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  • Textbook
  • © 2019

Mathematical Models in Epidemiology

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  • A modern description of many important areas of mathematical epidemiology

  • Provides an introduction to the formation and analysis of disease transmission models

  • Exercise sets and some projects included

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

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  • ISBN: 978-1-4939-9828-9
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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xviii
  2. Basic Concepts of Mathematical Epidemiology

    1. Front Matter

      Pages 1-1
    2. Introduction: A Prelude to Mathematical Epidemiology

      • Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 3-19
    3. Simple Compartmental Models for Disease Transmission

      • Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 21-61
    4. Endemic Disease Models

      • Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 63-116
    5. Epidemic Models

      • Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 117-178
    6. Models with Heterogeneous Mixing

      • Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 179-227
    7. Models for Diseases Transmitted by Vectors

      • Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 229-245
  3. Models for Specific Diseases

    1. Front Matter

      Pages 247-247
    2. Models for Tuberculosis

      • Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 249-272
    3. Models for HIV/AIDS

      • Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 273-310
    4. Models for Influenza

      • Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 311-350
    5. Models for Ebola

      • Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 351-390
    6. Models for Malaria

      • Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 391-408
    7. Dengue Fever and the Zika Virus

      • Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 409-425
  4. More Advanced Concepts

    1. Front Matter

      Pages 427-427
    2. Disease Transmission Models with Age Structure

      • Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 429-455
    3. Spatial Structure in Disease Transmission Models

      • Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 457-476
    4. Epidemiological Models Incorporating Mobility, Behavior, and Time Scales

      • Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
      Pages 477-504
  5. The Future

    1. Front Matter

      Pages 505-505

About this book

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

Reviews

“The projects and exercises at the end of each chapter are well thought and planned out, and probably my favorite part of the whole book. … I would recommend this book to anyone with the requisite mathematics background, who is more interested in the modeling aspects of epidemiology. I think it’s a nice complement to the existing literature, and I will likely be referring to it for useful examples in my own teaching.” (Roslyn Hickson, SIAM Review, Vol. 63 (3), September, 2021)

“Every practicing mathematical epidemiologist will want this book to occupy a prominent place in their library.” (Glenn Ledder, MAA Reviews, June 14, 2020)

“This book is suitable for upper level university students, it is also useful for public health professionals as many of the model discussions are found accessible.” (Yilun Shang, zbMATH 1433.92001, 2020)

Authors and Affiliations

  • Department of Mathematics, University of British Columbia, Vancouver, Canada

    Fred Brauer

  • Mathematical and Computational Modeling Center (MCMSC), Department of Mathematics and Statistics, Arizona State University, Tempe, USA

    Carlos Castillo-Chavez

  • Department of Mathematics, Purdue University, West Lafayette, USA

    Zhilan Feng

About the authors

Fred Brauer is a Professor Emeritus at the University of Wisconsin - Madison and an Honorary professor at the University of British Columbia. His research interests are in dynamical systems and mathematical models in epidemiology. He has been active in the China - Canada Joint Program on Infectious Diseases and in the organization of several summer programs organized by MITACS ( Mathematics for Information Technology and Complex Systems) to present mathematical epidemiology to a mixed audience of mathematicians and public health professionals and encourage contacts between these groups.

Carlos Castillo-Chavez is a Regents Professor, Joaquin Bustoz Jr.  Professor of Mathematical Biology, Distinguished Sustainability Scientist and Founding Director of the Simon A. Levin Mathematical, Computational and Modeling Sciences Center at ASU. He has co-authored over 250 publications, most at the interface of the life, mathematics and social sciences. He was recognized with three White House Awards (1992, 1997, 2011), served on President Obama’s Committee on the National Medal of Science (2010-2015) and per the Mathematics Genealogy Project, is among the top 200 mentors of PhD students in the history of mathematics.  He is a George Polya Lecturer (2017-19). He serves as a Provost Visiting Professor at Brown University (2019).

Zhilan Feng is a Professor of Mathematics at Purdue University. She is an editor for Journal of Theoretical Biology, Mathematical Biosciences, Mathematical Biosciences and Engineering, Journal of Biological Dynamics, and SIAM Journal on Applied Mathematics. She is a program director for the NSF Mathematical Biology Program 2019-2020.



Bibliographic Information

Buying options

eBook
USD 79.99
Price excludes VAT (USA)
  • ISBN: 978-1-4939-9828-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book
USD 99.99
Price excludes VAT (USA)