# Semigroup Analysis of Structured Parasite Populations

J. Z. Farkas; D. M. Green; P. Hinow

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 5, Issue: 3, page 94-114
- ISSN: 0973-5348

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topFarkas, J. Z., Green, D. M., and Hinow, P.. "Semigroup Analysis of Structured Parasite Populations." Mathematical Modelling of Natural Phenomena 5.3 (2010): 94-114. <http://eudml.org/doc/197676>.

@article{Farkas2010,

abstract = {Motivated by structured parasite populations in aquaculture we consider a class of
size-structured population models, where individuals may be recruited into the population
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 the 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.},

author = {Farkas, J. Z., Green, D. M., Hinow, P.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {aquaculture; quasicontraction semigroups; positivity; spectral methods; stability},

language = {eng},

month = {4},

number = {3},

pages = {94-114},

publisher = {EDP Sciences},

title = {Semigroup Analysis of Structured Parasite Populations},

url = {http://eudml.org/doc/197676},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Farkas, J. Z.

AU - Green, D. M.

AU - Hinow, P.

TI - Semigroup Analysis of Structured Parasite Populations

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/4//

PB - EDP Sciences

VL - 5

IS - 3

SP - 94

EP - 114

AB - Motivated by structured parasite populations in aquaculture we consider a class of
size-structured population models, where individuals may be recruited into the population
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 the 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.

LA - eng

KW - aquaculture; quasicontraction semigroups; positivity; spectral methods; stability

UR - http://eudml.org/doc/197676

ER -

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