## Date of Award

Spring 1995

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## Department

Mathematics & Statistics

## Program/Concentration

Computational and Applied Mathematics

## Committee Director

John A. Adam

## Committee Member

Philip R. Wohl

## Committee Member

John Heinbockel

## Abstract

Several mathematical models are developed to describe the effects of chemotherapy on both cancerous and normal tissue. Each model is defined by either a single homogeneous equation or a system of heterogeneous equations which describe the states of the normal and/or cancer cells. Periodic terms are added to model the effects of the chemotherapy. What we obtain are regions, in parameter space (dose and period), of acceptable drug regimens.

The models take into account various aspects of chemotherapy. These include, interactions between the cancer and normal tissue, cell specific chemotherapeutic drug, the use of non-constant parameters to aid in modeling specific chemotherapeutic processes, and drug resistance. By studying the models we can obtain a better understanding of the dynamics of the chemotherapeutic drugs and how better to implement them.

The mathematical methods used are mostly in the area of dynamical systems in particular Floquet Theory. These methods are used on either a single equation or a system of periodic ordinary differential equations which model the chemotherapeutic process. These are reduced to difference equations that describe the state of the cancer at the beginning of each period. By studying the characteristic multipliers, we are able to determine the bifurcation between successful and unsuccessful regimens, if existing drug regimens seem reasonable from a mathematical model standpoint, and suggest ways to better implement the existing chemotherapeutic drugs.

## Rights

In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).

## DOI

10.25777/5aev-jk74

## Recommended Citation

Panetta, John C..
"Mathematical Models of Chemotherapy"
(1995). Doctor of Philosophy (PhD), Dissertation, Mathematics & Statistics, Old Dominion University, DOI: 10.25777/5aev-jk74

https://digitalcommons.odu.edu/mathstat_etds/43