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Bull Math Biol. 2008 Jul;70(5):1371-97. doi: 10.1007/s11538-008-9303-8. Epub 2008 Mar 4.

Allee effect and control of lake system invasion.

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1
Centre for Mathematical Biology, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada. apotapov@math.ualberta.ca

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.

PMID:
18317845
DOI:
10.1007/s11538-008-9303-8
[Indexed for MEDLINE]
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