Explorations of Mathematical Models in Biology with MATLAB(R)

[Book Description]

Explore and analyze the solutions of mathematical models from diverse disciplines As biology increasingly depends on data, algorithms, and models, it has become necessary to use a computing language, such as the user-friendly MATLAB, to focus more on building and analyzing models as opposed to configuring tedious calculations. Explorations of Mathematical Models in Biology with MATLAB provides an introduction to model creation using MATLAB, followed by the translation, analysis, interpretation, and observation of the models. With an integrated and interdisciplinary approach that embeds mathematical modeling into biological applications, the book illustrates numerous applications of mathematical techniques within biology, ecology, and environmental sciences. Featuring a quantitative, computational, and mathematical approach, the book includes: * Examples of real-world applications, such as population dynamics, genetics, drug administration, interacting species, and the spread of contagious diseases, to showcase the relevancy and wide applicability of abstract mathematical techniques * Discussion of various mathematical concepts, such as Markov chains, matrix algebra, eigenvalues, eigenvectors, first-order linear difference equations, and nonlinear first-order difference equations * Coverage of difference equations to model a wide range of real-life discrete time situations in diverse areas as well as discussions on matrices to model linear problems * Solutions to selected exercises and additional MATLAB codes Explorations of Mathematical Models in Biology with MATLAB is an ideal textbook for upper-undergraduate courses in mathematical models in biology, theoretical ecology, bioeconomics, forensic science, applied mathematics, and environmental science. The book is also an excellent reference for biologists, ecologists, mathematicians, biomathematicians, and environmental and resource economists.

Preface                                            ix
Acknowledgments                                    xiii
    1 Overview of Discrete Dynamical Modeling      1   (27)
    and Matlab®
      1.1 Introduction to Modeling and             1   (7)
      Difference Equations
      1.2 The Modeling Process                     8   (5)
      1.3 Getting Started with MATLAB              13  (15)
    2 Modeling with First-Order Difference         28  (57)
    Equations
      2.1 Modeling with First-Order Linear         28  (14)
      Homogenous Difference Equations with
      Constant Coefficients
      2.2 Modeling with Nonhomogenous              42  (16)
      First-Order Linear Difference Equations
      2.3 Modeling with Nonlinear Difference       58  (16)
      Equations: Logistic Growth Models
      2.4 Logistic Equations and Chaos             74  (11)
    3 Modeling with Matrices                       85  (110)
      3.1 Systems of Linear Equations Having       85  (14)
      Unique Solutions
      3.2 The Gauss-Jordan Elimination Method      99  (20)
      with Models
      3.3 Introduction to Matrices                 119 (28)
      3.4 Determinants and Systems of Linear       147 (13)
      Equations
      3.5 Eigenvalues and Eigenvectors             160 (25)
      3.6 Eigenvalues and Stability of Linear      185 (10)
      Models
    4 Modeling with Systems of Linear              195 (54)
    Difference Equations
      4.1 Modeling with Markov Chains              195 (24)
      4.2 Age-Structured Population Models         219 (12)
      4.3 Modeling with Second-Order Linear        231 (18)
      Difference Equations
    5 Modeling with Nonlinear Systems of           249 (28)
    Difference Equations
      5.1 Modeling of Interacting Species          249 (15)
      5.2 The SIR Model of Infectious Disease      264 (6)
      5.3 Modeling with Second-Order Nonlinear     270 (7)
      Difference Equations
References                                         277 (2)
Index                                              279