Krabs Modelling, Analysis and Optimization of Biosystems

1. Auflage 2007
ISBN: 978-3-540-71453-8
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 203 Seiten

In general, several mathematical models can be designed in order to describe a biological or medical process and there is no unique criterion which model gives the best description. This book presents several of these models and shows applications of them to different biological and medical problems. The book shows that operations research expertise is necessary in respect to modeling, analysis and optimization of biosystems.

Autoren/Hrsg.

Krabs, Werner

Inhaltsverzeichnis

1;Preface;5
2;Contents;7
3;List of Figures;11
4;1 Growth Models;12
4.1;1.1 A Growth Model for one Population;12
4.2;1.2 Interacting Growth of two Populations;20
4.3;1.3 Interacting Growth of n = 2 Populations;26
4.4;1.4 Discretization of the Time-Continuous Model;34
4.5;1.5 Determination of Model Parameters from Data;47
4.6;References;50
5;2 A Game-Theoretic Evolution Model;51
5.1;2.1 Evolution-Matrix-Games for one Population;51
5.2;2.2 Evolution-Bi-Matrix-Games for two Populations;89
5.3;References;112
6;3 Four Models of Optimal Control in Medicine;113
6.1;3.1 Controlled Growth of Cancer Cells;113
6.2;3.2 Optimal Administration of Drugs;121
6.3;3.3 Optimal Control of Diabetes Mellitus;129
6.4;3.4 Optimal Control Aspects of the Blood Circulation in the Heart;140
6.5;References;149
7;4 A Mathematical Model of Hemodialysis;150
7.1;4.1 A One-Compartment Model;150
7.2;4.2 A Two-Compartment Model;161
7.3;4.3 Computation of Periodic Toxin Concentrations;167
7.4;4.4 A Three-Compartment Model;182
7.5;References;192
8;A Appendix;193
8.1;A.1 A Problem of Optimal Control;193
8.2;A.2 Existence of Positive Periodic Solutions in a General Diffusion Model;197
8.3;A.3 Asymptotic Stability of Fixed Points;203
9;Index;208