Appl Math Optim 54:1–15 (2006)
2006 Springer Science+Business Media, Inc.
Optimal Harvesting in an Age-Structured Predator–Prey Model
K. Renee Fister
and Suzanne Lenhart
Department of Mathematics and Statistics, Murray State University,
Murray, KY 42071-3341, USA
Department of Mathematics, University of Tennessee,
Knoxville, TN 37996-1300, USA
Computer Science and Mathematics Division, Oak Ridge National Laboratory,
Oak Ridge, TN 37831-6016, USA
Communicated by D. Kinderlehrer
Abstract. We investigate optimal harvesting control in a predator–prey model in
which the prey population is represented by a ﬁrst-order partial differential equa-
tion with age-structure and the predator population is represented by an ordinary
differential equation in time. The controls are the proportions of the populations to
be harvested, and the objective functional represents the proﬁt from harvesting. The
existence and uniqueness of the optimal control pair are established.
Key Words. Optimal control, Age-structure, Predator–prey.
AMS Classiﬁcation. 49K20, 35F20.
We consider optimal harvesting control in a predator–prey model in which only the prey
population has age-structure. The life cycle of the predator is deemed signiﬁcantly longer
The research of the ﬁrst author was partially supported by the Kentucky NSF EPSCoR Research
Enhancement Grant #9874764 and the AWM Collaborative Research Grant. The research of the second author
was partially supported by the National Science Foundation Grant EF-ITR 0427471.