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Explorations of Mathematical Models in Biology with MATLAB(R) [Hardcover]

Mazen Shahin

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Table of Contents

PREFACE ix

ACKNOWLEDGMENTS xiii

1 OVERVIEW OF DISCRETE DYNAMICAL MODELING AND MATLAB® 1

1.1 Introduction to Modeling and Difference Equations 1

1.2 The Modeling Process 8

1.3 Getting Started with MATLAB 13

2 MODELING WITH FIRST–ORDER DIFFERENCE EQUATIONS 28

2.1 Modeling with First–Order Linear Homogenous Difference Equations with Constant Coefficients 28

2.2 Modeling with Nonhomogenous First–Order Linear Difference Equations 42

2.3 Modeling with Nonlinear Difference Equations: Logistic Growth Models 58

2.4 Logistic Equations and Chaos 74

3 MODELING WITH MATRICES 85

3.1 Systems of Linear Equations Having Unique Solutions 85

3.2 The Gauss–Jordan Elimination Method with Models 99

3.3 Introduction to Matrices 119

3.4 Determinants and Systems of Linear Equations 147

3.5 Eigenvalues and Eigenvectors 160

3.6 Eigenvalues and Stability of Linear Models 185

4 MODELING WITH SYSTEMS OF LINEAR DIFFERENCE EQUATIONS 195

4.1 Modeling with Markov Chains 195

4.2 Age–Structured Population Models 219

4.3 Modeling with Second–Order Linear Difference Equations 231

5 MODELING WITH NONLINEAR SYSTEMS OF DIFFERENCE EQUATIONS 249

5.1 Modeling of Interacting Species 249

5.2 The SIR Model of Infectious Disease 264

5.3 Modeling with Second–Order Nonlinear Difference Equations 270

REFERENCES 277

INDEX 279

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