Mathematical modeling of complex biological systems: a kinetic theory approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2006
|
| Schriftenreihe: | Modeling and simulation in science, engineering and technology
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Includes bibliographical references (p. 181-186) and index |
| Beschreibung: | X, 188 S. Ill., graph. Darst. |
| ISBN: | 0817643958 9780817643959 |
Internformat
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| 100 | 1 | |a Bellouquid, Abdelghani |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical modeling of complex biological systems |b a kinetic theory approach |c Abdelghani Bellouquid ; Marcello Delitala |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2006 | |
| 300 | |a X, 188 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Modeling and simulation in science, engineering and technology | |
| 500 | |a Includes bibliographical references (p. 181-186) and index | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Biological systems |x Mathematical models | |
| 650 | 4 | |a Kinetic theory of matter |x Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1804136232647655424 |
|---|---|
| adam_text | Contents
Preface
vu
Chapter
1.
On the Modelling of Complex Biological Systems
1
1.1
Introduction
.....................1
1.2
Motivations and Aims
................3
1.3
Mathematical Background
..............6
1.4
Contents
......................6
Chapter
2.
Mathematical Frameworks of the Generalized
Kinetic (Boltzmann) Theory
11
2.1
Introduction
................... 11
2.2
Mathematical Representation
............ 13
2.3
Modelling Microscopic Interactions
......... 16
2.4
Mathematical Frameworks
............. 21
2.5
Some Simplified Models
............... 22
2.6
Discrete Models
.................. 24
2.7
Critical Analysis
................. 27
Chapter
3.
Modelling the Immune Competition and
Applications
33
3.1
Introduction
................... 33
3.2
Phenomenological Description
........... 34
3.3
Modelling the Immune Competition
......... 42
3.4
Some Technical Particularizations
.......... 48
3.5
Critical Analysis and Additional Applications
..... 54
Chapter
4.
On the Cauchy Problem
57
4.1
Introduction
...................57
4.2
The Cauchy Problem
...............58
vi
Contents
4.3
Asymptotic Behavior
...............64
4.4
Perspectives
...................82
Chapter
5.
Simulations, Biological Interpretations,
and Further Modelling Perspectives
85
5.1
Introduction
...................85
5.2
Simulation of Immune Competition
.........87
5.3
Tumor-Immune Competition
............105
5.4
Comparison with Experimental Data
........113
5.5
Developments and Perspectives
...........115
Chapter
6.
Models with Space Structure and the
Derivation of Macroscopic Equations
119
6.1
Introduction
...................119
6.2
Models with Space Dynamics
............122
6.3
Asymptotic Limit for Mass-Conserving Systems
.... 131
6.4
Models with Proliferation and Destruction
......136
6.5
Application
....................144
6.5
Critical Analysis
.................148
Chapter
7.
Critical Analysis and Forward Perspectives
151
7.1
Critical Analysis
.................151
7.2
Developments Toward New Models
.........153
7.3
Mean Field Interactions
..............154
7.4
On the Interaction Between Biological and
Mathematical Sciences
...............156
Appendix. Basic Tools of Mathematical Kinetic Theory
159
1
Introduction
.................... 159
2
Multiparticle Systems and Statistical Distribution
. . . 160
3
The Distribution Function
............. 164
4
On the Derivation of the Boltzmann Equation
.... 166
5
Mathematical Properties of the Boltzmann Equation
. . 168
6
The Discrete Boltzmann Equation
.......... 172
Glossary
175
References
181
Index
187
Mathematical Modeling of
Complex Biological Systems
A Kinetic Theory Approach
Abdelghani Bellouquid and
Marcello
Dentala
This book describes the evolution of several socio-biological systems using
mathematical kinetic theory. Specifically, it deals with modeling and simulations
of biological systems
—
comprised of large populations of interacting cells
—
whose dynamics follow the rules of mechanics as well as rules governed by their
own ability to organize movement and biological functions. The authors propose
a new biological model for the analysis of competition between cells of an
aggressive host and cells of a corresponding immune system.
