This book is written with the reality of biology students and their apprehension about mathematics in mind. The applications of mathematical models to real biological problems are not contrived, as they are in a number of other texts. And the biology examples are taken from the current literature--a wonderful help to those who will be teaching with this book.--Jim Keener, University of Utah, author of Principles of Applied Mathematics and Mathematical PhysiologyDynamic Models in Biology is a new and significant contribution to the field. Very well written and clearly presented, it fulfills its goal of bringing dynamic models into the undergraduate biology curriculum. Indeed it puts biology first, and then seeks to show how biological phenomena can be explained in mathematical terms.--Martin Henry H. Stevens, Miami UniversityThis excellent book is a major contribution to the literature. Strong biologically and mathematically, well-organized, and engagingly written, it introduces the subject of dynamical models in biology in as coherent a way as I have seen anywhere. Few authors could approach this topic as authoritatively as do Ellner and Guckenheimer.--Simon Levin, Princeton University, author of The Importance of Species and The Encyclopedia of Biodiversity From controlling disease outbreaks to predicting heart attacks, dynamic models are crucial for understanding biological processes. This book teaches how to use dynamic models in biology. It is organized around biological applications, with mathematics and computing developed through case studies at the molecular, cellular, and population levels. List of Figures
ix
List of Tables
xv
Preface
xvii
What Are Dynamic Models?
1(30)
Descriptive versus Mechanistic Models
2(2)
Chinook Salmon
4(2)
Bathtub Models
6(1)
Many Bathtubs: Compartment Models
7(9)
Enzyme Kinetics
8(3)
The Modeling Process
11(2)
Pharmacokinetic Models
13(3)
Physics Models: Running and Hopping
16(4)
Optimization Models
20(1)
Why Bother?
21(3)
Theoretical versus Practical Models
24(2)
What's Next?
26(2)
References
28(3)
Matrix Models and Structured Population Dynamics
31(40)
The Population Balance Law
32(1)
Age-Structured Models
33(5)
The Leslie Matrix
34(3)
Warning: Prebreeding versus Postbreeding Models
37(1)
Matrix Models Based on Stage Classes
38(4)
Matrices and Matrix Operations
42(2)
Review of Matrix Operations
43(1)
Solution of the Matrix Model
44(1)
Eigenvalues and a Second Solution of the Model
44(5)
Left Eigenvectors
48(1)
Some Applications of Matrix Models
49(10)
Why Do We Age?
49(3)
Elasticity Analysis and Conservation Biology
52(6)
How Much Should We Trust These Models?
58(1)
Generalizing the Matrix Model
59(7)
Stochastic Matrix Models
59(2)
Density-Dependent Matrix Models
61(2)
Continuous Size Distributions
63(3)
Summary and Conclusions
66(1)
Appendix
67(1)
Existence and Number of Eigenvalues
67(1)
Reproductive Value
67(1)
References
68(3)
Membrane Channels and Action Potentials
71(36)
Membrane Currents
72(5)
Channel Gating and Conformational States
74(3)
Markov Chains
77(13)
Coin Tossing
78(4)
Markov Chains
82(4)
The Neuromuscular Junction
86(4)
Voltage-Gated Channels
90(2)
Membranes as Electrical Circuits
92(11)
Reversal Potential
94(1)
Action Potentials
95(8)
Summary
103(1)
Appendix: The Central Limit Theorem
104(2)
References
106(1)
Cellular Dynamics: Pathways of Gene Expression
107(28)
Biological Background
108(2)
A Gene Network That Acts as a Clock
110(9)
Formulating a Model
111(2)
Model Predictions
113(6)
Networks That Act as a Switch
119(6)
Systems Biology
125(6)
Complex versus Simple Models
129(2)
Summary
131(1)
References
132(3)
Dynamical Systems
135(48)
Geometry of a Single Differential Equation
136(2)
Mathematical Foundations: A Fundamental Theorem
138(3)
Linearization and Linear Systems
141(10)
Equilibrium Points
141(1)
Linearization at Equilibria
142(2)
Solving Linear Systems of Differential Equations
144(5)
Invariant Manifolds
149(1)
Periodic Orbits
150(1)
Phase Planes
151(3)
An Example: The Morris-Lecar Model
154(6)
Bifurcations
160(15)
Numerical Methods
175(6)
Summary
181(1)
References
181(2)
Differential Equation Models for Infectious Disease
183(34)
Sir Ronald Ross and the Epidemic Curve
183(4)
Rescaling the Model
187(4)
Endemic Diseases and Oscillations
191(9)
Analysis of the SIR Model with Births
193(4)
Summing Up
197(3)
Gonorrhea Dynamics and Control
200(6)
A Simple Model and a Paradox
200(1)
The Core Group
201(2)
Implications for Control
203(3)
Drug Resistance
206(3)
Within-Host Dynamics of HIV
209(4)
Conclusions
213(1)
References
214(3)
Spatial Patterns in Biology
217(26)
Reaction-Diffusion Models
218(5)
The Turing Mechanism
223(3)
Pattern Selection: Steady Patterns
226(6)
Moving Patterns: Chemical Waves and Heartbeats
232(9)
References
241(2)
Agent-Based and Other Computational Models for Complex Systems
243(40)
Individual-Based Models in Ecology
245(7)
Size-Dependent Predation
245(2)
Swarm
247(1)
Individual-Based Modeling of Extinction Risk
248(4)
Artificial Life
252(7)
Tierra
253(2)
Microbes in Tierra
255(2)
Avida
257(2)
The Immune System and the Flu
259(1)
What Can We Learn from Agent-Based Models?
260(1)
Sensitivity Analysis
261(8)
Correlation Methods
264(2)
Variance Decomposition
266(3)
Simplifying Computational Models
269(8)
Separation of Time Scales
269(3)
Simplifying Spatial Models
272(4)
Improving the Mean Field Approximation
276(1)
Conclusions
277(1)
Appendix: Derivation of Pair Approximation
278(1)
References
279(4)
Building Dynamic Models
283(40)
Setting the Objective
284(1)
Building an Initial Model
285(6)
Conceptual Model and Diagram
286(5)
Developing Equations for Process Rates
291(11)
Linear Rates: When and Why?
291(2)
Nonlinear Rates from ``First Principles''
293(1)
Nonlinear Rates from Data: Fitting Parametric Models
294(4)
Nonlinear Rates from Data: Selecting a Parametric Model
298(4)
Nonlinear Rates from Data: Nonparametric Models
302(4)
Multivariate Rate Equations
304(2)
Stochastic Models
306(5)
Individual-Level Stochasticity
306(3)
Parameter Drift and Exogenous Shocks
309(2)
Fitting Rate Equations by Calibration
311(3)
Three Commandments for Modelers
314(1)
Evaluating a Model
315(5)
Comparing Models
317(3)
References
320(3)
Index
323
Ik heb een vraag over het boek: ‘Dynamic Models in Biology - Ellner, Stephen P., Guckenheimer, John’.
Vul het onderstaande formulier in.
We zullen zo spoedig mogelijk antwoorden.