A Numerical Study of a Delay Differential Equation Model for Breast Cancer

dc.contributor.authorNewbury, Golnaren
dc.contributor.committeechairBurns, John A.en
dc.contributor.committeememberZietsman, Lizetteen
dc.contributor.committeememberHerdman, Terry L.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:43:00Zen
dc.date.adate2007-08-24en
dc.date.available2014-03-14T20:43:00Zen
dc.date.issued2007-08-03en
dc.date.rdate2007-08-24en
dc.date.sdate2007-08-08en
dc.description.abstractIn this thesis we construct a new model of the immune response to the growth of breast cancer cells and investigate the impact of certain drug therapies on the cancer. We use delay differential equations to model the interaction of breast cancer cells with the immune system. The new model is constructed by combining two previous models. The first model accounts for different cell cycles and includes terms to evaluate drug treatments, but ignores quiescent tumor cells. The second model includes quiescent cells, but ignores the immune response and drug treatments. The new model is obtained by combining and modifying these two models to account for quiescent cells, immune cells and includes drug intervention terms. This new model is used to evaluate the effects of pulsed applications of the drug Paclitaxel for models with and without quiescent cells. We use sensitivity equation methods to analyze the sensitivity of the model with respect to the initial number of immune cytotoxic T-cells. Numerical experiments are conducted to compare the model predictions to observed behavior.en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-08082007-114126en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-08082007-114126/en
dc.identifier.urihttp://hdl.handle.net/10919/34420en
dc.publisherVirginia Techen
dc.relation.haspartfinalthesis.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectdelay differential equationsen
dc.subjectcancer modelen
dc.subjectparameter sensitivityen
dc.subjectordinary differential equationsen
dc.subjectPaclitaxelen
dc.subjectcell cycleen
dc.subjectcycle specific chemotherapyen
dc.subjectproliferating cellsen
dc.subjectquiescent cellsen
dc.titleA Numerical Study of a Delay Differential Equation Model for Breast Canceren
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen
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