An Introduction to Mathematical Modeling of Infectious Diseases

by Michael Y. Li

Overview

This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies. The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis. Matlab codes are also included for numerical implementations.

It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases. Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.

Product Details

ISBN-13:	9783319721217
Publisher:	Springer International Publishing
Publication date:	02/01/2018
Series:	Mathematics of Planet Earth , #2
Edition description:	1st ed. 2018
Pages:	156
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Michael Y. Li is a Professor of Mathematics at the University of Alberta, Canada. His research includes mathematical theory of differential equations and dynamical systems, mathematical modeling of immune systems, and mathematical modeling in public health sciences.

Table of Contents

Important Concepts.- Five Classic Examples.- Basic Tools.- Nonlinear Least Squares.- Special Topics.

Editorial Reviews

Reviewer: Puja Sitwala, MD (East Tennessee State University Quillen College of Medicine)
Description: Based on a lecture set that the author has been using for a disease modeling course at the University of Alberta, this book imparts important modeling skills and techniques for the study of infectious disease.
Purpose: The purpose is to present the proper expertise and techniques for the study of infectious disease either via self-study or as a semester course. The information also may be beneficial for public health science students with analytical skills.
Audience: This book is written essentially for senior undergraduate and graduate students who are focused on or interested in mathematical modeling of infectious disease. The author recommends that reader should have the basic prerequisite knowledge of advanced calculus and an understanding of the matrix theory in order to gain maximum benefit and understanding.
Features: The first of the book's five chapters is introductory, with detailed discussions of the basic concepts in infectious disease epidemiology such as vaccination, route of transmission, heterogeneity etc. Chapter 2 centers on model analysis and mathematical concepts such as stability, bifurcation, and threshold phenomenon, with five classic epidemic models used as examples to demonstrate a mathematical approach to model analysis. Chapter 3 consists of the abstract theory of differential equations that are used in the previous chapter. Chapter 4 includes algorithms for nonlinear least-squares estimation using Matlab codes to assist beginner students to use them in their projects. Chapter 5 is divided into two sections; the first further exemplifies how the principles used in chapter 2 can be applied to complex models, while the second shows how modeling skills can be applied to a microbial level through the example of HTLV 1 virus. The book contains plenty of excellent examples in an easy to understand format.
Assessment: This is an excellent resource for undergraduates, graduates, public health science students, or anyone interested in mathematical modeling. Although the examples mostly pertain to infectious diseases, the book could be applicable to various fields. I highly recommend this book, especially to the targeted audience.

Doody's Review Service

The purpose is to present the proper expertise and techniques for the study of infectious disease either via self‐study or as a semester course. … This is an excellent resource for undergraduates, graduates, public health science students, or anyone interested in mathematical modeling. Although the examples mostly pertain to infectious diseases, the book could be applicable to various fields. I highly recommend this book, especially to the targeted audience.” (Puja Sitwala, Doody's Book Reviews, April, 2018)

“This book is a unique contribution to Springer's Mathematics of Planet Earth series, in which I have indulged myself for the past few weeks. It is suitable for upper undergraduate and beginning graduate students who are interested in mathematical modeling of epidemics.” (Yilun Shang, zbMATH 1396.92003, 2018)

From the Publisher