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Mathematical Modeling of Complex Biological Systems
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Mathematical Modeling of Complex Biological Systems

Mathematical Modeling of Complex Biological Systems

A Kinetic Theory Approach

Abdelghani Bellouquid - Collection Modeling and Simulation Science, Engineering and Technology

188 pages, parution le 31/03/2006

Résumé

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 traditional macroscopic approach. The proposed models are related to the generalized Boltzmann 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 integro-differential equations, defining the evolution of the distribution 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 proposed 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 field 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.

Sommaire

  • Preface
  • On the Modelling of Complex Biological Systems
  • Mathematical Frameworks of the Generalized Kinetic (Boltzmann) Theory
  • Modelling the Immune Competition and Applications
  • On the Cauchy Problem
  • Simulations, Biological Interpretations, and Further Modelling Perspectives
  • Models with Space Structure and Derivation of Macroscopic Equations
  • Critical Analysis and Forward Perspectives
  • Appendix. Basic Tools of Mathematical Kinetic Theory
  • Glossary
  • References
  • Index
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  PAPIER
Éditeur(s) Birkhäuser
Auteur(s) Abdelghani Bellouquid
Collection Modeling and Simulation Science, Engineering and Technology
Parution 31/03/2006
Nb. de pages 188
Format 16 x 24
Couverture Relié
Poids 477g
Intérieur Noir et Blanc
EAN13 9780817643959
ISBN13 978-0-8176-4395-9

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