Modeling and Dynamical Analysis of a Fractional-Order Predation Model Incorporating Disease and Cooperative Hunting

This study constructs a novel fractional-order eco-epidemiological predator–prey model, in which disease spreads among predators through environmental transmission, and both cooperative hunting behavior and disease latency delay are incorporated simultaneously. Different from classical integer-order predator–prey models, fractional derivative is adopted to describe the memory-dependent mechanism of ecological populations, and the infection can alter the hunting strategy of diseased predators. The existence, non-negativity, and boundedness of system solutions are proved theoretically. The local stability of all equilibrium points is analyzed, and the conditions for the occurrence of Hopf bifurcation induced by latency delay are derived. Numerical simulations further verify the theoretical results, and quantitatively reveal the separate and combined effects of the fractional order, cooperative hunting coefficient, and latency delay on the dynamical evolution of the population system.