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Analysis and implementation of robust numerical methods to solve mathematical models of HIV and Malaria co-infection

Philosophiae Doctor - PhD / There is a growing interest in the dynamics of the co-infection of these two diseases. In this thesis, firstly we focus on studying the effect of a distributed delay representing the incubation period for the malaria parasite in the mosquito vector to possibly reduce the initial transmission and prevalence of malaria. This model can be regarded as a generalization of SEI models (with a class for the latently infected mosquitoes) and SI models with a discrete delay for the incubation period in mosquitoes. We study the possibility of occurrence of backward bifurcation. We then extend these ideas to study a full model of HIV and malaria co-infection. To get further inside into the dynamics of the model, we use the geometric singular perturbation theory to couple the fast and slow models from the full model. Finally, since the governing models are very complex, they cannot be solved analytically and hence we develop and analyze a special class of numerical methods to solve them. / South Africa

Identiferoai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uwc/oai:etd.uwc.ac.za:11394/1784
Date January 2011
CreatorsElsheikh, Sara Mohamed Ahmed Suleiman
ContributorsPatidar, Kailash C., Ouifki, Rachid, Dept. of Mathematics, Faculty of Science
PublisherUniversity of the Western Cape
Source SetsSouth African National ETD Portal
LanguageEnglish
Detected LanguageEnglish
TypeThesis
RightsUniversity of the Western Cape

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