Math Department
Kansas Wesleyan University
Salina, KS 67401, USA
email: rahangar@kwu.edu or rahangar@alltel.net
Math Department
North Carolina State University
Raleigh, NC 27695-8205, USA
email: xblin@math.ncsu.edu
Reza Ahangar & Xiao-Biao Lin
Abstract:
We developed a mathematical model for carcinogenesis mutations
based on the reaction diffusion, logistic behavior,
and interactions between normal, benign, and premalignant mutant
cells. We adopted a deterministic view of the multistage evolution
of the mutant cell to a tumor with a fast growth rate, and its
progress to a malignant stage. In a simple case of this model,
the interaction between normal and tumor cells with one or two
stages of mutations was analyzed. The stability of the dynamical
system and the travelling wave solutions for different stages of
evolution of mutant cells were investigated. We observed the effect
of variation and natural selection in shaping the carcinogenesis
malignant mutation.
Published February 28, 2003.
Subject classifications: 92C30, 62P10, 92D10, 92D25.
Key words: Cancer, mutation, interaction, travelling waves,
singular perturbation.
Show me the PDF file (334K), TEX file, and other files for this article.
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Reza Ahangar Math Department Kansas Wesleyan University Salina, KS 67401, USA email: rahangar@kwu.edu or rahangar@alltel.net |
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Xiao-Biao Lin Math Department North Carolina State University Raleigh, NC 27695-8205, USA email: xblin@math.ncsu.edu |
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