The modelling of the immune competition by generalized kinetic (Boltzmann) models: Review and research perspectives

被引:36
作者
Bellomo, N [1 ]
Bellouquid, A [1 ]
De Angelis, E [1 ]
机构
[1] Politecn Torino, Dept Math, I-10129 Turin, Italy
关键词
kinetic theory; cell populations; population dynamics; immune competition;
D O I
10.1016/S0895-7177(03)80007-9
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
The first part of this paper deals with a review of mathematical topics related to the modeling of the immune competition, at the cellular level, by mathematical methods and structures developed by the models and methods of the classical kinetic theory. Special attention is devoted to the competition between tumor and immune cells. The second part develops a critical analysis of the existing literature and proposes some research perspectives with special attention to modeling relatively more general aspects of the immune competition and control therapeutical actions. (C) 2003 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码:65 / 86
页数:22
相关论文
共 56 条
[1]  
Adam J., 1996, SURVEY MODELS TUMOR
[2]  
Alt W, 1997, DYNAMICS CELL TISSUE
[3]   On the closure of mass balance models for tumor growth [J].
Ambrosi, D ;
Preziosi, L .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2002, 12 (05) :737-754
[4]  
AMBROSI ED, 2002, J THEOR MED, V4, P51
[5]  
[Anonymous], 1995, DYNAMICAL DIS MATH A
[6]   Kinetic equations modelling population dynamics [J].
Arlotti, L ;
Bellomo, N ;
Lachowicz, M .
TRANSPORT THEORY AND STATISTICAL PHYSICS, 2000, 29 (1-2) :125-139
[7]   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
[8]  
Arlotti L., 2002, J. Theor. Med, V4, P39, DOI [10.1080/10273660290015170, DOI 10.1080/10273660290015170]
[9]   DYNAMICS OF TUMOR INTERACTION WITH THE HOST IMMUNE-SYSTEM [J].
BELLOMO, N ;
FORNI, G .
MATHEMATICAL AND COMPUTER MODELLING, 1994, 20 (01) :107-122
[10]   Strategies of applied mathematics towards an immuno-mathematical theory on tumors and immune system interactions [J].
Bellomo, N ;
De Angelis, E .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 1998, 8 (08) :1403-1429