Résumé
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.
Contents
- Some General Remarks on Mathematical Modeling
- Basic Population Growth Models
- Birth, Death, and Migration
- Unconstrained Population Growth for Single Species
- Von Bertalanffy Growth of Body Size
- Classic Models of Density-Dependent Population Growth for Single Species
- Sigmoid Growth
- The Allee Effect
- Nonautonomous Population Growth: Asymptotic Equality of Population Sizes
- Discrete-Time Single-Species Models
- Dynamics of an Aquatic Population Interacting with a Polluted Environment
- Population Growth Under Basic Stage Structure
- Stage Transitions And Demographics
- The Transition Through a Stage
- Stage Dynamics with Given Input
- Demographics in an Unlimiting Constant Environment
- Some Demographic Lessons from Balanced Exponential Growth
- Some Nonlinear Demographics
- Host-Parasite Population Growth : Epidemiology of
infectious diseases
- Background
- The Simplified Kermack-McKendrick Epidemic Model
- Generalization of the Mass-Action Law of Infection
- The Kermack-McKendrick Epidemic Model with Variable Infectivity
- Age-Structured Models for Endemic Diseases and Optimal Vaccination Strategies
- Endemic Models with Multiple Groups or Populations
- Toolbox
- Appendices
- References
- Index
L'auteur - Horst R. Thieme
Horst R. Thieme is Professor of Mathematics at Arizona State University. He has published more than seventy research papers and is an associate editor of the Journal of Mathematical Analysis and Applications.
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Princeton University Press |
| Auteur(s) | Horst R. Thieme |
| Parution | 02/09/2003 |
| Nb. de pages | 562 |
| Format | 15,5 x 23,5 |
| Couverture | Broché |
| Poids | 785g |
| Intérieur | Noir et Blanc |
| EAN13 | 9780691092911 |
| ISBN13 | 978-0-691-09291-1 |
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