Fifth Mississippi State Conference on Differential Equations and Computational Simulations,
Electron. J. Diff. Eqns., Conf. 10, 2003, pp. 33-53.

Multistage evolutionary model for carcinogenesis mutations

Reza Ahangar & Xiao-Biao Lin

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.

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Reza Ahangar
Math Department
Kansas Wesleyan University
Salina, KS 67401, USA
email: or
Xiao-Biao Lin
Math Department
North Carolina State University
Raleigh, NC 27695-8205, USA

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