Mathematical Models in Epidemiology

by Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng

Overview

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.

Product Details

ISBN-13:	9781493998265
Publisher:	Springer New York
Publication date:	10/11/2019
Series:	Texts in Applied Mathematics , #69
Edition description:	1st ed. 2019
Pages:	619
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

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.

Table of Contents

Introduction; A prelude to mathematical epidemiology.- Simple compartmental models for disease transmission.- Endemic disease models.- Epidemic models.- Models with heterogeneous mixing.- Models for diseases transmitted by vectors.- models for tuberculosis.- Models for HIV-AIDS.- Models for influenza.- Models for Ebola.- Models for malaria.- Dengue fever and the Zika virus.- Disease transmission models withagedpendence.- Spatial structure in disease transmission models.- Epidemiological models incorporating mobility, behavior, and time scales.- Challenges, opportunities, and theoretical epidemiology.

Editorial 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 manyof the model discussions are found accessible.” (Yilun Shang, zbMATH 1433.92001, 2020)

From the Publisher