|Appears in Collections:
|Aquaculture Journal Articles
|Peer Review Status:
|Semigroup analysis of structured parasite populations
|Farkas, Jozsef Zoltan
Aquaculture Mathematical models
|Farkas JZ, Green D & Hinow P (2010) Semigroup analysis of structured parasite populations. Mathematical Modelling of Natural Phenomena, 5 (3), pp. 94-114. http://www.mmnp-journal.org/action/displayJournal?jid=MNP; https://doi.org/10.1051/mmnp/20105307
|Motivated by the modelling of structured parasite populations in aquaculture we consider a class of physiologically structured population models, where individuals may be recruited into the population at different sizes in general. That is, we consider a size-structured population model with distributed states-at-birth. The mathematical model which describes the evolution of such a population is a first order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In case of a separable fertility function we deduce a characteristic equation and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.
|Published in Mathematical Modelling of Natural Phenomena. Copyright © EDP Sciences, 2010.; Rights according to Copyright Transfer Agreement: http://journals.cambridge.org/images/fileUpload/documents/mnp_copyright.pdf; The original publication is available at http://www.mmnp-journal.org.; http://www.mmnp-journal.org/action/displayAbstract?fromPage=online&aid=8014468
|Fulltext - Accepted Version
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