Mathematical methods and tools of kinetic theory towards modelling complex biological systems

被引：82

作者：

Bellouquid, A ^{[1
]}

Delitala, M

机构：

[1] Univ Cadi Ayyad, Dept Math, Ecole Natl Sci Appliquees, Safi, Morocco

[2] Politecn Torino, Dept Math, I-101293 Turin, Italy

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2005年 / 15卷 / 11期

关键词：

kinetic theory; statistical mechanics; population models; nonlinearity;

D O I：

10.1142/S0218202505000923

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper develops a variety of mathematical tools to model the dynamics of large systems of interacting cells. Interactions are ruled not only by laws of classical mechanics, but also by some biological functions. The mathematical approach is the one of kinetic theory and non-equilibrium statistical mechanics. The paper deals both with the derivation of evolution equations and with the design of specific models consistent with the above-mentioned mathematical framework. Various hints for research perspectives are proposed in the last part of the paper.

引用

页码：1639 / 1666

页数：28

共 17 条

[1]

Adam J. A., 1997, A survey of models for tumor-immune system dynamics, DOI 10.1007/978-0-8176-8119-7

[2] Generalized kinetic (Boltzmann) models: Mathematical structures and applications [J].

Arlotti, L ;

Bellomo, N ;

De Angelis, E .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2002, 12 (04) :567-591

[3]

ARLOTTI L, 2003, LECT NOTES MATH PROB

[4]

Arlotti L., 2002, J. Theor. Med, V4, P39, DOI [10.1080/10273660290015170, DOI 10.1080/10273660290015170]

[5] DYNAMICS OF TUMOR INTERACTION WITH THE HOST IMMUNE-SYSTEM [J].

BELLOMO, N ;

FORNI, G .

MATHEMATICAL AND COMPUTER MODELLING, 1994, 20 (01) :107-122

[6] Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition [J].

Bellomo, N ;

Bellouquid, A ;

Delitala, M .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2004, 14 (11) :1683-1733

[7]

BELLOMO N, 2004, IN PRESS MATH MOD ME

[8]

BELLOMO N, 2000, MODELLING APPL SCI K

[9] Kinetic (cellular) models of cell progression and competition with the immune system [J].

Bellouquid, A ;

Delitala, M .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2004, 55 (02) :295-317

[10] From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences [J].

Bertotti, ML ;

Delitala, M .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2004, 14 (07) :1061-1084

← 1 2 →