The mathematical modelling of the transmission dynamics of HIV/AIDS and the impact of antiviral therapies

4.00
Hdl Handle:
http://hdl.handle.net/10547/581882
Title:
The mathematical modelling of the transmission dynamics of HIV/AIDS and the impact of antiviral therapies
Authors:
Hajian, Emad
Abstract:
This thesis is concerned with the structure, analysis and numerical solution of the mathematical models used to estimate the transmission dynamics of the Human Immunodeficiency Virus (HIV)) the causative agent of Acquired Immune Deficiency Syndrome (AIDS). Investigations show that the devised deterministic mathematical models in term of system of first-order non-linear ordinary differential equations (ODEs) follow the stochastic nature of the problem at any time. In this thesis a generic form of the deterministic mathematical models is introduced which mirrors the transmission dynamics of HIV/AIDS in populations with different states of affairs, which leads to the division of large-scale and complex mathematical models. When analysing and;or solving a large-scale system of ODEs numerically, the key element in speeding up the process is selecting the maximum possible time step. This work introduces some new techniques used to estimate the maximum possible time step, avoiding the appearance of chaos and divergence in the solution when they are not features of the system. The solution to these mathematical models are presented graphically and numerically, aiming to identify the effect of the anti-HIV therapies and sex education in controlling the disease. The numerical results presented in this thesis indicate that lowering the average number of sexual partners per year is more effective in controlling the disease than the current anti-HIV treatments. For the purpose of this study the mathematical software 'Mathematica 3.0' was used to solve the system of differential equations, modelling HIV/AIDS propagation. This package also provided the graphical detail incorporated in the thesis.
Citation:
Hajian, E. (2000) 'The mathematical modelling of the transmission dynamics of HIV/AIDS and the impact of antiviral therapies'. PhD thesis. University of Bedfordshire.
Publisher:
University of Bedfordshire
Issue Date:
Apr-2000
URI:
http://hdl.handle.net/10547/581882
Type:
Thesis or dissertation
Language:
en
Description:
Thesis presented for the degree of Doctor of Philosophy, Department of Electronics and Mathematics, Faculty of Science, Technology and Design, the University of Luton
Appears in Collections:
PhD e-theses

Full metadata record

DC FieldValue Language
dc.contributor.authorHajian, Emaden
dc.date.accessioned2015-11-06T12:44:28Zen
dc.date.available2015-11-06T12:44:28Zen
dc.date.issued2000-04en
dc.identifier.citationHajian, E. (2000) 'The mathematical modelling of the transmission dynamics of HIV/AIDS and the impact of antiviral therapies'. PhD thesis. University of Bedfordshire.en
dc.identifier.urihttp://hdl.handle.net/10547/581882en
dc.descriptionThesis presented for the degree of Doctor of Philosophy, Department of Electronics and Mathematics, Faculty of Science, Technology and Design, the University of Lutonen
dc.description.abstractThis thesis is concerned with the structure, analysis and numerical solution of the mathematical models used to estimate the transmission dynamics of the Human Immunodeficiency Virus (HIV)) the causative agent of Acquired Immune Deficiency Syndrome (AIDS). Investigations show that the devised deterministic mathematical models in term of system of first-order non-linear ordinary differential equations (ODEs) follow the stochastic nature of the problem at any time. In this thesis a generic form of the deterministic mathematical models is introduced which mirrors the transmission dynamics of HIV/AIDS in populations with different states of affairs, which leads to the division of large-scale and complex mathematical models. When analysing and;or solving a large-scale system of ODEs numerically, the key element in speeding up the process is selecting the maximum possible time step. This work introduces some new techniques used to estimate the maximum possible time step, avoiding the appearance of chaos and divergence in the solution when they are not features of the system. The solution to these mathematical models are presented graphically and numerically, aiming to identify the effect of the anti-HIV therapies and sex education in controlling the disease. The numerical results presented in this thesis indicate that lowering the average number of sexual partners per year is more effective in controlling the disease than the current anti-HIV treatments. For the purpose of this study the mathematical software 'Mathematica 3.0' was used to solve the system of differential equations, modelling HIV/AIDS propagation. This package also provided the graphical detail incorporated in the thesis.en
dc.language.isoenen
dc.publisherUniversity of Bedfordshireen
dc.subjectG150 Mathematical Modellingen
dc.subjectmathematical modellingen
dc.subjectmodellingen
dc.subjectHIV/AIDSen
dc.subjectHIVen
dc.subjectAIDSen
dc.subjecttransmission dynamicsen
dc.titleThe mathematical modelling of the transmission dynamics of HIV/AIDS and the impact of antiviral therapiesen
dc.typeThesis or dissertationen
dc.type.qualificationnamePhDen_GB
dc.type.qualificationlevelPhDen
dc.publisher.institutionUniversity of Bedfordshireen
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