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dc.contributor.advisorPatidar, Kailash
dc.contributor.authorShikongo, Albert
dc.date.accessioned2020-06-01T08:23:56Z
dc.date.issued2020
dc.identifier.urihttp://hdl.handle.net/11394/7250
dc.descriptionPhilosophiae Doctor - PhDen_US
dc.description.abstractCancer is a complex disease that involves a sequence of gene-environment interactions in a progressive process that cannot occur without dysfunction in multiple systems. From a mathematical point of view, the sequence of gene-environment interactions often leads to mathematical models which are hard to solve analytically. Therefore, this thesis focuses on the design and implementation of reliable numerical methods for nonlinear, first order delay differential equations, second order non-linear time-dependent parabolic partial (integro) differential problems and optimal control problems arising in cancer modeling. The development of cancer modeling is necessitated by the lack of reliable numerical methods, to solve the models arising in the dynamics of this dreadful disease. Our focus is on chemotherapy, biological stoichometry, double infections, micro-environment, vascular and angiogenic signalling dynamics. Therefore, because the existing standard numerical methods fail to capture the solution due to the behaviors of the underlying dynamics. Analysis of the qualitative features of the models with mathematical tools gives clear qualitative descriptions of the dynamics of models which gives a deeper insight of the problems. Hence, enabling us to derive robust numerical methods to solve such models.en_US
dc.language.isoenen_US
dc.publisherUniversity of the Western Capeen_US
dc.subjectCancer modelingen_US
dc.subjectImmune systemen_US
dc.subjectMathematical biologyen_US
dc.subjectNumerical methodsen_US
dc.subjectCanceren_US
dc.subjectBiological stoichometryen_US
dc.titleRobust numerical methods to solve differential equations arising in cancer modelingen_US
dc.rights.holderUniversity of the Western Capeen_US
dc.description.embargo2021-04-30


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