Allee effect and control of lake system invasion.
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.
Potapov
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Centre for Mathematical Biology, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada. apotapov@math.ualberta.ca
Lewis
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MA
D000465:Algorithms; D000818:Animals; D003362:Cost-Benefit Analysis; D049875:Dreissena / Q000502:physiology*; D017753:Ecosystem; D005618:Fresh Water; D008954:Models, Biological; D011155:Population Control / Q000191:economics / Q000379:methods; D011157:Population Dynamics; D045483:Rivers; D012767:Ships