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Multiscale modeling and mathematical problems related to tumor evolution and medical therapy. (English) Zbl 1107.92020
Summary: This paper provides a survey of mathematical models and methods dealing with the analysis and simulation of tumor dynamics in competition with the immune system. The characteristic scales of the phenomena are identified and the mathematical literature on models and problems developed on each scale is reviewed and critically analyzed. Moreover, this paper deals with the modeling and optimization of therapeutical actions. The aim of this critical analysis and review consists in providing the background framework towards the development of research perspectives in this promising new field of applied mathematics.

MSC:
92C50 Medical applications (general)
49N90 Applications of optimal control and differential games
93C20 Control/observation systems governed by partial differential equations
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