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Download Mathematical Modelling of Complex Biological Systems. A Kinetic
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Abstract thesis Department of Mathematics Marcello Edoardo Delitala Mathematics for Engineering Sciences MATHEMATICAL MODELLING OF COMPLEX BIOLOGICAL SYSTEMS. A KINETIC THEORY APPROACH Marcello Edoardo Delitala [email protected] Mathematics for Engineering Sciences Supervisor: Professor N. Bellomo Keywords: Kinetic theory; Stochastic games; Evolution; Mutations; System biology; Active particles; Genes and genome; Multicellular systems Abstract The research background is “modelling complex systems” in applied sciences, and the related analysis of the mathematical problems which are generated by the application of modelling techniques to real world phenomena. The underlying idea is to develop methods of mathematical kinetic theory able to describe the evolution of “active multiparticle systems”, defined as complex systems constituted by interacting populations, whose individuals are characterized by mechanical and socio-biological microscopic state. The Thesis focus on the modelling of the immune system response to an aggressive host, like a population of progressing cells: models suitable to describe the evolution of the system are developed, and the related qualitative and computational analysis is performed. The first part deals with some methodological aspects on the derivation of the generalized kinetic (Boltzmann-type) equation for large systems of interacting entities. Then, a model able to describe some aspects of the competition between immune cells and tumor cells is derived. Finally, a more general model of immune response is proposed. The second part deals with a qualitative and quantitative analysis of the models. Well posedness of the initial value problems is analyzed, and special attention is paid to study the asymptotic behaviour of the solutions. A computational analysis is carried out with attention to the biological interpretation of the results. The contents of the Thesis have been collected and published in the book: A. Bellouquid, M. Delitala, Mathematical Modeling of Complex Biological Systems. A Kinetic Theory Approach, Birkhauser, Boston, 2006.
