# Mathematics in Population Biology

Princeton University Press, 2003 - 543 Seiten

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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### Inhalt

 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

 Polluted Environment 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 Index 537 Urheberrecht

### Verweise auf dieses Buch

 Mathematics for Life Science and MedicineEingeschränkte Leseprobe - 2007
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### Über den Autor (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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