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© 2016

Introduction to Mathematical Biology

Modeling, Analysis, and Simulations

Textbook

Table of contents

  1. Front Matter
    Pages i-vii
  2. Ching-Shan Chou, Avner Friedman
    Pages 1-2
  3. Ching-Shan Chou, Avner Friedman
    Pages 3-27
  4. Ching-Shan Chou, Avner Friedman
    Pages 29-42
  5. Ching-Shan Chou, Avner Friedman
    Pages 43-50
  6. Ching-Shan Chou, Avner Friedman
    Pages 51-63
  7. Ching-Shan Chou, Avner Friedman
    Pages 65-74
  8. Ching-Shan Chou, Avner Friedman
    Pages 75-85
  9. Ching-Shan Chou, Avner Friedman
    Pages 87-95
  10. Ching-Shan Chou, Avner Friedman
    Pages 97-104
  11. Ching-Shan Chou, Avner Friedman
    Pages 105-115
  12. Ching-Shan Chou, Avner Friedman
    Pages 117-128
  13. Ching-Shan Chou, Avner Friedman
    Pages 129-136
  14. Ching-Shan Chou, Avner Friedman
    Pages 137-146
  15. Ching-Shan Chou, Avner Friedman
    Pages 147-156
  16. Ching-Shan Chou, Avner Friedman
    Pages 157-164
  17. Back Matter
    Pages 165-172

About this book

Introduction

This book is based on a one semester course that the authors have been teaching for several years, and includes two sets of case studies.  The first includes chemostat models, predator-prey interaction, competition among species, the spread of infectious diseases, and oscillations arising from bifurcations.  In developing these topics, readers will also be introduced to the basic theory of ordinary differential equations, and how to work with MATLAB without having any prior programming experience.


The second set of case studies were adapted from recent and current research papers to the level of the students.  Topics have been selected based on public health interest.  This includes the risk of atherosclerosis associated with high cholesterol levels, cancer and immune interactions, cancer therapy, and tuberculosis.  Readers will experience how mathematical models and their numerical simulations can provide explanations that guide biological and biomedical research.


Considered to be the undergraduate companion to the more advanced book "Mathematical Modeling of Biological Processes" (A. Friedman, C.-Y. Kao, Springer – 2014), this book is geared towards undergraduate students with little background in mathematics and no biological background.

Keywords

Bifurcation Theory Linear Differential Equations Mathematical Biology Mathematical Modeling Numerical Simulations Predator-prey Spread of Disease

Authors and affiliations

  1. 1.Math TowerOhio State UnivColumbusUSA
  2. 2.Dept of MathematicsOhio State UnivColumbusUSA

About the authors

Ching-Shan Chou is an Associate Professor in the Department of Mathematics at Ohio State University.  She received her Ph.D. in the area of applied mathematics from Brown University.  She is currently working in the area of computational and mathematical biology.

Avner Friedman is a Distinguished University Professor at Ohio State University.  He received his Ph.D. in 1956 from the Hebrew University.  His research interests include partial differential equations, both general mathematical theory as well as applications to models that arise in the physical and life sciences, in engineering, and in industry.

Bibliographic information

Reviews

“The book under review is an interesting addition to the list of mathematical biology texts and is designed for students, in both mathematics and biology, who have completed a semester or two of calculus. … The biological applications are well chosen and indicate how differential equations are used in biological research. Overall, this is a nice textbook for a first introduction to mathematical biology.” (Jason M. Graham, Mathematical Reviews, November, 2016)