Because the microscopic description of a biological system is far more complex
than that of a physical system of inert matter, a higher level of analysis is needed
to deal with such complexity. Mathematical models using kinetic theory may
represent a way to deal with such complexity, allowing for an understanding of
phenomena of nonequilibrium statistical mechanics not described by the tradi¬
tional macroscopic approach. The proposed models are related to the generalized
Boitzmann equation and describe the population dynamics of several interacting
elements (kinetic population models).
The particular models proposed by the authors are based on a framework related
to a system of
mtegro-differentiai
equations, defining the evolution of the distri¬
bution function over the microscopic state of each element in a given system.
Macroscopic information on the behavior of the system is obtained from suitable
moments of the distribution function over the microscopic states of the elements
involved. The book follows a classical research approach applied to modeling
real systems, linking the observation of biological phenomena, collection of
experimental data, modeling, and computational simulations to validate the pro¬
posed models. Qualitative analysis techniques are used to identify the prediction
ability of specific models.
The book will be a valuable resource for applied mathematicians as well as
researchers in the Held of biological sciences. It may be used for advanced
graduate courses and seminars in biological systems modeling with applications
to collective social behavior, immunology, and epidemiology.
|
| adam_txt |
Contents
Preface
vu
Chapter
1.
On the Modelling of Complex Biological Systems
1
1.1
Introduction
.1
1.2
Motivations and Aims
.3
1.3
Mathematical Background
.6
1.4
Contents
.6
Chapter
2.
Mathematical Frameworks of the Generalized
Kinetic (Boltzmann) Theory
11
2.1
Introduction
. 11
2.2
Mathematical Representation
. 13
2.3
Modelling Microscopic Interactions
. 16
2.4
Mathematical Frameworks
. 21
2.5
Some Simplified Models
. 22
2.6
Discrete Models
. 24
2.7
Critical Analysis
. 27
Chapter
3.
Modelling the Immune Competition and
Applications
33
3.1
Introduction
. 33
3.2
Phenomenological Description
. 34
3.3
Modelling the Immune Competition
. 42
3.4
Some Technical Particularizations
. 48
3.5
Critical Analysis and Additional Applications
. 54
Chapter
4.
On the Cauchy Problem
57
4.1
Introduction
.57
4.2
The Cauchy Problem
.58
vi
Contents
4.3
Asymptotic Behavior
.64
4.4
Perspectives
.82
Chapter
5.
Simulations, Biological Interpretations,
and Further Modelling Perspectives
85
5.1
Introduction
.85
5.2
Simulation of Immune Competition
.87
5.3
Tumor-Immune Competition
.105
5.4
Comparison with Experimental Data
.113
5.5
Developments and Perspectives
.115
Chapter
6.
Models with Space Structure and the
Derivation of Macroscopic Equations
119
6.1
Introduction
.119
6.2
Models with Space Dynamics
.122
6.3
Asymptotic Limit for Mass-Conserving Systems
. 131
6.4
Models with Proliferation and Destruction
.136
6.5
Application
.144
6.5
Critical Analysis
.148
Chapter
7.
Critical Analysis and Forward Perspectives
151
7.1
Critical Analysis
.151
7.2
Developments Toward New Models
.153
7.3
Mean Field Interactions
.154
7.4
On the Interaction Between Biological and
Mathematical Sciences
.156
Appendix. Basic Tools of Mathematical Kinetic Theory
159
1
Introduction
. 159
2
Multiparticle Systems and Statistical Distribution
. . . 160
3
The Distribution Function
. 164
4
On the Derivation of the Boltzmann Equation
. 166
5
Mathematical Properties of the Boltzmann Equation
. . 168
6
The Discrete Boltzmann Equation
. 172
Glossary
175
References
181
Index
187
Mathematical Modeling of
Complex Biological Systems
A Kinetic Theory Approach
Abdelghani Bellouquid and
Marcello
Dentala
This book describes the evolution of several socio-biological systems using
mathematical kinetic theory. Specifically, it deals with modeling and simulations
of biological systems
—
comprised of large populations of interacting cells
—
whose dynamics follow the rules of mechanics as well as rules governed by their
own ability to organize movement and biological functions. The authors propose
a new biological model for the analysis of competition between cells of an
aggressive host and cells of a corresponding immune system.
