Abstract
We consider the model of invasion prevention in a system of lakes that are connected via traffic of recreational boats. It is shown that in presence of an Allee effect, the general optimal control problem can be reduced to a significantly simpler stationary optimization problem of optimal invasion stopping. We consider possible values of model parameters for zebra mussels. The general N-lake control problem has to be solved numerically, and we show a number of typical features of solutions: distribution of control efforts in space and optimal stopping configurations related with the clusters in lake connection structure.
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Potapov, A.B., Lewis, M.A. Allee Effect and Control of Lake System Invasion. Bull. Math. Biol. 70, 1371–1397 (2008). https://doi.org/10.1007/s11538-008-9303-8
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DOI: https://doi.org/10.1007/s11538-008-9303-8