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Mathematical Biosciences and Engineering

2007, Volume 4, Issue 1: 101-112. doi: 10.3934/mbe.2007.4.101
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Optimal control for management of an invasive plant species

  • 1.
    Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300
  • 2.
    Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300
  • 3.
    Department of Mathematics & Department of Ecology and Evolutionary Biology, University of Tennessee, Knoxville, TN 37996-1300
  • Received: 01 January 2006 Accepted: 29 June 2018 Published: 01 November 2006

  • MSC : 92D40.

  • Invasive plant populations typically consist of a large (main) focus and several smaller outlier populations. Management of the spread of invasives requires repeated control measures, constrained by limited funding and effort. Posing this as a control problem, we investigate whether it is best to apply control to the main focus, the outlier populations, or some combination of these. We first formulate and solve a discrete-time optimal control problem to determine where control is best applied over a finite time horizon. However, if limited funds are available for control, this optimal solution may not be feasible. In this case, we add an additional constraint to account for the fixed budget and solve the new optimality system. Our results have a variety of practical implications for invasive species management.

    Citation: Andrew J. Whittle, Suzanne Lenhart, Louis J. Gross. Optimal control for management of an invasive plant species[J]. Mathematical Biosciences and Engineering, 2007, 4(1): 101-112. doi: 10.3934/mbe.2007.4.101

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  • Invasive plant populations typically consist of a large (main) focus and several smaller outlier populations. Management of the spread of invasives requires repeated control measures, constrained by limited funding and effort. Posing this as a control problem, we investigate whether it is best to apply control to the main focus, the outlier populations, or some combination of these. We first formulate and solve a discrete-time optimal control problem to determine where control is best applied over a finite time horizon. However, if limited funds are available for control, this optimal solution may not be feasible. In this case, we add an additional constraint to account for the fixed budget and solve the new optimality system. Our results have a variety of practical implications for invasive species management.


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  • © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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