Table 2.

Summary of dynamical regimes of system (4.1) for different parameter variations. The regimes are classified based on long-term numerical simulations.

Parameter variation	Range	Fractional-order	Observed regime
Fear factor	Small ()		Stable periodic oscillations
	Moderate ()		Large-amplitude periodic oscillations
	Large ()		Complex/irregular dynamics
	Large ()		Damped oscillations or steady state
Conversion efficiency	Low		Stable equilibrium
	Intermediate		Periodic oscillations (Hopf-type)
	High		Complex oscillatory dynamics
	High		Regular periodic or stable equilibrium
Hunting efficiency	Low		Disease persistence with small oscillations
	Moderate		Periodic outbreaks
	High		Strong predator control, complex oscillations
	High		Suppressed oscillations
Infection rate	Below threshold		Disease-free equilibrium
	Near threshold		Endemic steady state
	Above threshold		Periodic or complex endemic dynamics
	Above threshold		Reduced oscillations or steady endemic state