Nonlinear dynamics and memory effects of an eco-epidemiological model: a bifurcation study with Allee thresholds and behavioral feedback
摘要
This paper presents an eco-epidemiological modeling framework based on both standard and fractional-order differential equations. The models incorporate behavioral dynamics, namely, prey self-awareness and predator hunting adaptations, which facilitated a refined comprehension of how individual actions and perceptions affect epidemic persistence and ecological stability, and a pronounced Allee effect to elucidate the intricate dynamics between environmental and epidemiological processes in a host-pathogen system. The model employs ABC fractional derivatives to account for memory-dependent transmission dynamics, providing a more accurate representation of biological systems with genetic influences. We analyze susceptible and infected prey populations affected by predation and disease-related mortality, whereas diseased prey impacts predators and demonstrates adaptive behavioral responses. The pronounced Allee effect is integrated into the prey reproductive function, indicating the essential population threshold under which the species cannot persist. We comprehensively examine the model, including the existence, uniqueness, and positivity of the solutions. The stability of equilibrium points is analyzed by fractional-order linearization and numerical simulations. Our results indicate that the interaction of disease prevalence, behavioral responses, and the Allee threshold produces complex dynamical behaviors, including population extinction, persistence, and oscillatory dynamics. Boundedness and positivity of trajectories, stability assessments of disease-free and endemic equilibria, coupled with bifurcation studies, revealed intricate dynamical phenomena, including transcritical, saddle-node, cusp, Hopf, and Bogdanov-Takens bifurcations, as well as bifurcation diagrams of their interactions. Numerical investigations validate the essential roles of the fractional-order parameter, predator response strength, and initial population numbers in influencing system outcomes. This study emphasizes the integration of ecological realism and memory effects into epidemiological models, which affects conservation strategies and disease control in predator–prey ecosystems.