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Dynamic Models in Biology

Author John Guckenheimer , Stephen P. Ellner
Release Date: 2011/09/01
ISBN: 9781400840960
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Book Description

From controlling disease outbreaks to predicting heart attacks, dynamic models are increasingly crucial for understanding biological processes. Many universities are starting undergraduate programs in computational biology to introduce students to this rapidly growing field. In Dynamic Models in Biology, the first text on dynamic models specifically written for undergraduate students in the biological sciences, ecologist Stephen Ellner and mathematician John Guckenheimer teach students how to understand, build, and use dynamic models in biology.


Developed from a course taught by Ellner and Guckenheimer at Cornell University, the book is organized around biological applications, with mathematics and computing developed through case studies at the molecular, cellular, and population levels. The authors cover both simple analytic models--the sort usually found in mathematical biology texts--and the complex computational models now used by both biologists and mathematicians.


Linked to a Web site with computer-lab materials and exercises, Dynamic Models in Biology is a major new introduction to dynamic models for students in the biological sciences, mathematics, and engineering.

Table of Contents

  1. Cover
  2. Half title
  3. Title
  4. Copyright
  5. Contents
  6. List of Figures
  7. List of Tables
  8. Preface
  9. 1 What Are Dynamic Models?
    1. 1.1 Descriptive versus Mechanistic Models
    2. 1.2 Chinook Salmon
    3. 1.3 Bathtub Models
    4. 1.4 Many Bathtubs: Compartment Models
      1. 1.4.1 Enzyme Kinetics
      2. 1.4.2 The Modeling Process
      3. 1.4.3 Pharmacokinetic Models
    5. 1.5 Physics Models: Running and Hopping
    6. 1.6 Optimization Models
    7. 1.7 Why Bother?
    8. 1.8 Theoretical versus Practical Models
    9. 1.9 What’s Next?
    10. 1.10 References
  10. 2 Matrix Models and Structured Population Dynamics
    1. 2.1 The Population Balance Law
    2. 2.2 Age-Structured Models
      1. 2.2.1 The Leslie Matrix
      2. 2.2.2 Warning: Prebreeding versus Postbreeding Models
    3. 2.3 Matrix Models Based on Stage Classes
    4. 2.4 Matrices and Matrix Operations
      1. 2.4.1 Review of Matrix Operations
      2. 2.4.2 Solution of the Matrix Model
    5. 2.5 Eigenvalues and a Second Solution of the Model
      1. 2.5.1 Left Eigenvectors
    6. 2.6 Some Applications of Matrix Models
      1. 2.6.1 Why Do We Age?
      2. 2.6.2 Elasticity Analysis and Conservation Biology
      3. 2.6.3 How Much Should We Trust These Models?
    7. 2.7 Generalizing the Matrix Model
      1. 2.7.1 Stochastic Matrix Models
      2. 2.7.2 Density-Dependent Matrix Models
      3. 2.7.3 Continuous Size Distributions
    8. 2.8 Summary and Conclusions
    9. 2.9 Appendix
      1. 2.9.1 Existence and Number of Eigenvalues
      2. 2.9.2 Reproductive Value
    10. 2.10 References
  11. 3 Membrane Channels and Action Potentials
    1. 3.1 Membrane Currents
      1. 3.1.1 Channel Gating and Conformational States
    2. 3.2 Markov Chains
      1. 3.2.1 Coin Tossing
      2. 3.2.2 Markov Chains
      3. 3.2.3 The Neuromuscular Junction
    3. 3.3 Voltage-Gated Channels
    4. 3.4 Membranes as Electrical Circuits
      1. 3.4.1 Reversal Potential
