The name is absent

Result(s)

Sufficient condition

Optimal policy

Proposition 1 and

Proposition 2

All sufficiently small invasions are currently controlled and
a < γ + δaf_x(0)

There exists a ζ such that eradication is optimal
from every invasion of size y e (0,ζ].

Proposition 3

a < γexp(-aK) + δ[(a-β) + βexp(-aK)]f_x(x) for all x e (0,K]

Eradication is optimal from every invasion size.

Proposition 4

Every invasion smaller than f(y) is currently controlled,
a > β, and aexp((a-β)y) < γ + δa infp^y, exp(-βf(x))fx(x)_________

Immediate eradication is optimal for an invasion of
size y.

Proposition 5.a

aexp((a-β)y) > γ + δaf_x(0)

Immediate eradication is not optimal.

Proposition 5 .b

a > β and aexp(-βy) > γexp(γy) +

δsup о _s x _s y [(α-β)exp((α-β)f(x)) + βexp(-βf(x))]fx_t(x)

or

β > a and aexp(-βy) >

___________γexp(γy) + δa sup о s x s y [exp(-βf(x))fx(x)]_______________

It is optimal not to control an invasion of size y.

Proposition 6

a > γ + δaf_x(0)

It is optimal not to control an invasion if it is of
sufficiently small size.