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).