Chapter 9. Discrete-Time Single-Species Models

Chapters in this book

1. Frontmatter i
2. Contents vii
3. Preface xiii
4. Chapter 1. Some General Remarks on Mathematical Modeling 1
5. PART 1. Basic Population Growth Models
6. Chapter 2. Birth, Death, and Migration 7
7. Chapter 3. Unconstrained Population Growth for Single Species 13
8. Chapter 4. Von Bertalanffy Growth of Body Size 33
9. Chapter 5. Classic Models of Density-Dependent Population Growth for Single Species 37
10. Chapter 6. Sigmoid Growth 51
11. Chapter 7. The Allee Effect 65
12. Chapter 8. Nonautonomous Population Growth: Asymptotic Equality of Population Sizes 75
13. Chapter 9. Discrete-Time Single-Species Models 81
14. Chapter 10. Dynamics of an Aquatic Population Interacting with a Polluted Environment 107
15. Chapter 11. Population Growth Under Basic Stage Structure 151
16. PART 2. Stage Transitions and Demographics
17. Chapter 12. The Transition Through a Stage 185
18. Chapter 13. Stage Dynamics with Given Input 211
19. Chapter 14. Demographics in an Unlimiting Constant Environment 239
20. Chapter 15. Some Demographic Lessons from Balanced Exponential Growth 255
21. Chapter 16. Some Nonlinear Demographics 273
22. PART 3. Host–Parasite Population Growth: Epidemiology of Infectious Diseases
23. Chapter 17. Background 283
24. Chapter 18. The Simplified Kermack–McKendrick Epidemic Model 293
25. Chapter 19. Generalization of the Mass-Action Law of Infection 305
26. Chapter 20. The Kermack–McKendrick Epidemic Model with Variable Infectivity 311
27. Chapter 21. SEIR (→ S) Type Endemic Models for “Childhood Diseases” 317
28. Chapter 22. Age-Structured Models for Endemic Diseases and Optimal Vaccination Strategies 341
29. Chapter 23. Endemic Models with Multiple Groups or Populations 383
30. PART 4. Toolbox
31. Appendix A. Ordinary Differential Equations 421
32. Appendix B. Integration, Integral Equations, and Some Convex Analysis 453
33. Appendix C. Some MAPLE Worksheets with Comments for Part 1 493
34. References 519
35. Index 537