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Mathematics in Population Biology : Princeton Series in Theoretical and Computational Biology - Horst R. Thieme

Mathematics in Population Biology

Princeton Series in Theoretical and Computational Biology

Paperback

Published: 22nd July 2003
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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.

Mathematics in Population Biology provides a rigorous mathematical treatment of a wide variety of [models]. The attention to mathematical details is emphasized much more in this book than in many other popular mathematical biology textbooks and will be of particular interest to mathematicians... In addition, this book is an excellent reference for researchers interested in learning more about the mathematics behind the models of population biology."--Linda J. S. Allen, SIAM Review

Preface
Some General Remarks on Mathematical Modelingp. 1
Basic Population Growth Modelsp. 5
Birth, Death, and Migrationp. 7
Unconstrained Population Growth for Single Speciesp. 13
Von Bertalanffy Growth of Body Sizep. 33
Classic Models of Density-Dependent Population Growth for Single Speciesp. 37
Sigmoid Growthp. 51
The Allee Effectp. 65
Nonautonomous Population Growth: Asymptotic Equality of Population Sizesp. 75
Discrete-Time Single-Species Modelsp. 81
Dynamics of an Aquatic Population Interacting with a Polluted Environmentp. 107
Population Growth Under Basic Stage Structurep. 151
Stage Transitions and Demographicsp. 183
The Transition Through a Stagep. 185
Stage Dynamics with Given Inputp. 211
Demographics in an Unlimiting Constant Environmentp. 239
Some Demographic Lessons from Balanced Exponential Growthp. 255
Some Nonlinear Demographicsp. 273
Host-Parasite Population Growth: Epidemiology of Infectious Diseasesp. 281
Backgroundp. 283
The Simplified Kermack-McKendrick Epidemic Modelp. 293
Generalization of the Mass-Action Law of Infectionp. 305
The Kermack-McKendrick Epidemic Model with Variable Infectivityp. 311
SEIR ([approaches]S) Type Endemic Models for "Childhood Diseases"p. 317
Age-Structured Models for Endemic Diseases and Optimal Vaccination Strategiesp. 341
Endemic Models with Multiple Groups or Populationsp. 383
Toolboxp. 419
Ordinary Differential Equationsp. 421
Integration, Integral Equations, and Some Convex Analysisp. 453
Some MAPLE Worksheets with Comments for Part 1p. 493
Referencesp. 519
Indexp. 537
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780691092911
ISBN-10: 0691092915
Series: Princeton Series in Theoretical and Computational Biology
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 568
Published: 22nd July 2003
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 23.32 x 16.2  x 3.1
Weight (kg): 0.77