This book describes the evolution of several socio-biological systems using mathematical kinetic theory. Specifically, it deals with modeling and simulations of biological systems whose dynamics follow the rules of mechanics as well as rules governed by their own ability to organize movement and biological functions. It proposes a new biological model focused on the analysis of competition between cells of an aggressive host and cells of a corresponding immune system. Proposed models are related to the generalized Boltzmann equation. The book may be used for advanced graduate courses and seminars in biological systems modeling.
Author(s): Abdelghani Bellouquid, Marcello Delitala,
Edition: 1
Year: 2006
Language: English
Pages: 198
Contents......Page 7
Preface......Page 9
1.1 Introduction......Page 13
1.2 Motivations and Aims......Page 15
1.4 Contents......Page 18
2.1 Introduction......Page 22
2.2 Mathematical Representation......Page 24
2.3 Modelling Microscopic Interactions......Page 27
2.4 Mathematical Frameworks......Page 32
2.5 Some Simplified Models......Page 33
2.6 Discrete Models......Page 35
2.7 Critical Analysis......Page 38
3.1 Introduction......Page 43
3.2 Phenomenological Description......Page 44
3.3 Modelling the Immune Competition......Page 52
3.4 Some Technical Particularizations......Page 58
3.5 Critical Analysis and Additional Applications......Page 64
4.1 Introduction......Page 67
4.2 The Cauchy Problem......Page 68
4.3 Asymptotic Behavior......Page 74
4.4 Perspectives......Page 92
5.1 Introduction......Page 94
5.2 Simulation of Immune Competition......Page 96
5.3 Tumor–Immune Competition......Page 114
5.4 Comparison with Experimental Data......Page 122
5.5 Developments and Perspectives......Page 124
6.1 Introduction......Page 127
6.2 Models with Space Dynamics......Page 130
6.3 Asymptotic Limit for Mass-Conserving Systems......Page 139
6.4 Models with Proliferation and Destruction......Page 144
6.5 Application......Page 152
6.6 Critical Analysis......Page 156
7.1 Critical Analysis......Page 158
7.2 DevelopmentsToward New Models......Page 160
7.3 Mean Field Interactions......Page 161
7.4 On the Interaction Between Biological and Mathematical Sciences......Page 163
1. Introduction......Page 166
2. Multiparticle Systems and Statistical Distribution......Page 167
3. The Distribution Function......Page 171
4. On the Derivation of the Boltzmann Equation......Page 173
5. Mathematical Properties of the Boltzmann Equation......Page 175
6. The Discrete Boltzmann Equation......Page 179
A......Page 182
C......Page 183
L......Page 184
P......Page 185
W......Page 186
References......Page 187
D......Page 193
W......Page 194
