The name is absent

examined in Brown, Lynch and Zilberman. Sharov and Leibhold [1998] examine the economics of using
barrier zones to control the spread of invasive species. Costello and McAusland [2002] consider the
links between trade, protectionism and damage arising from exotic species introductions. Jensen [2002]
examines optimal protection and damage mitigation in a model where the probability of invasion is
exponentially distributed, but where there is no growth and spread of an established invasion. In a
separate paper (Olson and Roy [2002]), we examine the economics of controlling a stochastic biological
invasion when the costs of control are independent of the invasion size.

The paper is organized as follows. Section two develops the model. The basic properties of a
controlled invasion are discussed in section three. Section four studies the economic and ecological
conditions for eradication of an invasive species. Circumstances under which eradication does not make
sense are examined in section five. Section six develops an example to illustrate the main results.
Concluding remarks are given in Section seven and all proofs are in the appendix.

2. The model

Let y_t represent the size of the biological invasion at the beginning of time t and let a_t represent
the amount of control at time t. The invasion that remains at the end of period t is given by x_t = y_t - a_t.
The invasion is assumed to grow and spread according to an invasion growth function y_t+1 = f(x_t). The
invasion growth function is assumed to satisfy the following properties:

A1.    f(x) has a continuous derivative, f_x(x).

A2.    f(0) = 0.

A3.     fx(x) ≥ 0.

A4.    fx(0) > 1.

A5. There exists an K e (k,∞) such that f(x) < x for all x > K and f_x(K) > 0.

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