#### Date of Award

Spring 1998

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mathematics and Statistics

#### Program/Concentration

Computational and Applied Mathematics

#### Committee Director

John A. Adam

#### Committee Member

Mark Dorrepaal

#### Committee Member

Richard D. Noren

#### Committee Member

Roger Perry

#### Committee Member

John Tweed

#### Abstract

The phenomenological modeling of the spatial distribution and temporal evolution of one-dimensional models of cancer dispersion are studied. The models discussed pertain primarily to the transition of a tumor from an initial neoplasm to the dormant avascular state, i.e. just prior to the vascular state, whenever that may occur. Initiating the study is the mathematical analysis of a reaction-diffusion model describing the interaction between cancer cells, normal cells and growth inhibitor. The model leads to several predictions, some of which are supported by experimental data and clinical observations $\lbrack25\rbrack$. We will examine the effects of additional terms on these characteristics. First, we study the model after incorporating the effects of the immune system at a rate proportional to the existing tumor population. Secondly, we assume that the immune system harvests the tumor population at a constant rate independent of the tumor population followed by inclusion of logistic growth of the cancer cells into the behavior of the growth inhibitor.

Next, we consider a model which consists of only two interacting populations, cancer cells and enzyme. We study this system of equations via two existing approaches.

We conclude with a nonlinear problem of cancer dispersion in which an integral equation governing the propagation of the cancer front is obtained. A primary difference between this model and the previous models is the inclusion of another major transport process called convection. For a special case we find an approximate solution to this equation.

#### DOI

10.25777/0nny-xb64

#### ISBN

9780591815979

#### Recommended Citation

Ward, Kim Y..
"Reaction-Diffusion Models of Cancer Dispersion"
(1998). Doctor of Philosophy (PhD), dissertation, Mathematics and Statistics, Old Dominion University, DOI: 10.25777/0nny-xb64

https://digitalcommons.odu.edu/mathstat_etds/68

#### Included in

Biological Phenomena, Cell Phenomena, and Immunity Commons, Cell Biology Commons, Mathematics Commons, Oncology Commons