Title page for ETD etd-08082007-114126

Type of Document Master's Thesis
Author Newbury, Golnar
URN etd-08082007-114126
Title A Numerical Study of a Delay Differential Equation Model for Breast Cancer
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Burns, John A. Committee Chair
Herdman, Terry L. Committee Member
Zietsman, Lizette Committee Member
  • delay differential equations
  • cancer model
  • parameter sensitivity
  • ordinary differential equations
  • Paclitaxel
  • cell cycle
  • cycle specific chemotherapy
  • proliferating cells
  • quiescent cells
Date of Defense 2007-08-03
Availability unrestricted
In 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.

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