Table 2.

Effects of α₁ and α₂ on dynamics.

Values of R 0		Effects when $R_0^{\theta }<1$	Effects when $R_0^{\theta }>1$
Intensity of values
Small values of	α 1	Either can keep the infected population in a low level or Destabilize the system then drive the whole population extinct through a catastrophic event.	Either exhibits disease-driven extinction (Theorem 3.2, condition C) or disease persists with large infected population (this may be caused by switching Allee thresholds).
	α 2	Disease persists with large infected population.	Disease persists with large infected population.
Intermedium values of	α 1	Hysteresis occurs	Either disease persists or exhibits disease-driven extinction.
	α 2	Hysteresis occurs	Either disease persists or exhibits disease-driven extinction.
Large values of	α 1	The infected population persists and is relatively large.	Disease persists.
	α 2	Either can keep the infected population in a low level or Destabilize the system then drive the whole population extinct through a catastrophic event.	Either exhibits disease-driven extinction (Theorem 3.2, condition C) or disease persists.