Mathematical Biology Seminar
Peter Hinow, University of Wisconsin, Milwaukee,
Wednesday March 17, 2010
3:05pm in LCB 215
Semigroup Analysis of Structured Parasite Populations
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 that 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
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 semi-group 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.
This is joint work with Jozsef Z. Farkas and Darren Green (University
of
Stirling, Scotland).
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