Book Review ?Modelling Disease Ecology with Mathematics by Robert Smith?
This volume admirably fulfils the author’s primary purpose of using infectious disease modeling as a framework in which to explore the usefulness of mathematical modeling. Biologists and public health researchers will benefit from the clear explanations of the modeling process and details of some of the mathematical topics used. The volume is laid out in an accessible format, serving as a link between biologists and mathematicians and an aid in communication between the two groups.
Specifically, each of the Chapters 2-13 begins with a flow chart outlining the flow of ideas to be presented, and also states what the reader should know by the end of the chapter. After the main part of a chapter, some computer lab work illustrated with Matlab programs is given, followed by some exercises for the] reader. A valuable overview of Matlab is given in an appendix. The structure of the volume thus lends itself well to self-study or a workshop environment, as well as a more traditional course.
Chapter 2 sets the scene by constructing simple epidemic models with continuous time, yielding ordinary differential equations. Equilibrium points and their stability are examined, and this theme is continued in Chapter 3 where the important threshold parameter R0 is introduced. This parameter plays a pivotal role in designing disease control strategies. Chapters 4 and 5 deal with vector borne diseases, for example, yellow fever and malaria. The models developed build on those of previous chapters, with the calculation of R0 requiring some tools from matrix algebra, which are clearly described in some appendices. Spatial spread of disease is introduced in Chapters 6 and 7, and the reader is given an appreciation of the added complexity. It is good to see the inclusion of chapters on fitting curves to data (Chapter 8) illustrated with data from epidemics, and splines (Chapter 9). In Chapters 10 and 11, time is taken as a discrete variable, yielding difference equation models. Stability of equilibria and possible bifurcations are briefly discussed. The final two chapters consider applications, modeling AIDS and end-stage renal disease incorporating treatment with antiretroviral drugs, and extending the malaria model to include time delays for incubation in humans and mosquitoes. Some mathematical details used in the volume are expanded as appendices.
After working through this volume, a reader will have a broad understanding of deterministic modeling of infectious diseases, and should be able to read current articles and discuss disease control strategies. This volume is highly recommended for public health workers seeking to facilitate communication with mathematicians and for mathematics students interested in an effective introduction to disease modeling.