書誌事項

Compartmental modeling with networks

Gilbert G. Walter, Martha Contreras

(Modeling and simulation in science, engineering & technology)

Birkhäuser, c1999

大学図書館所蔵 件 / 7

この図書・雑誌をさがす

注記

Includes bibliographical references (p. 242-246) and index

内容説明・目次

巻冊次

ISBN 9780817640194

内容説明

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.

目次

1 Introduction and Simple Examples.- 2 Digraphs and Graphs: Definitions and Examples.- 3 A Little Simple Graph Theory.- 4 Orientation of Graphs and Related Properties.- 5 Tournaments.- 6 Planar Graphs.- 7 Graphs and Matrices.- 8 Introduction to Markov Chains.- 9 Classification of Markov Chains.- 10 Regular Markov Chains.- 11 Absorbing Markov Chains.- 12 From Markov Chains to Compartmental Models.- 13 Introduction to Compartmental Models.- 14 Models for the Spread of Epidemics.- 15 Three Traditional Examples as Compartmental Models.- 16 Ecosystem Models.- 17 Fisheries Models.- 18 Drug Kinetics.- 19 Basic Properties of Linear Models.- 20 Structure and Dynamical Properties.- 21 Identifiability of a Compartmental System.- 22 Parameter Estimation.- 23 Complexity and Stability.- A Mathematical Prerequisites.- A.1 Matrix Operations.- A.2 Finding Eigenvalues and Eigenvectors.- A.3 Systems of Differential Equations.- A.4 Matrices with Maple.
巻冊次

ISBN 9783764340193

内容説明

This reference presents compartmental models or flow models, from an applications perspective. Key applications discussed include: ecosystem models; fluid transfer; competition models; tracer kinetic experiments; and network flows. All topics are presented in an accessible and integrated style.

目次

  • Introducation and simple examples. Part 1 Structure of models - directed graphs: diagraphs and graphs
  • a little simple graph theory
  • orientation of graphs and diagraphs
  • tournaments
  • planer graphs
  • graphs and matrices. Part 2 Diagraphs and probabilities - Markov chains: introduction to Markov chains
  • classification of Markov chains
  • regular Markov chains
  • absorbing Maarkov chains
  • from Markov chains to compartmental models. Part 3 Compartmental models - applications: introduction to compartmental models
  • models for the spread of epidemics
  • three traditional examples of compartmental models
  • ecosystem models
  • fisheries models
  • drug kinetics. Part 4 Compartmental model theory: basic properties of linear models
  • structure and dynamical properties
  • identifiability of a compartmental system
  • parameter estimation
  • complexity and stability.

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