Mathematics in Population Biology

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Princeton University Press, 2003 - Mathematics - 543 pages
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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.

  

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Contents

Some General Remarks on Mathematical Modeling
1
Birth Death and Migration
7
Unconstrained Population Growth for Single Species
13
Von Bertalanffy Growth of Body Size
33
Sigmoid Growth
51
The Allee Effect
65
Asymptotic Equality
75
DiscreteTime SingleSpecies Models
81
Some Nonlinear Demographics
273
Background
283
The Simplified KermackMcKendrick Epidemic Model
293
Generalization of the MassAction Law of Infection
305
The KermackMcKendrick Epidemic Model with
311
SEIR S Type Endemic Models for Childhood Diseases
317
AgeStructured Models for Endemic Diseases
341
Endemic Models with Multiple Groups or Populations
383

Dynamics of an Aquatic Population Interacting with
107
Population Growth Under Basic Stage Structure
151
The Transition Through a Stage
185
Stage Dynamics with Given Input
211
Demographics in an Unlimiting Constant Environment
239
Some Demographic Lessons from Balanced Exponential Growth
255
Appendix A Ordinary Differential Equations
421
Appendix B Integration Integral Equations and Some Convex Analysis
453
Some MAPLE Worksheets with Comments for Part 1
493
References
519
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About the author (2003)

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." .

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