TABLE 1
Optimal control of an invasion: exponential costs and damages
Result(s) |
Sufficient condition |
Optimal policy |
Proposition 1 and Proposition 2 |
All sufficiently small invasions are currently controlled and |
There exists a ζ such that eradication is optimal |
Proposition 3 |
a < γexp(-aK) + δ[(a-β) + βexp(-aK)]fx(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, |
Immediate eradication is optimal for an invasion of |
Proposition 5.a |
aexp((a-β)y) > γ + δafx(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))]fxt(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 + δafx(0) |
It is optimal not to control an invasion if it is of |
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