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

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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2007

Author dc:creator

• Newbury, Golnar

Chair dc:contributor.committeechair

• Burns, John A.

Committee members dc:contributor.committeemember

• Zietsman, Lizette
• Herdman, Terry L.

• delay differential equations
• cancer model
• parameter sensitivity
• ordinary differential equations
• Paclitaxel
• cell cycle
• cycle specific chemotherapy
• proliferating cells
• quiescent cells

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-08082007-114126

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/34420