Memory Effects in Eco-Epidemiology: A Dynamical Systems Approach to Fear-Disease-Harvesting Interactions

Abstract

This research proposes a novel fractional-order eco-epidemiological model to investigate predator-preyinteractions under the combined effects of fear-induced behavioral changes, disease transmission in predators, and controlledharvesting. Unlike classical integer-order models, our approach employs Caputo fractional derivatives to incorporate memoryeffects and hereditary traits in ecological processes, offering a more realistic representation of long-term dynamics. Weestablish 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 simulationsdemonstrate that: (1) fear effects significantly reduce prey extinction risk by dampening predation rates, (2) harvestingintensity critically influences system stability, with excessive harvesting driving predator extinction, and (3) fractional-orderdynamics reveal memory-dependent transitions not observable in traditional models. These findings provide actionableinsights for ecosystem management, particularly in designing harvesting policies that balance biodiversity conservationand disease control. The model’s framework is adaptable to empirical data, bridging theoretical ecology and practicalconservation strategies.