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
Description
Summary: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

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