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

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