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Infectious Disease Modeling

A Hybrid System Approach

  • Xinzhi Liu
  • Peter Stechlinski

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

Authors and affiliations

  • Xinzhi Liu
    • 1
  • Peter Stechlinski
    • 2
  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-53208-0
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-53206-6
  • Online ISBN 978-3-319-53208-0
  • Series Print ISSN 2195-9994
  • Series Online ISSN 2196-0003
  • Buy this book on publisher's site
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