Optimal Culling and Biocontrol in a Predator–Prey Model

Eric Numfor, Frank M. Hilker, Suzanne Lenhart

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Invasive species cause enormous problems in ecosystems around the world. Motivated by introduced feral cats that prey on bird populations and threaten to drive them extinct on remote oceanic islands, we formulate and analyze optimal control problems. Their novelty is that they involve both scalar and time-dependent controls. They represent different forms of control, namely the initial release of infected predators on the one hand and culling as well as trapping, infecting, and returning predators on the other hand. Combinations of different control methods have been proposed to complement their respective strengths in reducing predator numbers and thus protecting endangered prey. Here, we formulate and analyze an eco-epidemiological model, provide analytical results on the optimal control problem, and use a forward–backward sweep method for numerical simulations. By taking into account different ecological scenarios, initial conditions, and control durations, our model allows to gain insight how the different methods interact and in which cases they could be effective.

Original languageEnglish (US)
Pages (from-to)88-116
Number of pages29
JournalBulletin of Mathematical Biology
Volume79
Issue number1
DOIs
StatePublished - Jan 1 2017

Fingerprint

Biocontrol
culling
culling (animals)
Predator-prey Model
biological control
Predator
predator
predators
Prey
Raptors
Introduced Species
Optimal Control Problem
Duration Models
Islands
invasive species
Epidemiological Model
Ecosystem
trapping
control methods
complement

Cite this

Optimal Culling and Biocontrol in a Predator–Prey Model. / Numfor, Eric; Hilker, Frank M.; Lenhart, Suzanne.

In: Bulletin of Mathematical Biology, Vol. 79, No. 1, 01.01.2017, p. 88-116.

Research output: Contribution to journalArticle

Numfor, Eric ; Hilker, Frank M. ; Lenhart, Suzanne. / Optimal Culling and Biocontrol in a Predator–Prey Model. In: Bulletin of Mathematical Biology. 2017 ; Vol. 79, No. 1. pp. 88-116.
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