Mathematical Models for Society and Biology

Preface ix


1 Crabs and Criminals


1.1 Background

1.2 Absorbing Markov Chains

1.3 Social Mobility

1.4 Recidivism

1.5 Exercises

1.6 Further Readings


2 It Isn't Fair: Municipal Workers, Congressional Seats, and the Talmud


2.1 Background

2.2 Manpower Scheduling

2.3 Apportionment

2.4 An Inheritance

2.5 Exercises

2.6 Further Readings


3 While the City Burns


3.1 Background

3.2 Poisson Processes

3.3 The Inverse Square Root Law

3.4 How Busy Are the Fire Companies?

3.5 Optimal Deployment of Fire Companies

3.6 Exercises

3.7 Further Readings


4 Clean Streets


4.1 Background

4.2 Euler Tour

4.3 Street Sweeping

4.4 Vehicle Scheduling

4.5 Exercises

4.6 Further Readings


5 The Coil of Life


5.1 Background

5.2 The Gauss Linking Number

5.3 Twisting and Writhing of DNA

5.4 Exercises

5.5 Further Readings


6 Measles and Blood Clots


6.1 Background

6.2 Equilibria and Stability

6.3 Linearization

6.4 Measles Epidemics

6.5 Chaotic Dynamics or Randomness?

6.6 Blood Clotting

6.7 Exercises

6.8 Further Readings


7 Sardines and Algae Blooms


7.1 Background

7.2 A Catastrophe Model of Fishing

7.3 Unusual Blooms

7.4 Cycles

7.5 Another View of Fish Harvesting

7.6 Exercises

7.7 Further Readings


8 Red Tides and What Ever Happened to the Red Squirrel?


8.1 Background

8.2 Diffusion

8.3 Algal Patches

8.4 Traveling Waves

8.5 The Spread of the Gray Squirrel

8.6 Exercises

8.7 Further Readings


9 Submarines and Trawlers


9.1 Background

9.2 A Variational Lemma

9.3 Hide and Seek

9.4 A Restricted Access Fishery

9.5 A Comment about Strategy

9.6 Exercises

9.7 Further Readings

Afterthoughts on Modeling

Appendix. Conditional Probability

References

Solutions to Select Exercises

Index