Allee Effect and Control of Lake System Invasion

Original Article

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.

Keywords

Biological invasions Spatial control Optimal control Aquatic invaders Zebra mussels 

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Copyright information

© Society for Mathematical Biology 2008

Authors and Affiliations

  1. 1.Centre for Mathematical Biology, Department of Mathematical and Statistical SciencesUniversity of AlbertaAlbertaCanada
  2. 2.Centre for Mathematical Biology, Department of Mathematical and Statistical Sciences and Department of Biological SciencesUniversity of AlbertaAlbertaCanada

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