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Peter Hinow

  1. Structured and unstructured continuous models for Wolbachia infections.

    Thu, 12/10/2009 - 16:01 — SomNambul
    Authors: Jozsef Z. Farkas, Peter Hinow
    Subjects: Classical Analysis and ODEs
    Abstract

    We introduce and investigate a series of models for an infection of a
    diplodiploid host species by the bacterial endosymbiont \textit{Wolbachia}. The
    continuous models are characterized by partial vertical transmission,
    cytoplasmic incompatibility and fitness costs associated with the infection. A
    particular aspect of interest is competitions between mutually incompatible
    strains. We further introduce an age-structured model that takes into account
    different fertility and mortality rates at different stages of the life cycle
    of the individuals.

  2. On a size-structured two-phase population model with infinite states-at-birth.

    Tue, 09/29/2009 - 15:21 — SomNambul
    Authors: Jozsef Z. Farkas, Peter Hinow
    Subjects: Analysis of PDEs
    Abstract

    In this work we introduce and analyze a linear size-structured population
    model with infinite states-at-birth. We model the dynamics of a population in
    which individuals have two distinct life-stages: an "active" phase when
    individuals grow, reproduce and die and a second "resting" phase when
    individuals only grow. Transition between these two phases depends on
    individuals' size. First we show that the problem is governed by a positive
    quasicontractive semigroup on the biologically relevant state space.

  3. Semigroup analysis of structured parasite populations.

    Tue, 09/08/2009 - 12:16 — SomNambul
    Authors: Jozsef Z. Farkas, Darren Green, Peter Hinow
    Subjects: Analysis of PDEs
    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.

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