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 sizestructured 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 firstorder nonlinear partial integrodifferential 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 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.
This is joint work with Jozsef Z. Farkas and Darren Green (University
of
Stirling, Scotland).
