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Modelling the response of cytotoxic t-lymphocytes in controlling solid tumour invasion.

dc.contributor.advisorMambili-Mamboundou, H.
dc.contributor.advisorSibanda, Precious.
dc.contributor.authorMalinzi, Joseph.
dc.date.accessioned2013-12-20T08:53:22Z
dc.date.available2013-12-20T08:53:22Z
dc.date.created2013
dc.date.issued2013
dc.descriptionThesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.en
dc.description.abstractWe present mathematical models to study the mechanism of interaction of tumour infiltrating cytotoxic lymphocytes (TICLs) with tumour cells. We focus on the phase spaces of the systems and the nature of the solutions for the cell densities in the short and long term. The first model describes the production of offspring through cell proliferation, death and local kinetic interactions. The second model characterises the spatial distribution dynamics of the cell densities through reaction diffusion, which describes the random movement of the cells, and chemotaxis, which describes the immune cell movements towards the tumour cells. We then extend these models further to incorporate the effects of immunotherapy by developing two new models. In both situations, we analyse the phase spaces of the homogeneous models, investigate the presence of travelling wave solutions in our systems, and provide numerical simulations. Our analysis shows that cancer dormancy can be attributed to TICLs. Our study also shows that TICLs reduce the tumour cell density to a cancer dormant state but even with immunotherapy do not completely eliminate tumour cells from body tissue. Travelling wave solutions were confirmed to exist in the heterogeneous model, a linear stability analysis of the homogeneous models and numerical simulations show the existence of a stable tumour dormant state and a phase space analysis confirms that there are no limit cycles.en
dc.identifier.urihttp://hdl.handle.net/10413/10281
dc.language.isoen_ZAen
dc.subjectMathematical statistics.en
dc.subjectCancer--Mathematical models.en
dc.subjectCancer invasiveness--Mathematical models.en
dc.subjectTheses--Applied mathematics.en
dc.titleModelling the response of cytotoxic t-lymphocytes in controlling solid tumour invasion.en
dc.typeThesisen

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