Overview
- One of the first books to apply mathematical kinetic theory to biological systems
- Proposes a new biological model focused on the analysis of competition between cells of an aggressive host and cells of a corresponding immune system
- Applications to collective social behavior, immunology, and epidemiology
- Proposed models are related to the generalized Boltzmann equation and describe the population dynamics of several interacting elements (kinetic population models)
- For a broad audience of applied mathematicians, bioengineers, and graduate students
- May be used in advanced graduate courses and seminars on biological systems modeling with applications to collective social behavior, immunology, and epidemiology
Part of the book series: Modeling and Simulation in Science, Engineering and Technology (MSSET)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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
Authors and Affiliations
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 asresearchers 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.
Bibliographic Information
Book Title: Mathematical Modeling of Complex Biological Systems
Book Subtitle: A Kinetic Theory Approach
Authors: Abdelghani Bellouquid, Marcello Delitala
Series Title: Modeling and Simulation in Science, Engineering and Technology
DOI: https://doi.org/10.1007/978-0-8176-4503-8
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2006
Hardcover ISBN: 978-0-8176-4395-9Published: 17 August 2006
eBook ISBN: 978-0-8176-4503-8Published: 10 October 2007
Series ISSN: 2164-3679
Series E-ISSN: 2164-3725
Edition Number: 1
Number of Pages: XII, 188
Number of Illustrations: 47 b/w illustrations
Topics: Life Sciences, general, Mathematical Modeling and Industrial Mathematics, Mathematical and Computational Biology, Applications of Mathematics, Genetics and Population Dynamics, Physiological, Cellular and Medical Topics