Optimal control for management of an invasive plant species
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...
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| Format: | Article |
| Language: | English |
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AIMS Press
2006-10-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.101 |
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| author | Andrew J. Whittle Suzanne Lenhart Louis J. Gross |
| author_facet | Andrew J. Whittle Suzanne Lenhart Louis J. Gross |
| author_sort | Andrew J. Whittle |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8150df6a99274c968a679a0b4b482d3a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2006-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-8150df6a99274c968a679a0b4b482d3a2025-01-24T01:52:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182006-10-014110111210.3934/mbe.2007.4.101Optimal control for management of an invasive plant speciesAndrew J. Whittle0Suzanne Lenhart1Louis J. Gross2Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300Invasive 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.https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.101invasive speciesdiscrete timeoptimal controlnatural resources.biological invasions |
| spellingShingle | Andrew J. Whittle Suzanne Lenhart Louis J. Gross Optimal control for management of an invasive plant species Mathematical Biosciences and Engineering invasive species discrete time optimal control natural resources. biological invasions |
| title | Optimal control for management of an invasive plant species |
| title_full | Optimal control for management of an invasive plant species |
| title_fullStr | Optimal control for management of an invasive plant species |
| title_full_unstemmed | Optimal control for management of an invasive plant species |
| title_short | Optimal control for management of an invasive plant species |
| title_sort | optimal control for management of an invasive plant species |
| topic | invasive species discrete time optimal control natural resources. biological invasions |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.101 |
| work_keys_str_mv | AT andrewjwhittle optimalcontrolformanagementofaninvasiveplantspecies AT suzannelenhart optimalcontrolformanagementofaninvasiveplantspecies AT louisjgross optimalcontrolformanagementofaninvasiveplantspecies |