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Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition. (English) Zbl 1060.92029

Summary: This paper deals with a critical analysis and some developments related to the mathematical literature on multiscale modelling of multicellular systems involving tumor immune cells competition at the cellular level. The analysis is focused on the development of mathematical methods of the classical kinetic theory to model the above physical system and to recover macroscopic equations from the microscopic description.
Various hints are given toward research perspectives, with special attention on the modelling of the interplay of microscopic (at the cellular level) biological and mechanical variables on the overall evolution of the system. Indeed, the final aim of this paper consists in organizing the various contributions available in the literature into a mathematical framework suitable to generate a mathematical theory for complex biological systems.

MSC:

92C37 Cell biology
92C30 Physiology (general)
92C05 Biophysics
92C50 Medical applications (general)
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