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Topics in mathematical biology

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...

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Detalles Bibliográficos
Autor principal: Hadeler, Karl Peter
Lenguaje:eng
Publicado: Springer 2017
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-65621-2
http://cds.cern.ch/record/2300465
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author Hadeler, Karl Peter
author_facet Hadeler, Karl Peter
author_sort Hadeler, Karl Peter
collection CERN
description 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.
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spelling cern-23004652021-04-21T18:56:50Zdoi:10.1007/978-3-319-65621-2http://cds.cern.ch/record/2300465engHadeler, Karl PeterTopics in mathematical biologyMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:23004652017
spellingShingle Mathematical Physics and Mathematics
Hadeler, Karl Peter
Topics in mathematical biology
title Topics in mathematical biology
title_full Topics in mathematical biology
title_fullStr Topics in mathematical biology
title_full_unstemmed Topics in mathematical biology
title_short Topics in mathematical biology
title_sort topics in mathematical biology
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-65621-2
http://cds.cern.ch/record/2300465
work_keys_str_mv AT hadelerkarlpeter topicsinmathematicalbiology