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Mathematical Models in Epidemiology

  • Fred Brauer
  • Carlos Castillo-Chavez
  • Zhilan Feng
Textbook

Part of the Texts in Applied Mathematics book series (TAM, volume 69)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Basic Concepts of Mathematical Epidemiology

    1. Front Matter
      Pages 1-1
    2. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 3-19
    3. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 21-61
    4. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 63-116
    5. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 117-178
    6. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 179-227
    7. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 229-245
  3. Models for Specific Diseases

    1. Front Matter
      Pages 247-247
    2. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 249-272
    3. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 273-310
    4. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 311-350
    5. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 351-390
    6. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 391-408
    7. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 409-425
  4. More Advanced Concepts

    1. Front Matter
      Pages 427-427
    2. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 429-455
    3. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 457-476
    4. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 477-504
  5. The Future

    1. Front Matter
      Pages 505-505
    2. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 507-531
  6. Back Matter
    Pages 533-619

About this book

Introduction

The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of disease transmission models. It includes (i) an introduction to the main concepts of compartmental models including models with heterogeneous mixing of individuals and models for vector-transmitted diseases, (ii) a detailed analysis of models for important specific diseases, including tuberculosis, HIV/AIDS, influenza, Ebola virus disease, malaria, dengue fever and the Zika virus, (iii) an introduction to more advanced mathematical topics, including age structure, spatial structure, and mobility, and (iv) some challenges and opportunities for the future.

There are exercises of varying degrees of difficulty, and projects leading to new research directions. For the benefit of public health professionals whose contact with mathematics may not be recent, there is an appendix covering the necessary mathematical background. There are indications which sections require a strong mathematical background so that the book can be useful for both mathematical modelers and public health professionals.   

Keywords

Stochastic Models Disease Transmission Models Metapopulation Models Mathematical models epidemiology epidemics endemic states communicable diseases analysis of models

Authors and affiliations

  • Fred Brauer
    • 1
  • Carlos Castillo-Chavez
    • 2
  • Zhilan Feng
    • 3
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Mathematical and Computational Modeling Center (MCMSC), Department of Mathematics and StatisticsArizona State UniversityTempeUSA
  3. 3.Department of MathematicsPurdue UniversityWest LafayetteUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-9828-9
  • Copyright Information Springer Science+Business Media, LLC, part of Springer Nature 2019
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-9826-5
  • Online ISBN 978-1-4939-9828-9
  • Series Print ISSN 0939-2475
  • Series Online ISSN 2196-9949
  • Buy this book on publisher's site
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