Controlling a Biological Invasion: A Non-classical Dynamic Economic Model by

The paper develops a dynamic economic model of a controlled biological invasion. Such problems are inherently non-convex for two reasons. First, the invasion growth function and the set of feasible time paths may be non-convex. Second, non-convexities in the objective function may arise naturally from the fact that control costs depend on the invasion size. The goal of this paper is to characterize the optimal value and policy functions in this non-classical setting with a particular focus on the long run dynamic behavior of an optimally controlled invasion and the corresponding implications for public policy. The value function may be non-convex and the optimal control may be a non-monotonic function of the invasion size. When costs depend on both control and the invasion size the optimal transition function for an invasion is not necessarily monotonic and optimal time paths may exhibit nonlinear dynamics; as a result, it may be optimal to let the invasion grow before eradication and there may be alternating intervals of eradication and non-eradication on the state space. We characterize these possibilities as well as the conditions under which it is optimal to eradicate an invasive species (immediately and eventually), the conditions under which maintenance control is optimal, and the conditions under which it is not efficient to control an invasive species at all.