UK Nonlinear News, August 2001

Mathematical Models in Population Biology and Epidemiology

By Fred Brauer and Carlos Castillo-Chavez

Reviewed by Geoffrey Aldis

Springer-Verlag 2001
Pages: 416
ISBN: 0-387-98902-1 (Hardcover)

This book is aimed at biological-science students but it deserves a wider audience. The range of examples included makes it a good read for mathematically-literate non-biologists. Science and engineering students could also read this book and it could be a good text for a biomathematics course. My review targets non-biologists with at least one year of university mathematics.

The authors don't try to cover all aspects of mathematical biology. Instead they give a coherent view of two related topics -- population biology and epidemiology. The book goes well beyond the simplest problems in each. Part 1 introduces the three main tools (differential equations, difference equations and differential-difference equations) and uses them on well-chosen biological examples. Part 2 extends the tools to study interacting populations. Part 3 is on deterministic epidemiological models. The theory developed here has applications to other structured populations. Epidemiology is also introduced through examples earlier in the book.

The authors' approach of not getting stuck in theory makes this book easier to read. Biological students might feel there is too much theory, but the emphasis is always on passing through to the applications. For a biomathematics course some extra mathematical detail could be added in lectures. The main difficulty would be deciding which sections to leave out.

In this reviewer's experience mathematics students relate well to biological research papers. Students are fascinated by the different thinking they find and it is well worth letting students see the original papers. The population dynamics of flour beetles (section 2.8) is a marvellous example of difference equation modelling. The book's treatment is a good introduction to the original work. Epidemiology is a naturally interesting topic for students when background reading is encouraged. It also serves to remind students that science often spills over discipline boundaries.

A strength of the book is the large number of biologically-motivated problem sets. These and the references to the original biological papers would be valuable resources for an instructor.

The book was written as a textbook but anyone who is curious about mathematical biology would benefit from reading it. There is enough theory to prevent the book from being trivial and the emphasis on applications carries the reader into unexpected territory.

A listing of books reviewed in UK Nonlinear News is available.

UK Nonlinear News thanks Springer Verlag for providing a review copy of this book.

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Last Updated: 6th August 2001.