UK Nonlinear News, November 2002
The IMA Volumes in Mathematics and its Applications
|Volume 125||Volume 126|
|82 figures. X. 368 pages||69 figures. X. 368 pages|
|Hardcover. ISBN 0-387-95354-X||Hardcover. ISBN 0-387-95355-8|
|Springer Verlag, 2002|
This two-volume set is based on a week-long workshop sponsored by the Institute of Mathematics and its Applications (the IMA) and held at the University of Minnesota in May 1999. Papers from the distinguished contributors are grouped into an introductory first volume and a mathematically more sophisticated second volume. The arrangement of papers does not always match this intended division.
The publisher's note on the back cover says that the books would be useful to ``beginning graduate students in applied mathematics, scientists in the natural, social, or health sciences, or mathematicians who want to enter the fields of mathematical epidemiology and theoretical epidemiology''. The review is written with those aims in mind.
Nonlinearity and dynamical systems arise naturally in infectious disease modelling. The volumes cover a wide range of mathematical models including sets of ordinary and partial differential equations, difference equations, integral equations, differential-delay equations and stochastic models.
The books are dedicated to two influential teachers and researchers: Fred Brauer and Kenneth Cooke. Chapters about them and an introduction by Simon Levin are repeated in both volumes. The first volume then gathers momentum with two tutorial papers by Fred Brauer introducing some common notation and concepts of mathematical epidemiology. The material is based on chapter 7 of Brauer and Castillo-Chavez (2001). Another 15 papers and an epilogue complete the first volume. Some of the papers are expository and tutorial-like while others dive rapidly into detail. The titles and the order of appearance do not indicate which. The papers appear to be grouped in themes rather than in an order to assist a new researcher in the field. However most of the papers include extra explanation and a valuable reference list.
The second volume contains 16 additional papers. While the first volume contains some papers which are clearly tutorial-like, the majority of papers could have appeared in either volume. The set of topics is not complete as noted by the editors in the epilogue. For example, the considerable world-wide effort on malaria is not represented. However the material in the two books offers a fine introduction to research-level mathematical epidemiology. The amount of space devoted to dynamical systems would also please readers of UK Nonlinear News.
How could a beginning graduate student or a curious scientist learn about mathematical epidemiology? Expository books such as Brauer and Castillo-Chavez (2001) or Anderson and May (1991) are excellent starting points. The quirky book by Diekmann and Heesterbeek (2000) covers a lot of territory, is recent and actively engages the reader. Then compilations such as the two-volume set reviewed here connect directly with the research literature.
As with most `conference proceedings' the writing style and the topic change frequently. A reader intent on digesting the lot will be feeling a little queasy at the end. The Newton Institute books edited by Mollison (1995), Isham and Medley (1996) and Grenfell and Dobson (1995) are also multi-authored and are still an impressive resource. The IMA volumes reviewed here offer an update on some of that material.
In summary, there is a lot of valuable work in this two-volume set which could meet the intended aim of introducing people to research-level mathematical epidemiology. The volumes belong together as a set to maximise the coverage. Nevertheless the first volume on its own provides the reader with the introductory papers and papers showing several different mathematical approaches in action.
R.M. Anderson and R.M. May (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford University Press.
F. Brauer and C. Castillo-Chavez (2001). Mathematical Models in Population Biology and Epidemiology. Springer-Verlag. (Reviewed in UK Nonlinear News.)
O. Diekmann and J.A.P. Heesterbeek (2000). Mathematical Epidemiology of Infectious Diseases -- Model Building, Analysis and Interpretation. Wiley.
B.T. Grenfell and A.P. Dobson (editors) (1995). Ecology of Infectious Diseases in Natural Populations. Cambridge University Press.
V. Isham and G. Medley (editors) (1996). Models for Infectious Diseases: Their Structure and Relation to Data. Cambridge University Press.
D. Mollison (editor) (1995). Epidemic Models: Their Structure and Relation to Data. Cambridge University Press.
UK Nonlinear News thanks Springer-Verlag for providing a review copy of this book.
A listing of books reviewed in UK Nonlinear News is available.