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Dynamic Models in Biology

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ISBN-10: 0691125899

ISBN-13: 9780691125893

Edition: 2006

Authors: Stephen P. Ellner, John Guckenheimer

List price: $95.00
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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. InDynamic 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…    
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Book details

List price: $95.00
Copyright year: 2006
Publisher: Princeton University Press
Publication date: 4/16/2006
Binding: Paperback
Pages: 352
Size: 6.75" wide x 9.50" long x 0.80" tall
Weight: 1.672
Language: English

List of Figures
List of Tables
Preface
What Are Dynamic Models?
Descriptive versus Mechanistic Models
Chinook Salmon
Bathtub Models
Many Bathtubs: Compartment Models
Enzyme Kinetics
The Modeling Process
Pharmacokinetic Models
Physics Models: Running and Hopping
Optimization Models
Why Bother?
Theoretical versus Practical Models
What's Next?
References
Matrix Models and Structured Population Dynamics
The Leslie Matrix
Warning: Prebreeding versus Postbreeding Models
Matrix Models Based on Stage Classes
Matrices and Matrix Operations
Review of Matrix Operations
Solution of the Matrix Model
Eigenvalues and a Second Solution of the Model
Left Eigenvectors
Some Applications of Matrix Models
Why Do We Age?
Elasticity Analysis and Conservation Biology
How Much Should We Trust These Models?
Generalizing the Matrix Model
Stochastic Matrix Models
Density-Dependent Matrix Models
Continuous Size Distributions
Summary and Conclusions
Appendix
Existence and Number of Eigenvalues
Reproductive Value
References
Membrane Channels and Action Potentials
Membrane Currents
Channel Gating and Conformational States
Markov Chains
Coin Tossing
Markov Chains
The Neuromuscular Junction
Voltage-Gated Channels
Membranes as Electrical Circuits
Reversal Potential
Action Potentials
Summary
Appendix: The Central Limit Theorem
References
Cellular Dynamics: Pathways of Gene Expression
Biological Background
A Gene Network That Acts as a Clock
Formulating a Model
Model Predictions
Networks That Act as a Switch
Systems Biology 125
Complex versus Simple Models
Summary
References
Dynamical Systems
Geometry of a Single Differential Equation
Mathematical Foundations: A Fundamental Theorem
Linearization and Linear Systems
Equilibrium Points
Linearization at Equilibria
Solving Linear Systems of Differential Equations
Invariant Manifolds
Periodic Orbits
Phase Planes
An Example: The Morris-Lecar Model
Bifurcations
Numerical Methods
Summary
References
Differential Equation Models for Infectious Disease
Sir Ronald Ross and the Epidemic Curve
Rescaling the Model
Endemic Diseases and Oscillations
Analysis of the SIR Model with Births
Summing Up
Gonorrhea Dynamics and Control
A Simple Model and a Paradox
The Core Group
Implications for Control
Drug Resistance
Within-Host Dynamics of HIV
Conclusions
References
Spatial Patterns in Biology
Reaction-Diffusion Models
The Turing Mechanism
Pattern Selection: Steady Patterns
Moving Patterns: Chemical Waves and Heartbeats
References
Agent-Based and Other Computational Models for Complex Systems
Individual-Based Models in Ecology
Size-Dependent Predation
Swarm
Individual-Based Modeling of Extinction Risk
Artificial Life
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