American Institute of Mathematical Sciences

Advanced
2007, 4(1): 101-112. doi: 10.3934/mbe.2007.4.101

Optimal control for management of an invasive plant species

Andrew J. Whittle 1, , Suzanne Lenhart 2, and  Louis J. Gross 3,

1. 

Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300, United States
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, United States

Received  January 2006 Revised  July 2006 Published  November 2006

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.
Keywords: invasive species, discrete time, optimal control, natural resources., biological invasions.
Mathematics Subject Classification: 92D4.
Citation: Andrew J. Whittle, Suzanne Lenhart, Louis J. Gross. Optimal control for management of an invasive plant species. Mathematical Biosciences & Engineering, 2007, 4 (1) : 101-112. doi: 10.3934/mbe.2007.4.101
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