Because the microscopic description of a biological system is far more complex
than that of a physical system of inert matter, a higher level of analysis is needed
to deal with such complexity. Mathematical models using kinetic theory may
represent a way to deal with such complexity, allowing for an understanding of
phenomena of nonequilibrium statistical mechanics not described by the tradi¬
tional macroscopic approach. The proposed models are related to the generalized
Boitzmann equation and describe the population dynamics of several interacting
elements (kinetic population models).
The particular models proposed by the authors are based on a framework related
to a system of
mtegro-differentiai
equations, defining the evolution of the distri¬
bution function over the microscopic state of each element in a given system.
Macroscopic information on the behavior of the system is obtained from suitable
moments of the distribution function over the microscopic states of the elements
involved. The book follows a classical research approach applied to modeling
real systems, linking the observation of biological phenomena, collection of
experimental data, modeling, and computational simulations to validate the pro¬
posed models. Qualitative analysis techniques are used to identify the prediction
ability of specific models.
The book will be a valuable resource for applied mathematicians as well as
researchers in the Held of biological sciences. It may be used for advanced
graduate courses and seminars in biological systems modeling with applications
to collective social behavior, immunology, and epidemiology. |
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| id | DE-604.BV022240913 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:35:57Z |
| indexdate | 2024-07-09T20:53:08Z |
| institution | BVB |
| isbn | 0817643958 9780817643959 |
| language | English |
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| physical | X, 188 S. Ill., graph. Darst. |
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| spelling | Bellouquid, Abdelghani Verfasser aut Mathematical modeling of complex biological systems a kinetic theory approach Abdelghani Bellouquid ; Marcello Delitala Boston [u.a.] Birkhäuser 2006 X, 188 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Modeling and simulation in science, engineering and technology Includes bibliographical references (p. 181-186) and index Mathematisches Modell Biological systems Mathematical models Kinetic theory of matter Mathematical models Biologisches System (DE-588)4122930-7 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Biologisches System (DE-588)4122930-7 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Delitala, Marcello Sonstige oth Erscheint auch als Online-Ausgabe 0-8176-4503-9 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015451835&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015451835&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Bellouquid, Abdelghani Mathematical modeling of complex biological systems a kinetic theory approach Mathematisches Modell Biological systems Mathematical models Kinetic theory of matter Mathematical models Biologisches System (DE-588)4122930-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4122930-7 (DE-588)4114528-8 |
| title | Mathematical modeling of complex biological systems a kinetic theory approach |
| title_auth | Mathematical modeling of complex biological systems a kinetic theory approach |
| title_exact_search | Mathematical modeling of complex biological systems a kinetic theory approach |
| title_exact_search_txtP | Mathematical modeling of complex biological systems a kinetic theory approach |
| title_full | Mathematical modeling of complex biological systems a kinetic theory approach Abdelghani Bellouquid ; Marcello Delitala |
| title_fullStr | Mathematical modeling of complex biological systems a kinetic theory approach Abdelghani Bellouquid ; Marcello Delitala |
| title_full_unstemmed | Mathematical modeling of complex biological systems a kinetic theory approach Abdelghani Bellouquid ; Marcello Delitala |
| title_short | Mathematical modeling of complex biological systems |
| title_sort | mathematical modeling of complex biological systems a kinetic theory approach |
| title_sub | a kinetic theory approach |
| topic | Mathematisches Modell Biological systems Mathematical models Kinetic theory of matter Mathematical models Biologisches System (DE-588)4122930-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Mathematisches Modell Biological systems Mathematical models Kinetic theory of matter Mathematical models Biologisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015451835&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015451835&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bellouquidabdelghani mathematicalmodelingofcomplexbiologicalsystemsakinetictheoryapproach AT delitalamarcello mathematicalmodelingofcomplexbiologicalsystemsakinetictheoryapproach |