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© 2017

Infectious Disease Modeling

A Hybrid System Approach

  • 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.

Book

Part of the Nonlinear Systems and Complexity book series (NSCH, volume 19)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Mathematical Background

    1. Front Matter
      Pages 1-1
    2. Xinzhi Liu, Peter Stechlinski
      Pages 3-20
    3. Xinzhi Liu, Peter Stechlinski
      Pages 21-39
  3. Hybrid Infectious Disease Models

    1. Front Matter
      Pages 41-41
    2. Xinzhi Liu, Peter Stechlinski
      Pages 43-82
    3. Xinzhi Liu, Peter Stechlinski
      Pages 83-132
  4. Control Strategies

    1. Front Matter
      Pages 133-133
    2. Xinzhi Liu, Peter Stechlinski
      Pages 135-178
    3. Xinzhi Liu, Peter Stechlinski
      Pages 179-226
    4. Xinzhi Liu, Peter Stechlinski
      Pages 227-257
  5. Conclusions and Future Work

    1. Front Matter
      Pages 259-259
    2. Xinzhi Liu, Peter Stechlinski
      Pages 261-263
  6. Back Matter
    Pages 265-271

About this book

Introduction

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.


Keywords

Basic reproduction number Control strategies Epidemic models Hybrid system Infectious diseases Pulse vaccination Stability theory Switched system complexity

Authors and affiliations

  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada

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

Industry Sectors
Finance, Business & Banking

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 field of epidemic modeling … .” (Yilun Shang, zbMATH 1362.92002, 2017)