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Selected Topics in Cancer ModelingFrom Kinetic Theory for Active Particles to Modelling Immune Competition

Selected Topics in Cancer Modeling: From Kinetic Theory for Active Particles to Modelling Immune... From Kinetic Theory for Active Particles to Modelling Immune Competition 1 2 Abdelghani Bellouquid and Marcello Delitala University Cadi Ayyad, Ecole Nationale des Sciences Appliqu´ ees, Safi, Maroc bellouquid@gmail.com Dipartimento di Matematica, Politecnico di Torino, Torino, Italy marcello.delitala@polito.it 2.1 Introduction Methods of mathematical kinetic theory for active particles have been re- cently developed to describe the collective behavior of large populations of interacting individuals, where each individual is characterized not only by a mechanical variable (typically position and velocity), but also by a biological variable related to the organized, somehow intelligent, behavior of the whole population. The interest in this type of mathematical approach to modelling complex systems in biological sciences is documented in the review papers [1], [2], and in the book [3]. A generalization of the classical Boltzmann equation has been proposed in [4] showing that it includes, as a particular case, the well-known model of mathematical kinetic theory. Following [5], the interacting entities are called active particles. The state of each particle, called the microscopic state, is described by a variable related to the mechanical state of the particle, classically position and velocity, and by an additional variable, called the activity, related to specific biological functions http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Selected Topics in Cancer ModelingFrom Kinetic Theory for Active Particles to Modelling Immune Competition

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Publisher
Birkhäuser Boston
Copyright
© Birkhäuser Boston 2008
ISBN
978-0-8176-4712-4
Pages
1 –17
DOI
10.1007/978-0-8176-4713-1_2
Publisher site
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Abstract

From Kinetic Theory for Active Particles to Modelling Immune Competition 1 2 Abdelghani Bellouquid and Marcello Delitala University Cadi Ayyad, Ecole Nationale des Sciences Appliqu´ ees, Safi, Maroc bellouquid@gmail.com Dipartimento di Matematica, Politecnico di Torino, Torino, Italy marcello.delitala@polito.it 2.1 Introduction Methods of mathematical kinetic theory for active particles have been re- cently developed to describe the collective behavior of large populations of interacting individuals, where each individual is characterized not only by a mechanical variable (typically position and velocity), but also by a biological variable related to the organized, somehow intelligent, behavior of the whole population. The interest in this type of mathematical approach to modelling complex systems in biological sciences is documented in the review papers [1], [2], and in the book [3]. A generalization of the classical Boltzmann equation has been proposed in [4] showing that it includes, as a particular case, the well-known model of mathematical kinetic theory. Following [5], the interacting entities are called active particles. The state of each particle, called the microscopic state, is described by a variable related to the mechanical state of the particle, classically position and velocity, and by an additional variable, called the activity, related to specific biological functions

Published: Aug 21, 2008

Keywords: Immune Cell; Neoplastic Cell; Abnormal Cell; Active Particle; Probable Output

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