Global dynamics in a chemostat and an epidemic model
Thesis (M.Sc.)--Memorial University of Newfoundland, 2008. Mathematics and Statistics Includes bibliographical references (leaves 78-81) 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 ep...
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ftmemorialunivdc:oai:collections.mun.ca:theses4/58161 2023-05-15T17:23:33+02:00 Global dynamics in a chemostat and an epidemic model White, Mike Charles, 1983- Memorial University of Newfoundland. Dept. of Mathematics and Statistics 2008 viii, 81 leaves : ill. Image/jpeg; Application/pdf http://collections.mun.ca/cdm/ref/collection/theses4/id/58161 Eng eng Electronic Theses and Dissertations (7.63 MB) -- http://collections.mun.ca/PDFs/theses/White_Mike.pdf a2544303 http://collections.mun.ca/cdm/ref/collection/theses4/id/58161 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. Paper copy kept in the Centre for Newfoundland Studies, Memorial University Libraries Phytoplankton--Growth--Simulation methods Text Electronic thesis or dissertation 2008 ftmemorialunivdc 2015-08-06T19:22:05Z Thesis (M.Sc.)--Memorial University of Newfoundland, 2008. Mathematics and Statistics Includes bibliographical references (leaves 78-81) 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. Thesis Newfoundland studies University of Newfoundland Memorial University of Newfoundland: Digital Archives Initiative (DAI) |
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Memorial University of Newfoundland: Digital Archives Initiative (DAI) |
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English |
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Phytoplankton--Growth--Simulation methods |
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Phytoplankton--Growth--Simulation methods White, Mike Charles, 1983- Global dynamics in a chemostat and an epidemic model |
topic_facet |
Phytoplankton--Growth--Simulation methods |
description |
Thesis (M.Sc.)--Memorial University of Newfoundland, 2008. Mathematics and Statistics Includes bibliographical references (leaves 78-81) 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. |
author2 |
Memorial University of Newfoundland. Dept. of Mathematics and Statistics |
format |
Thesis |
author |
White, Mike Charles, 1983- |
author_facet |
White, Mike Charles, 1983- |
author_sort |
White, Mike Charles, 1983- |
title |
Global dynamics in a chemostat and an epidemic model |
title_short |
Global dynamics in a chemostat and an epidemic model |
title_full |
Global dynamics in a chemostat and an epidemic model |
title_fullStr |
Global dynamics in a chemostat and an epidemic model |
title_full_unstemmed |
Global dynamics in a chemostat and an epidemic model |
title_sort |
global dynamics in a chemostat and an epidemic model |
publishDate |
2008 |
url |
http://collections.mun.ca/cdm/ref/collection/theses4/id/58161 |
genre |
Newfoundland studies University of Newfoundland |
genre_facet |
Newfoundland studies University of Newfoundland |
op_source |
Paper copy kept in the Centre for Newfoundland Studies, Memorial University Libraries |
op_relation |
Electronic Theses and Dissertations (7.63 MB) -- http://collections.mun.ca/PDFs/theses/White_Mike.pdf a2544303 http://collections.mun.ca/cdm/ref/collection/theses4/id/58161 |
op_rights |
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. |
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1766113252904796160 |