      2. 3.4.2 Action Potentials
    5. 3.5 Summary
    6. 3.6 Appendix: The Central Limit Theorem
    7. 3.7 References
  12. 4 Cellular Dynamics: Pathways of Gene Expression
    1. 4.1 Biological Background
    2. 4.2 A Gene Network That Acts as a Clock
      1. 4.2.1 Formulating a Model
      2. 4.2.2 Model Predictions
    3. 4.3 Networks That Act as a Switch
    4. 4.4 Systems Biology
      1. 4.4.1 Complex versus Simple Models
    5. 4.5 Summary
    6. 4.6 References
  13. 5 Dynamical Systems
    1. 5.1 Geometry of a Single Differential Equation
    2. 5.2 Mathematical Foundations: A Fundamental Theorem
    3. 5.3 Linearization and Linear Systems
      1. 5.3.1 Equilibrium Points
      2. 5.3.2 Linearization at Equilibria
      3. 5.3.3 Solving Linear Systems of Differential Equations
      4. 5.3.4 Invariant Manifolds
      5. 5.3.5 Periodic Orbits
    4. 5.4 Phase Planes
    5. 5.5 An Example: The Morris-Lecar Model
    6. 5.6 Bifurcations
    7. 5.7 Numerical Methods
    8. 5.8 Summary
    9. 5.9 References
  14. 6 Differential Equation Models for Infectious Disease
    1. 6.1 Sir Ronald Ross and the Epidemic Curve
    2. 6.2 Rescaling the Model
    3. 6.3 Endemic Diseases and Oscillations
      1. 6.3.1 Analysis of the SIR Model with Births
      2. 6.3.2 Summing Up
    4. 6.4 Gonorrhea Dynamics and Control
      1. 6.4.1 A Simple Model and a Paradox
      2. 6.4.2 The Core Group
      3. 6.4.3 Implications for Control
    5. 6.5 Drug Resistance
    6. 6.6 Within-Host Dynamics of HIV
    7. 6.7 Conclusions
    8. 6.8 References
  15. 7 Spatial Patterns in Biology
    1. 7.1 Reaction-Diffusion Models
    2. 7.2 The Turing Mechanism
    3. 7.3 Pattern Selection: Steady Patterns
    4. 7.4 Moving Patterns: Chemical Waves and Heartbeats
    5. 7.5 References
  16. 8 Agent-Based and Other Computational Models for Complex Systems
    1. 8.1 Individual-Based Models in Ecology
      1. 8.1.1 Size-Dependent Predation
      2. 8.1.2 Swarm
      3. 8.1.3 Individual-Based Modeling of Extinction Risk
    2. 8.2 Artificial Life
      1. 8.2.1 Tierra
      2. 8.2.2 Microbes in Tierra
      3. 8.2.3 Avida
    3. 8.3 The Immune System and the Flu
    4. 8.4 What Can We Learn from Agent-Based Models?
    5. 8.5 Sensitivity Analysis
      1. 8.5.1 Correlation Methods
      2. 8.5.2 Variance Decomposition
    6. 8.6 Simplifying Computational Models
      1. 8.6.1 Separation of Time Scales
      2. 8.6.2 Simplifying Spatial Models
      3. 8.6.3 Improving the Mean Field Approximation
    7. 8.7 Conclusions
    8. 8.8 Appendix: Derivation of Pair Approximation
    9. 8.9 References
  17. 9 Building Dynamic Models
    1. 9.1 Setting the Objective
    2. 9.2 Building an Initial Model
      1. 9.2.1 Conceptual Model and Diagram
    3. 9.3 Developing Equations for Process Rates
      1. 9.3.1 Linear Rates: When and Why?
      2. 9.3.2 Nonlinear Rates from “First Principles”
      3. 9.3.3 Nonlinear Rates from Data: Fitting Parametric Models
      4. 9.3.4 Nonlinear Rates from Data: Selecting a Parametric Model
    4. 9.4 Nonlinear Rates from Data: Nonparametric Models
      1. 9.4.1 Multivariate Rate Equations
    5. 9.5 Stochastic Models
      1. 9.5.1 Individual-Level Stochasticity
      2. 9.5.2 Parameter Drift and Exogenous Shocks
    6. 9.6 Fitting Rate Equations by Calibration
    7. 9.7 Three Commandments for Modelers
    8. 9.8 Evaluating a Model
      1. 9.8.1 Comparing Models
    9. 9.9 References
  18. Index
18.223.160.61