Open AccessOptimal control for management of an invasive plant species
Author(s) -
Andrew J. Whittle,
Suzanne Lenhart,
Louis J. Gross
Publication year - 2007
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2007.4.101
Subject(s) - optimal control , mathematical optimization , control (management) , constraint (computer aided design) , variety (cybernetics) , budget constraint , focus (optics) , outlier , computer science , time horizon , operations research , mathematics , economics , artificial intelligence , physics , geometry , neoclassical economics , optics
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.