Compartmental Modelling with Networks

Gilbert G. Walter and Martha Contreras BirkhauserBoston1999272 PagesISBN 0-8176-4019-3Price: £40.00 $56(Approx)

It seems to be the fashion at the moment for many cyberneticians and systemists to study their fields without close reference to either a formulation of a problem or to use any theory that demands more than an elementary knowledge of mathematics. The authors of this book seem aware of this problem and have taken great pains to make the mathematics understandable and to explain it as frequently as possible. They have even supplied a readable appendix to help those who they believe might be "mathematically challenged". Far from "dumbing down" the book it has made it more readable. Indeed the book offers an excellent introduction to the theory and practice of compartmental modelling. It has a large number of illustrative examples to help the reader through the parts of the book that might otherwise have presented difficulties.

We are told that a compartmental model of a system is an articulation of that system into a series of homogenous compartments. These are arranged so that matter and energy, for example, can be exchanged. Space is not included explicitly but it can be included in the interconnections of the compartments. This means that compartmental models can be more easily dealt with than models with spatial dependence. Each compartment is homogenised with the result that system interactions can be represented on a network of nodes and branches. The dynamics of the system is modelled using equations at each node describing how the corresponding compartment updates at each time step as a result of activity into and out of the compartment. This is only a brief description, the authors,on the other hand, have prepared an lucid intoduction to both the theory and practice of compartmental modelling, and show how such models can help towards the understanding of a large range of real world problems.

The book is well structured and presented in four parts: Introduction to Graph theory; Markov chains; Compartmental models; Theory of compartmental models. There is an extremely useful appendix which will help both the mathematical oriented reader as well as readers who need reminding of some of the basics of matrices and systems of differential equations. Eigenvalues and eigenvectors, matrix diagonalisation and methods of finding explicit solutions of linear systems of differential equations by diagonalisation of the system compartmental matrix are included.

The book would be a most useful aid for a basic modelling course since the models are simple to program and can be used with most of our current mathematical software packages. It is also a text that many cyberneticians and systemists, who are who are interested in modelling real systems would want to access.

C. J. Harwood