Mathematical Models for Society and Biology - 2nd Edition - ISBN: 9780124046245, 9780124046931

Mathematical Models for Society and Biology

2nd Edition

Authors: Edward Beltrami
Hardcover ISBN: 9780124046245
eBook ISBN: 9780124046931
Imprint: Academic Press
Published Date: 28th June 2013
Page Count: 288
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Mathematical Models for Society and Biology, 2e, is a useful resource for researchers, graduate students, and post-docs in the applied mathematics and life science fields. Mathematical modeling is one of the major subfields of mathematical biology. A mathematical model may be used to help explain a system, to study the effects of different components, and to make predictions about behavior.

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

Key Features

  • Offers 40% more content – 5 new chapters in addition to revisions to existing chapters
  • 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
  • Features expanded appendices with an extensive list of references, solutions to selected exercises in the book, and further discussion of various mathematical methods introduced in the book


Life science researchers, professionals, post-docs, and graduate students interested in how mathematics can be used to gain and convey a greater understanding of biology and society as well as applied mathematics professionals and students interested in exploring mathematical modeling in biology.

Table of Contents


Preface to the Second Edition


Chapter 1. Crabs and Criminals

1.1 Background

1.2 Transitions Between States

1.3 Social Mobility

1.4 Absorbing Chains

1.5 Recidivism

1.6 Concluding Thoughts

Chapter 2. It Isn’t Fair

2.1 Background

2.2 Manpower Scheduling

2.3 Apportionment

2.4 An Inheritance in the Talmud and Madoff’s Scheme

2.5 A Few Mathematical Details

2.6 Concluding Thoughts

Chapter 3. While the City Burns

3.1 Background

3.2 Poisson Events

3.3 The Inverse Square-Root Law

3.4 The Encumbrance of an Urban Grid

3.5 Equilibrium States

3.6 How Busy are the Fire Companies?

3.7 Optimal Deployment of Fire Companies

3.8 Concluding Thoughts

Chapter 4. Clean Streets

4.1 Background

4.2 Euler Tours

4.3 Street Sweeping

4.4 Vehicle Scheduling

4.5 Concluding Thoughts

Chapter 5. A Bayesian Take on Colorectal Screening, Baseball, Fund Managers, and a Murder

5.1 Background

5.2 Bayes’ Theorem

5.3 Colorectal Screening

5.4 Murder and OJ Simpson

5.5 Skeptical Bayesians

5.6 Batting Averages and a Paradox

5.7 A Few Mathematical Details

5.8 Comparing Apples and Oranges

5.9 Concluding Thoughts

Chapter 6. What Are the Odds of That?

6.1 Background

6.2 Coincidence and Near-Coincidence

6.3 A Few Mathematical Details

6.4 Fire Alarms, Bomb Hits, and Baseball Streaks

6.5 Not a Designer but a Gardener

6.6 Chi-Squared

6.7 Stock Funds and Baseball Streaks, Redux

6.8 Concluding Thoughts

Chapter 7. It’s Normal Not to Be Normal

7.1 Background

7.2 The One-Percenters

7.3 Market Volatility

7.4 A Few Mathematical Details

7.5 Concluding Thoughts

Chapter 8. Boom and Bust

8.1 Background

8.2 A Fishery Model

8.3 Unstable Equilibria and Cyclic Behavior

8.4 A Second Look at the Fishery Model

8.5 A Restricted-Access Fishery

8.6 Concluding Thoughts

Chapter 9. Viral Outbreaks and Blood Clots

9.1 Background

9.2 Measles Epidemics

9.3 Chaotic Dynamics or Randomness?

9.4 Predator-Mediated Coexistence

9.5 An Unusual Bloom

9.6 Viral Contamination of Algae

9.7 Blood Clotting

9.8 Concluding Thoughts

Chapter 10. Red Tides and Whatever Happened to the Red Squirrel?

10.1 Background

10.2 Reaction and Diffusion

10.3 Algal Patches

10.4 Traveling Waves

10.5 The Spread of the Gray Squirrel

10.6 Rabid Foxes and Traffic Congestion

10.7 Concluding Thoughts

Chapter 11. Spatial Patterns: The Cat’s Tail and Spreading Slime

11.1 Background

11.2 Stripes or Splotches?

11.3 Slime Molds

Chapter 12. The Coil of Life

12.1 Background

12.2 Link, Twist, and Writhe

12.3 Loopy DNA

12.4 The Gauss Linking Number

12.5 Concluding Thoughts

Afterthoughts on Modeling

Appendix A. The Normal Density

Appendix B. Poisson Events

Appendix C. Nonlinear Differential Equations and Oscillations

Appendix D. Conditional Probability




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About the Author

Edward Beltrami

Affiliations and Expertise

State University of New York, Stony Brook, U.S.A.


"…this is a very good introduction to mathematical modeling, one of the best that I have seen…he presents his book as a reference or a tool for self-study by mathematically prepared undergraduates who wish to see interesting and unusual applications in the biological and social sciences…This is a delightful book. By design it is not a textbook, but it would be a wonderful accompaniment to any course in modeling.", February 17, 2014