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Topics in Mathematical Biology

  • Karl Peter Hadeler

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Karl-Peter Hadeler
    Pages 1-78
  3. Karl-Peter Hadeler
    Pages 79-126
  4. Karl-Peter Hadeler
    Pages 127-176
  5. Karl-Peter Hadeler
    Pages 177-211
  6. Karl-Peter Hadeler
    Pages 213-229
  7. Karl-Peter Hadeler
    Pages 231-264
  8. Karl-Peter Hadeler
    Pages 265-299
  9. Karl-Peter Hadeler
    Pages 301-337
  10. Back Matter
    Pages 339-353

About this book

Introduction

This book analyzes the impact of quiescent phases on biological models. Quiescence arises, for example, when moving individuals stop moving, hunting predators take a rest, infected individuals are isolated, or cells enter the quiescent compartment of the cell cycle. In the first chapter of Topics in Mathematical Biology general principles about coupled and quiescent systems are derived, including results on shrinking periodic orbits and stabilization of oscillations via quiescence. In subsequent chapters classical biological models are presented in detail and challenged by the introduction of quiescence. These models include delay equations, demographic models, age structured models, Lotka-Volterra systems, replicator systems, genetic models, game theory, Nash equilibria, evolutionary stable strategies, ecological models, epidemiological models, random walks and reaction-diffusion models. In each case we find new and interesting results such as stability of fixed points and/or periodic orbits, excitability of steady states, epidemic outbreaks, survival of the fittest, and speeds of invading fronts. 

The textbook is intended for graduate students and researchers in mathematical biology who have a solid background in linear algebra, differential equations and dynamical systems. Readers can find gems of unexpected beauty within these pages, and those who knew K.P. (as he was often called) well will likely feel his presence and hear him speaking to them as they read.


Keywords

35Q92, 37N25, 92Bxx Mathematical Biology Quiescent states Population dynamics Epidemic models Reaction-diffusion equations Stability and Bifurcations Travelling Fronts

Authors and affiliations

  • Karl Peter Hadeler
    • 1
  1. 1.Universität TübingenTübingenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-65621-2
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-65620-5
  • Online ISBN 978-3-319-65621-2
  • Series Print ISSN 2193-4789
  • Series Online ISSN 2193-4797
  • Buy this book on publisher's site
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