Modeling and Simulation in Science, Engineering and Technology

Mathematical Modeling of Complex Biological Systems

A Kinetic Theory Approach

Authors: Bellouquid, Abdelghani, Delitala, Marcello

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About this book

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.

 

About the authors

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 populations 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.

Reviews

The focus of the book is the development of this new mathematical framework, and an application to modeling the immune response, particularly interactions between cancer cells and immune cells, is considered in detail. The model involves integro-differential evolution equations. Much of the book is devoted to obtaining asymptotic solutions as well as numerical solutions of the model system. –MathSciNet


Table of contents (7 chapters)

  • On the Modelling of Complex Biological Systems

    Pages 1-9

  • Mathematical Frameworks of the Generalized Kinetic (Boltzmann) Theory

    Pages 11-31

  • Modelling the Immune Competition and Applications

    Pages 33-56

  • On the Cauchy Problem

    Pages 57-83

  • Simulations, Biological Interpretations, and Further Modelling Perspectives

    Pages 85-117

Buy this book

eBook $139.00
price for Brazil (gross)
  • ISBN 978-0-8176-4503-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.99
price for Brazil
  • ISBN 978-0-8176-4395-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Modeling of Complex Biological Systems
Book Subtitle
A Kinetic Theory Approach
Authors
Series Title
Modeling and Simulation in Science, Engineering and Technology
Copyright
2006
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4503-8
DOI
10.1007/978-0-8176-4503-8
Hardcover ISBN
978-0-8176-4395-9
Series ISSN
2164-3679
Edition Number
1
Number of Pages
XII, 188
Number of Illustrations
47 b/w illustrations
Topics