Global dynamics in a chemostat and an epidemic model

White, Mike Charles (2008) Global dynamics in a chemostat and an epidemic model. Masters thesis, Memorial University of Newfoundland.

[img] [English] PDF - Accepted Version
Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.

Download (3200Kb)

Abstract

Two models are studied in this work; a periodically forced Droop model for phytoplankton growth with two competing species in a chemostat and a time-delayed SIR epidemic model with dispersal. -- For the competition model, both uniform persistence and the existence of periodic coexistence state are established for a periodically forced Droop model on two phytoplankton species competition in a chemostat under some appropriate conditions. Numerical simulations using biological data are presented as well to illustrate the main result. -- The global dynamics of a time-delayed model with population dispersal between two patches is also investigated. For a general class of birth functions, persistence theory is applied to prove that a disease is persistent when the basic reproduction number is greater than one. It is also shown that the disease will die out if the basic reproduction number is less than one, provided that the invasion intensity is not strong. Numerical simulations are presented using some typical birth functions from biological literature to illustrate the main ideas and the relevance of dispersal.

Item Type: Thesis (Masters)
URI: http://research.library.mun.ca/id/eprint/8817
Item ID: 8817
Additional Information: Includes bibliographical references (leaves 78-81)
Department(s): Science, Faculty of > Mathematics and Statistics
Date: 2008
Date Type: Submission
Library of Congress Subject Heading: Phytoplankton--Growth--Simulation methods

Actions (login required)

View Item View Item

Downloads

Downloads per month over the past year

View more statistics