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 AM  Vol.6 No.7 , June 2015
Simple Linear Model of Tumor Growth in a Changing Environment
Abstract: In an environment that is neither static nor in equilibrium, but is dynamic and changing, the kinetics of the reactions that cause the growth of a tumor, which depend on the state of the evolving environment, cannot be parametrized in terms of constant rates. We propose a simple model for describing the growth on an untreated tumor in such environments, which is characterized by a minimal number of parameters and is generalizable to include the effects of various types of therapies. In the simplest version that we consider here, it consists of a linear equation with a time-dependent growth rate, which we interpret as the coupling of the system with a dynamic environment. A complete solution is given in terms of the integral of the growth rate. The essential features of the general solution are illustrated with a few examples, and comparison is made with the models that have been proposed to describe recent data.
Cite this paper: Nieves, J. and Ubriaco, M. (2015) Simple Linear Model of Tumor Growth in a Changing Environment. Applied Mathematics, 6, 1139-1147. doi: 10.4236/am.2015.67104.
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