Overview
- Written by a pioneer and expert in Mathematical Biology
- Analyzes the impact of quiescent phases in biology with mathematical models
- Presents classical mathematical biology models in detail with a focus on quiescence
- Casts new light on excitability of steady states, epidemic outbreaks, survival of the fittest and many more topics
- Holds in store many gems for the readers
Part of the book series: Lecture Notes on Mathematical Modelling in the Life Sciences (LMML)
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Table of contents (8 chapters)
Keywords
About this book
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.
Reviews
“This advanced textbook is well-suited for graduate students and researchers in mathematical biology with a solid background in mathematics, particularly linear algebra, differential equations and dynamical systems, and the material is put on a rigorous mathematical basis.” (W. Huyer, Monatshefte für Mathematik, Vol. 192 (4), August, 2020)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Topics in Mathematical Biology
Authors: Karl Peter Hadeler
Series Title: Lecture Notes on Mathematical Modelling in the Life Sciences
DOI: https://doi.org/10.1007/978-3-319-65621-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-65620-5Published: 22 January 2018
eBook ISBN: 978-3-319-65621-2Published: 20 December 2017
Series ISSN: 2193-4789
Series E-ISSN: 2193-4797
Edition Number: 1
Number of Pages: XIV, 353
Number of Illustrations: 26 b/w illustrations, 2 illustrations in colour