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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.
List of contents
Introduction.- Modelling the Spread of an Infectious Disease.- Hybrid Epidemic Models.- Control Strategies for Eradication.- Discussions and Conclusions.- References.- Appendix
About the author
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
Summary
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.
Additional text
“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)
Report
"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)
