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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: On the net reproduction rate of continuous structured populations with distributed states at birth
Author(s): Ackleh, Azmy S
Farkas, Jozsef Zoltan
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Keywords: Size-structured populations
Net reproduction rate
Distributed states at birth
Integral equations
Spectral theory
Issue Date: Nov-2013
Date Deposited: 19-Jul-2013
Citation: Ackleh AS & Farkas JZ (2013) On the net reproduction rate of continuous structured populations with distributed states at birth. Computers and Mathematics with Applications, 66 (9), pp. 1685-1694.
Abstract: We consider a nonlinear structured population model with a distributed recruitment term. The question of the existence of non-trivial steady states can be treated (at least) in three different ways. One approach is to study spectral properties of a parametrised family of unbounded operators. The alternative approach, which we develop here, is based on the reformulation of the partial differential equation as an integral equation. In this context we introduce a density dependent net reproduction rate and discuss its relationship to a biologically meaningful quantity. Finally, we discuss a third approach, which is based on a finite rank approximation of the recruitment operator.
DOI Link: 10.1016/j.camwa.2013.04.010
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