The subject of mathematical modeling has expanded considerably in the past twenty years. This is in part due to the appearance of the text by Kemeny and Snell, "Mathematical Models in the Social Sciences," as well as the one by Maki and Thompson, "Mathematical Models and Applica tions. " Courses in the subject became a widespread if not standard part of the undergraduate mathematics curriculum. These courses included var ious mathematical topics such as Markov chains, differential equations, linear programming, optimization, and probability. However, if our own experience is any guide, they failed to teach mathematical modeling; that is, few students who completed the course were able to carry out the mod eling paradigm in all but the simplest cases. They could be taught to solve differential equations or find the equilibrium distribution of a regular Markov chain, but could not, in general, make the transition from "real world" statements to their mathematical formulation. The reason is that this process is very difficult, much more difficult than doing the mathemat ical analysis. After all, that is exactly what engineers spend a great deal of time learning to do. But they concentrate on very specific problems and rely on previous formulations of similar problems. It is unreasonable to expect students to learn to convert a large variety of real-world problems to mathematical statements, but this is what these courses require.
Erscheinungsdatum: 23.10.2012

lgrsnf/A:\compressed\10.1007%2F978-1-4612-1590-5.pdf

nexusstc/Compartmental Modeling with Networks/1c0ef0b2b6de7924e76bd59abd62fe52.pdf

scihub/10.1007/978-1-4612-1590-5.pdf

zlib/Computers/Computer Science/Gilbert G. Walter, Martha Contreras (auth.)/Compartmental Modeling with Networks_2104863.pdf

by Gilbert G. Walter, Martha Contreras

Walter, Gilbert G, Contreras, Martha

Nicola Bellomo

Springer Science+Business Media, LLC

Birkhäuser Basel

BirkhaÌ#x88;user

Springer Nature

Modeling and Simulation in Science, Engineering and Technology, Modeling and simulation in science, engineering & technology, Boston, MA, United States, 1999

Modeling and simulation in science, engineering & technology, 1st ed. 1999, Boston, Massachusetts, 1999

Modeling and simulation in science, engineering & technology, New York, 1999

Softcover reprint of the original 1st ed. 1999, 2012

United States, United States of America

Springer Nature, Boston, MA, 2012

1, 20121206

lg950969

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Also available in print.
Mode of access: World Wide Web.

This new advanced text/reference book presents compartmental models or flow models from an applications perspective. Flow models are used when there is a flow of information or materials, such as fluid of money or energy between the components of a system. They are widely used in biomedicine but have also useful applications in studying ecosystems, input-output analysis, competition, models, and epidemology. In order to provide a complete and balanced presentation, the book is organized in four parts. Part 1 is devoted to the theory of digraphs; Part 2 addresses Markov chains; Part 3 discusses differential equations; and Part 4 presents the theory of compartmental models, addressing the relations between dynamics of the solution and structure of the model. Key applications discussed include ecosystem models, fluid transfer, competition models, tracer kinetic experiments, and network flows. Essential topics and methods are presented in an accessible style with many examples: directed graphs, differential equations, Markov chains, and compartmental model construction. The material provides a thorough and comprehensive presentation of compartmental models, model construction and applications. All advanced students, practitioners and professionals in bioscience and applied mathematical modeling will find the book a useful and excellent reference.

Front Matter....Pages i-xviii
Introduction and Simple Examples....Pages 1-8
Front Matter....Pages 9-9
Digraphs and Graphs: Definitions and Examples....Pages 11-16
A Little Simple Graph Theory....Pages 17-24
Orientation of Graphs and Related Properties....Pages 25-40
Tournaments....Pages 41-46
Planar Graphs....Pages 47-51
Graphs and Matrices....Pages 53-61
Front Matter....Pages 63-63
Introduction to Markov Chains....Pages 65-69
Classification of Markov Chains....Pages 71-80
Regular Markov Chains....Pages 81-87
Absorbing Markov Chains....Pages 89-99
From Markov Chains to Compartmental Models....Pages 101-108
Front Matter....Pages 109-109
Introduction to Compartmental Models....Pages 111-123
Models for the Spread of Epidemics....Pages 125-129
Three Traditional Examples as Compartmental Models....Pages 131-139
Ecosystem Models....Pages 141-148
Fisheries Models....Pages 149-162
Drug Kinetics....Pages 163-171
Front Matter....Pages 173-173
Basic Properties of Linear Models....Pages 175-182
Structure and Dynamical Properties....Pages 183-196
Front Matter....Pages 173-173
Identifiability of a Compartmental System....Pages 197-210
Parameter Estimation....Pages 211-217
Complexity and Stability....Pages 218-227
Back Matter....Pages 228-250

This new advanced text/reference book presents compartmental models or flow models from an applications perspective. Essential topics and methods are introduced in an accessible style with many examples, providing a thorough and comprehensive presentation of compartmental models, model construction and applications.

2013-08-01