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Talk Abstract

Analysis of a Mathematical Model

of the Effect of Inhibitors on the Growth of Tumors

Analysis of a Mathematical Model

of the Effect of Inhibitors on the Growth of Tumors

** Avner Friedman
Director
Minnesota Center for Industrial Mathematics **

University of Minnesota

friedman@math.umn.edu

In this paper we study a model of tumor growth in the presence
of inhibitors. The tumor is assumed to be spherically symmetric
and its boundary is an unknown function *r=R(t)*. Within
the tumor the concentration of nutrient and the concentration
of inhibitor (drug) satisfy a system of reaction diffusion equations.
The important parameters are .
_{0} (which depends on the tumor's parameters when no
inhibitors are present),
which depends only on the specific properties of the inhibitor,
and
which is the (normalized) external concentration of the inhibitor.
In this paper we give precise conditions under which there exist
one dormant tumor, two dormant tumors, or none. We then prove
that in the first case, the dormant tumor is globally asymptotically
stable, and in the second case, if the radii of the dormant
tumors are denoted by *R ^{-}_{s}, R^{+}_{s}
* with R