Optimal Control of Biological Invasions in Lake Networks

A metapopulation model for alien species invasion of a lake network is coupled with an economic model of prevention. The model restates a stochastic problem in deterministic terms. It provides a macroscopic description of the lake network with prevention methods controlling both the outflow of invaders at infected lakes and the inflow of invaders at uninfected lakes. Results indicate that optimal control implements no more than one of these methods at any moment in time. Typical optimal control measures change over time as the lake ecosystem becomes successively more invaded. Early control of outflow from infected lakes is replaced by later control of inflow to remaining uninfected lakes. Closedloop control trajectories are analytically characterized in the phase-plane for a limiting case, while in general a simple and stable numerical algorithm is developed for solving the optimal control problem. This research has been supported by a grant from the National Science Foundation (DEB 02-13698). The second author acknowledges support from Canada Research Chair, an NSERC Collaborative Research Opportunity grant, and an NSERC Discovery grant. Received by the editors on Sept. 8, 2005, and in revised form on Jan. 31, 2006. Copyright c ©2007 Rocky Mountain Mathematics Consortium 351 352 A.B. POTAPOV, M.A. LEWIS AND D.C. FINNOFF