Authors:
- Imparts a quantitative understanding of the roles seasonality and population behavior play in the spread of a disease;
- Illustrates formulation and theoretical analysis of mathematical disease models and control strategies;
- Investigates how abrupt changes in the model parameters or function forms affect control schemes;
- Explains techniques from switched and hybrid systems applicable to disease models as well as many other important applications in mathematics, engineering, and computer science;
- Adopts a treatment accessible to individuals with a background in dynamic systems or with a background in epidemic modeling.
Part of the book series: Nonlinear Systems and Complexity (NSCH, volume 19)
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Table of contents (8 chapters)
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Front Matter
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Mathematical Background
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Front Matter
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Hybrid Infectious Disease Models
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Front Matter
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Control Strategies
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Front Matter
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Conclusions and Future Work
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Front Matter
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Back Matter
About this book
This volume presents infectious diseases modeled mathematically, taking seasonality and changes in population behavior into account, using a switched and hybrid systems framework. The scope of coverage includes background on mathematical epidemiology, including classical formulations and results; a motivation for seasonal effects and changes in population behavior, an investigation into term-time forced epidemic models with switching parameters, and a detailed account of several different control strategies. The main goal is to study these models theoretically and to establish conditions under which eradication or persistence of the disease is guaranteed. In doing so, the long-term behavior of the models is determined through mathematical techniques from switched systems theory. Numerical simulations are also given to augment and illustrate the theoretical results and to help study the efficacy of the control schemes.
Reviews
“If you have a serious interest in the epidemiology of infectious diseases and are eager to roll up your sleeves, please consult this book … .” (Odo Diekmann, SIAM Review, Vol. 61 (1), March, 2019)
“This book focuses on infectious disease mathematical models, taking seasonality and changes in population behavior into account, using a switched and hybrid systems framework. … This book is strongly recommended to graduate level students with a background in dynamic system or epidemic modeling and an interest in mathematical biology, epidemic models, and physical problems exhibiting a mixture of continuous and discrete dynamics.” (Hemang B. Panchal, Doody’s Book Reviews, April, 2017)
“This book presents a new type of switched model for the spread of infectious diseases. … This book should be useful and attractive for students and researchers seeking updated progresses in the fieldof epidemic modeling … .” (Yilun Shang, zbMATH 1362.92002, 2017)
Authors and Affiliations
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Department of Applied Mathematics, University of Waterloo, Waterloo, Canada
Xinzhi Liu, Peter Stechlinski
About the authors
Xinzhi Liu is a Professor of Mathematics at the University of Waterloo. Peter Stechlinski is a Postdoctoral Fellow in the Process Systems Engineering Laboratory at the Massachusetts Institute of Technology
Bibliographic Information
Book Title: Infectious Disease Modeling
Book Subtitle: A Hybrid System Approach
Authors: Xinzhi Liu, Peter Stechlinski
Series Title: Nonlinear Systems and Complexity
DOI: https://doi.org/10.1007/978-3-319-53208-0
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-53206-6Published: 03 March 2017
Softcover ISBN: 978-3-319-85090-0Published: 21 July 2018
eBook ISBN: 978-3-319-53208-0Published: 25 February 2017
Series ISSN: 2195-9994
Series E-ISSN: 2196-0003
Edition Number: 1
Number of Pages: XVI, 271
Number of Illustrations: 5 b/w illustrations, 67 illustrations in colour
Topics: Mathematical Modeling and Industrial Mathematics, Infectious Diseases, Complexity, Applications of Nonlinear Dynamics and Chaos Theory, Epidemiology