Mathematics in Population Biology / / Horst R. Thieme.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013
• VerfasserIn: Thieme, Horst R.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2018]; ©2003
• Year of Publication: 2018
• Language: English
• Series: Princeton Series in Theoretical and Computational Biology ; 12
• Physical Description: 1 online resource

The formulation, analysis, and re-evaluation of mathematical models in population biology has become a valuable source of insight to mathematicians and biologists alike. This book presents an overview and selected sample of these results and ideas, organized by biological theme rather than mathematical concept, with an emphasis on helping the reader develop appropriate modeling skills through use of well-chosen and varied examples. Part I starts with unstructured single species population models, particularly in the framework of continuous time models, then adding the most rudimentary stage structure with variable stage duration. The theme of stage structure in an age-dependent context is developed in Part II, covering demographic concepts, such as life expectation and variance of life length, and their dynamic consequences. In Part III, the author considers the dynamic interplay of host and parasite populations, i.e., the epidemics and endemics of infectious diseases. The theme of stage structure continues here in the analysis of different stages of infection and of age-structure that is instrumental in optimizing vaccination strategies. Each section concludes with exercises, some with solutions, and suggestions for further study. The level of mathematics is relatively modest; a "toolbox" provides a summary of required results in differential equations, integration, and integral equations. In addition, a selection of Maple worksheets is provided. The book provides an authoritative tour through a dazzling ensemble of topics and is both an ideal introduction to the subject and reference for researchers.

Table of Contents

Frontmatter -- Contents -- Preface -- Chapter 1. Some General Remarks on Mathematical Modeling -- PART 1. Basic Population Growth Models -- Chapter 2. Birth, Death, and Migration -- Chapter 3. Unconstrained Population Growth for Single Species -- Chapter 4. Von Bertalanffy Growth of Body Size -- Chapter 5. Classic Models of Density-Dependent Population Growth for Single Species -- Chapter 6. Sigmoid Growth -- Chapter 7. The Allee Effect -- Chapter 8. Nonautonomous Population Growth: Asymptotic Equality of Population Sizes -- Chapter 9. Discrete-Time Single-Species Models -- Chapter 10. Dynamics of an Aquatic Population Interacting with a Polluted Environment -- Chapter 11. Population Growth Under Basic Stage Structure -- PART 2. Stage Transitions and Demographics -- Chapter 12. The Transition Through a Stage -- Chapter 13. Stage Dynamics with Given Input -- Chapter 14. Demographics in an Unlimiting Constant Environment -- Chapter 15. Some Demographic Lessons from Balanced Exponential Growth -- Chapter 16. Some Nonlinear Demographics -- PART 3. Host-Parasite Population Growth: Epidemiology of Infectious Diseases -- Chapter 17. Background -- Chapter 18. The Simplified Kermack-McKendrick Epidemic Model -- Chapter 19. Generalization of the Mass-Action Law of Infection -- Chapter 20. The Kermack-McKendrick Epidemic Model with Variable Infectivity -- Chapter 21. SEIR (→ S) Type Endemic Models for "Childhood Diseases" -- Chapter 22. Age-Structured Models for Endemic Diseases and Optimal Vaccination Strategies -- Chapter 23. Endemic Models with Multiple Groups or Populations -- PART 4. Toolbox -- Appendix A. Ordinary Differential Equations -- Appendix B. Integration, Integral Equations, and Some Convex Analysis -- Appendix C. Some MAPLE Worksheets with Comments for Part 1 -- References -- Index