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Mathematical Models for Society and Biology, 2nd Edition

Book Description

Mathematical Models for Society and Biology, 2nd edition draws on current issues to engagingly relate how to use mathematics to gain insight into problems in biology and contemporary society. For the new edition, the author uses mathematical models that are simple, transparent, and verifiable. Also new to the book is an introduction to mathematical notions that every quantitative scientist in the biological and social sciences should know. Additionally, each chapter will now include a detailed discussion on how to formulate a reasonable model to gain insight into the specific question that has been introduced.

This is an essential reference for life science researchers, professionals, post-docs, and graduate students as well as for applied mathematics professionals and graduate students interested in exploring mathematical modeling in biology.



  • Offers a fresh and appealing approach to modeling by using anecdotes and real-life topics.
  • Provides an introduction to useful modeling tools by covering topics such as the conundrums of chance and coincidences, Bayesian inference, spatial Poisson processes, and a comparison of normal and non-normal random processes.
  • Features expanded appendices section with an extensive list of references, solutions to selected exercises in the book, and further discussion of various mathematical methods introduced in the book.
  • Accessible for quick self study as well as a resource for courses in molecular biology, biochemistry, embryology and cell biology, medicine, ecology and evolution, bio-mathematics, and applied math in general.

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Dedication
  6. Preface to the Second Edition
    1. Acknowledgments
  7. Chapter 1. Crabs and Criminals
    1. 1.1 Background
    2. 1.2 Transitions Between States
    3. 1.3 Social Mobility
    4. 1.4 Absorbing Chains
    5. 1.5 Recidivism
    6. 1.6 Concluding Thoughts
  8. Chapter 2. It Isn’t Fair
    1. 2.1 Background
    2. 2.2 Manpower Scheduling
    3. 2.3 Apportionment
    4. 2.4 An Inheritance in the Talmud and Madoff’s Scheme
    5. 2.5 A Few Mathematical Details
    6. 2.6 Concluding Thoughts
  9. Chapter 3. While the City Burns
    1. 3.1 Background
    2. 3.2 Poisson Events
    3. 3.3 The Inverse Square-Root Law
    4. 3.4 The Encumbrance of an Urban Grid
    5. 3.5 Equilibrium States
    6. 3.6 How Busy are the Fire Companies?
    7. 3.7 Optimal Deployment of Fire Companies
    8. 3.8 Concluding Thoughts
  10. Chapter 4. Clean Streets
    1. 4.1 Background
    2. 4.2 Euler Tours
    3. 4.3 Street Sweeping
    4. 4.4 Vehicle Scheduling
    5. 4.5 Concluding Thoughts
  11. Chapter 5. A Bayesian Take on Colorectal Screening, Baseball, Fund Managers, and a Murder
    1. 5.1 Background
    2. 5.2 Bayes’ Theorem
    3. 5.3 Colorectal Screening
    4. 5.4 Murder and OJ Simpson
    5. 5.5 Skeptical Bayesians
    6. 5.6 Batting Averages and a Paradox
    7. 5.7 A Few Mathematical Details
    8. 5.8 Comparing Apples and Oranges
    9. 5.9 Concluding Thoughts
  12. Chapter 6. What Are the Odds of That?
    1. 6.1 Background
    2. 6.2 Coincidence and Near-Coincidence
    3. 6.3 A Few Mathematical Details
    4. 6.4 Fire Alarms, Bomb Hits, and Baseball Streaks
    5. 6.5 Not a Designer but a Gardener
    6. 6.6 Chi-Squared
    7. 6.7 Stock Funds and Baseball Streaks, Redux
    8. 6.8 Concluding Thoughts
  13. Chapter 7. It’s Normal Not to Be Normal
    1. 7.1 Background
    2. 7.2 The One-Percenters
    3. 7.3 Market Volatility
    4. 7.4 A Few Mathematical Details
    5. 7.5 Concluding Thoughts
  14. Chapter 8. Boom and Bust
    1. 8.1 Background
    2. 8.2 A Fishery Model
    3. 8.3 Unstable Equilibria and Cyclic Behavior
    4. 8.4 A Second Look at the Fishery Model
    5. 8.5 A Restricted-Access Fishery
    6. 8.6 Concluding Thoughts
  15. Chapter 9. Viral Outbreaks and Blood Clots
    1. 9.1 Background
    2. 9.2 Measles Epidemics
    3. 9.3 Chaotic Dynamics or Randomness?
    4. 9.4 Predator-Mediated Coexistence
    5. 9.5 An Unusual Bloom
    6. 9.6 Viral Contamination of Algae
    7. 9.7 Blood Clotting
    8. 9.8 Concluding Thoughts
  16. Chapter 10. Red Tides and Whatever Happened to the Red Squirrel?
    1. 10.1 Background
    2. 10.2 Reaction and Diffusion
    3. 10.3 Algal Patches
    4. 10.4 Traveling Waves
    5. 10.5 The Spread of the Gray Squirrel
    6. 10.6 Rabid Foxes and Traffic Congestion
    7. 10.7 Concluding Thoughts
  17. Chapter 11. Spatial Patterns: The Cat’s Tail and Spreading Slime
    1. 11.1 Background
    2. 11.2 Stripes or Splotches?
    3. 11.3 Slime Molds
  18. Chapter 12. The Coil of Life
    1. 12.1 Background
    2. 12.2 Link, Twist, and Writhe
    3. 12.3 Loopy DNA
    4. 12.4 The Gauss Linking Number
    5. 12.5 Concluding Thoughts
  19. Afterthoughts on Modeling
  20. Appendix A. The Normal Density
  21. Appendix B. Poisson Events
  22. Appendix C. Nonlinear Differential Equations and Oscillations
  23. Appendix D. Conditional Probability
  24. References
  25. Index