Drug-resistant mutations in models of HIV pathogenesis
Thesis (Ph.D.)--Memorial University of Newfoundland, 2009. Mathematics and Statistics Includes bibliographical references (leaves 191-197) Over the past quarter-century, considerable work has been invested in the study of the Human Immunodeficiency Virus (HIV). Within the mathematical arena, numerou...
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ftmemorialunivdc:oai:collections.mun.ca:theses4/119593 2023-05-15T17:23:33+02:00 Drug-resistant mutations in models of HIV pathogenesis Sullivan, Shannon Patrick, 1976- Memorial University of Newfoundland. Dept. of Mathematics and Statistics 2008 xvi, 197 leaves : ill. Image/jpeg; Application/pdf http://collections.mun.ca/cdm/ref/collection/theses4/id/119593 Eng eng Electronic Theses and Dissertations (21.20 MB) -- http://collections.mun.ca/PDFs/theses/Sullivan_ShannonPatrick.pdf a3241918 http://collections.mun.ca/cdm/ref/collection/theses4/id/119593 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 Drug resistance HIV infections--Chemotherapy HIV infections--Pathogenesis--Mathematical models T cells--Growth--Mathematical models Text 2008 ftmemorialunivdc 2015-08-06T19:22:24Z Thesis (Ph.D.)--Memorial University of Newfoundland, 2009. Mathematics and Statistics Includes bibliographical references (leaves 191-197) Over the past quarter-century, considerable work has been invested in the study of the Human Immunodeficiency Virus (HIV). Within the mathematical arena, numerous models have been developed to reflect various phenomena associated with the virus. We construct a new ordinary differential equation model for the evolution of the CD4+ T cell population-the white blood cells principally targeted by the virus - in the presence of HIV, incorporating mutation of the wild-type virus and virus response to imperfect drug therapy. In so doing, we make the investigation of the model more tractable by eliminating an explicit reference to the virus population itself. We analyse this model both from a dynamical systems perspective and via numerical simulation, and show that the only possible long-term behaviours are the elimination of both forms of the virus, the elimination of the wild-type virus only, or the co-existence of both virus strains with the uninfected T cell population. We generalise this model to investigate the presence of multiple mutations, and demonstrate that the behaviour of this augmented model reduces naturally to the single-mutant case. Finally, we consider the possibility of imperfect adherence to drug therapy by the patient, by introducing impulsive differential equations into the original model. We determine the impulsive periodic orbits of this model and inspect it numerically. Finally, we use this impulsive model to consider different frequencies and patterns of non-adherence on the part of the HIV sufferer. We determine that as interruptions to drug therapy occur more closely together, they become less harmful to the patient with regard to the progression of the virus. Text 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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Drug resistance HIV infections--Chemotherapy HIV infections--Pathogenesis--Mathematical models T cells--Growth--Mathematical models |
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Drug resistance HIV infections--Chemotherapy HIV infections--Pathogenesis--Mathematical models T cells--Growth--Mathematical models Sullivan, Shannon Patrick, 1976- Drug-resistant mutations in models of HIV pathogenesis |
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Drug resistance HIV infections--Chemotherapy HIV infections--Pathogenesis--Mathematical models T cells--Growth--Mathematical models |
description |
Thesis (Ph.D.)--Memorial University of Newfoundland, 2009. Mathematics and Statistics Includes bibliographical references (leaves 191-197) Over the past quarter-century, considerable work has been invested in the study of the Human Immunodeficiency Virus (HIV). Within the mathematical arena, numerous models have been developed to reflect various phenomena associated with the virus. We construct a new ordinary differential equation model for the evolution of the CD4+ T cell population-the white blood cells principally targeted by the virus - in the presence of HIV, incorporating mutation of the wild-type virus and virus response to imperfect drug therapy. In so doing, we make the investigation of the model more tractable by eliminating an explicit reference to the virus population itself. We analyse this model both from a dynamical systems perspective and via numerical simulation, and show that the only possible long-term behaviours are the elimination of both forms of the virus, the elimination of the wild-type virus only, or the co-existence of both virus strains with the uninfected T cell population. We generalise this model to investigate the presence of multiple mutations, and demonstrate that the behaviour of this augmented model reduces naturally to the single-mutant case. Finally, we consider the possibility of imperfect adherence to drug therapy by the patient, by introducing impulsive differential equations into the original model. We determine the impulsive periodic orbits of this model and inspect it numerically. Finally, we use this impulsive model to consider different frequencies and patterns of non-adherence on the part of the HIV sufferer. We determine that as interruptions to drug therapy occur more closely together, they become less harmful to the patient with regard to the progression of the virus. |
author2 |
Memorial University of Newfoundland. Dept. of Mathematics and Statistics |
format |
Text |
author |
Sullivan, Shannon Patrick, 1976- |
author_facet |
Sullivan, Shannon Patrick, 1976- |
author_sort |
Sullivan, Shannon Patrick, 1976- |
title |
Drug-resistant mutations in models of HIV pathogenesis |
title_short |
Drug-resistant mutations in models of HIV pathogenesis |
title_full |
Drug-resistant mutations in models of HIV pathogenesis |
title_fullStr |
Drug-resistant mutations in models of HIV pathogenesis |
title_full_unstemmed |
Drug-resistant mutations in models of HIV pathogenesis |
title_sort |
drug-resistant mutations in models of hiv pathogenesis |
publishDate |
2008 |
url |
http://collections.mun.ca/cdm/ref/collection/theses4/id/119593 |
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 (21.20 MB) -- http://collections.mun.ca/PDFs/theses/Sullivan_ShannonPatrick.pdf a3241918 http://collections.mun.ca/cdm/ref/collection/theses4/id/119593 |
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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