Cristian Morales Rodrigo one year 's stay will be devoted to the development of mathematical models, their mathematical analysis, algorithms, and computer software, related to the description of tumour growth at different levels (scales) and ways of its medical treatment. Special attention will be given to the models describing the interactions of the tumour cells, ECM, MDEs and endogenous inhibitors. Essential role will be in the development of the process of modeling starting from the phenomenological observation to simulation and validation through the design of mathematical models and their qualitative and quantitative study on different levels (scales) of description from "sub - cellular", across the level of interacting cells, to the macroscopic description. Mathematical relationships between different descriptions will be stated. Modeling at the "sub - cellular" and the interacting cells scales and the relationships between different models are the main task of the activity of Polish Team. The Polish Team co-ordinates Task 1 of the project, i.e. Mathematical modeling and computer simulation at the sub-cellular scale and cellular scale.
The mathematical methods that will be used in the investigations are dynamical systems, kinetic theory, stochastic processes, control theory, continuum mechanics, singular perturbations and the methods of a small parameter. Analytic methods will be supplemented by computer simulations.
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