An Introduction to Mathematical Modeling of Infectious Diseases

1. Front Matter

   Pages i-x

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2. Important Concepts in Mathematical Modeling of Infectious Diseases

   • Michael Y. Li

   Pages 1-33

3. Five Classic Epidemic Models and Their Analysis

   • Michael Y. Li

   Pages 35-77

4. Basic Mathematical Tools and Techniques

   • Michael Y. Li

   Pages 79-101

5. Parameter Estimation and Nonlinear Least-Squares Methods

   • Michael Y. Li

   Pages 103-124

6. Special Topics

   • Michael Y. Li

   Pages 125-150

7. Back Matter

   Pages 151-156

   PDF

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.

• Mathematical Epidemiology
• Infectious Disease
• Mathematical Modelling
• Public Health
• Kermack-McKendrick Model
• Nonlinear Least Squares
• Viral Dynamics
• Differential Equations
• Stability Analysis
• Bifurcation
• Basic Reproduction Number
• Parameter Estimation
• Mathematics of Planet Earth
• infectious diseases

“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)

• Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada

  Michael Y. Li

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.