Modelling and mathematical problems related to tumor evolution and its interaction with the immune system

被引：202

作者：

Bellomo, N ^{[1
]}

Preziosi, L ^{[1
]}

机构：

[1] Politecn Torino, Dept Math, I-10129 Turin, Italy

来源：

MATHEMATICAL AND COMPUTER MODELLING | 2000年 / 32卷 / 3-4期

关键词：

tumor modelling; kinetic models; nonlinear problems; moving boundary problems; control;

D O I：

10.1016/S0895-7177(00)00143-6

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

This paper provides a survey of mathematical models and methods dealing with the analysis and simulation of tumor dynamics in competition with the immune system. The characteristic scales of the phenomena are identified and the mathematical literature on models and problems developed on each scale is reviewed and critically analysed. The aim is to provide a general framework towards the development of immune-mathematical theories and to develop research perspectives in this promising new field of applied mathematics. (C) 2000 Elsevier Science Ltd. All rights reserved.

引用

页码：413 / 452

页数：40

共 67 条

[1] Adam J. A., 1996, SURVEY MODELS TUMOR, P15
[2] EQUILIBRIUM-MODEL OF A VASCULARIZED SPHERICAL CARCINOMA WITH CENTRAL NECROSIS - SOME PROPERTIES OF THE SOLUTION
ADAM, JA
NOREN, RD
[J]. JOURNAL OF MATHEMATICAL BIOLOGY, 1993, 31 (07) : 735 - 745
[3] ADAMS J, 1996, SURVEY MODELS TUMOR
[4] Agur Z, 1986, ANN NY ACAD SCI, V504, P274, DOI [DOI 10.1111/J.1749-6632.1987.TB48738.X, 10.1111/j.1749-6632.1987.tb48738.x]
[5] Alt W, 1997, DYNAMICS CELL TISSUE
[6] Qualitative analysis of a nonlinear integrodifferential equation modeling tumor-host dynamics
Arlotti, L
Lachowicz, M
[J]. MATHEMATICAL AND COMPUTER MODELLING, 1996, 23 (06) : 11 - 29
[7] Kinetic equations modelling population dynamics
Arlotti, L
Bellomo, N
Lachowicz, M
[J]. TRANSPORT THEORY AND STATISTICAL PHYSICS, 2000, 29 (1-2): : 125 - 139
[8] Strategies of applied mathematics towards an immuno-mathematical theory on tumors and immune system interactions
Bellomo, N
De Angelis, E
[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 1998, 8 (08) : 1403 - 1429
[9] Bellomo N., 1996, Journal of Biological Systems, V4, P479, DOI 10.1142/S0218339096000326
[10] Bifurcation analysis for a nonlinear system of integro-differential equations modelling tumor-immune cells competition
Bellomo, N
Firmani, B
Guerri, L
[J]. APPLIED MATHEMATICS LETTERS, 1999, 12 (02) : 39 - 44

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