Analysis and implementation of a positivity preserving numerical method for an HIV model

Analysis and implementation of a positivity preserving numerical method for an HIV model

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Magister Scientiae - MSc === This thesis deals with analysis and implementation of a positivity preserving numerical method for a vaccination model for the transmission dynamics of two HIVsubtypesnin a given community. The continuous model is analyzed for stability and equilibria. The qualitative in...

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Bibliographic Details
Main Author: Wyngaardt, Jo-Anne
Other Authors: Patidar, Kailash C.
Language:en
Published: 2014
Subjects:
HIV model(s)
Stability
Reproduction number
Quilibria
Method
Preservation of positivity
Online Access:http://hdl.handle.net/11394/3750
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record_format oai_dc
spelling ndltd-netd.ac.za-oai-union.ndltd.org-uwc-oai-etd.uwc.ac.za-11394-37502017-08-02T04:00:38Z Analysis and implementation of a positivity preserving numerical method for an HIV model Wyngaardt, Jo-Anne Patidar, Kailash C. HIV model(s) Stability Reproduction number Quilibria Method Preservation of positivity Magister Scientiae - MSc This thesis deals with analysis and implementation of a positivity preserving numerical method for a vaccination model for the transmission dynamics of two HIVsubtypesnin a given community. The continuous model is analyzed for stability and equilibria. The qualitative information thus obtained is used while designing numerical method(s). Three numerical methods, namely, Implicit Finite Difference Method (IFDM), Non-standard Finite Difference Method (NSFDM) and the Runge-Kutta method of order four (RK4), are designed and implemented. Extensive numerical simulation are carried out to justify theoretical outcomes 2014-10-01T13:11:49Z 2014-10-01T13:11:49Z 2007 http://hdl.handle.net/11394/3750 en uwc
collection NDLTD
language en
sources NDLTD
topic HIV model(s)
Stability
Reproduction number
Quilibria
Method
Preservation of positivity
spellingShingle HIV model(s)
Stability
Reproduction number
Quilibria
Method
Preservation of positivity
Wyngaardt, Jo-Anne
Analysis and implementation of a positivity preserving numerical method for an HIV model
description Magister Scientiae - MSc === This thesis deals with analysis and implementation of a positivity preserving numerical method for a vaccination model for the transmission dynamics of two HIVsubtypesnin a given community. The continuous model is analyzed for stability and equilibria. The qualitative information thus obtained is used while designing numerical method(s). Three numerical methods, namely, Implicit Finite Difference Method (IFDM), Non-standard Finite Difference Method (NSFDM) and the Runge-Kutta method of order four (RK4), are designed and implemented. Extensive numerical simulation are carried out to justify theoretical outcomes
author2 Patidar, Kailash C.
author_facet Patidar, Kailash C.
Wyngaardt, Jo-Anne
author Wyngaardt, Jo-Anne
author_sort Wyngaardt, Jo-Anne
title Analysis and implementation of a positivity preserving numerical method for an HIV model
title_short Analysis and implementation of a positivity preserving numerical method for an HIV model
title_full Analysis and implementation of a positivity preserving numerical method for an HIV model
title_fullStr Analysis and implementation of a positivity preserving numerical method for an HIV model
title_full_unstemmed Analysis and implementation of a positivity preserving numerical method for an HIV model
title_sort analysis and implementation of a positivity preserving numerical method for an hiv model
publishDate 2014
url http://hdl.handle.net/11394/3750
work_keys_str_mv AT wyngaardtjoanne analysisandimplementationofapositivitypreservingnumericalmethodforanhivmodel
_version_ 1718510752751419392

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