Oxford University Press, Oxford, 2000

249 pages

Hardback. £40. ISBN 0-19-850418-7

Paperback £19.50. ISBN 0-19-850417-9.

There is a saying attributed to Linus in the comic strip Peanuts by Charles Schultz, "If you can understand it, it can't be any good." Happily, this book is an exception to the rule.

Written by two of the most eminent authorities in the field, Virus Dynamics is a surprisingly good read. The main emphasis of the book is on understanding the dynamics of HIV pathogenesis in the context of immune regulation, and the implications for therapy. Each of the 15 chapters has essentially the same format - a brief introduction to the relevant biology, followed by a study of the mathematical model, and concluding with the relevance of the model for biology.

The brief introductions heading each chapter typically explain how the biology motivates the mathematics, and does this at a level appropriate for a physical scientist or mathematician. Immunologists, virologists and infectious disease physicians may also find this view of what biology looks like when filtered through a mathematician's brain quite entertaining.

The actual models are based on first order ODEs, and therefore do not require much mathematical sophistication to appreciate. Starting with a basic model of HIV dynamics similar to models from mathematical epidemiology, this is then elaborated in successive chapters to take into account the immune response, viral heterogeneity, evolutionary pressure resulting in escape mutants, and the emergence of drug resistance. Particularly impressive is the fact that the authors succeed in showing how mathematics can contribute to biology by providing insight into the mechanisms underlying biological data, pointing out clear experimental or clinical predictions, and showing what further experiments should be done to further our understanding of HIV dynamics.

This book will be great for anyone interested in learning how to apply quantitative approaches to biology. It demonstrates clearly how simple mathematical models that "stay close" to the biology can provide useful insights. It complements general texts in mathematical biology by staying far narrower in its scope, and therefore provides a useful and detailed case-study approach to modelling one of the most pressing medical problems of our age.

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

UK Nonlinear News thanks Oxford University Press for providing a review copy of this book.

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