murray mathematical biology vol II spatial models biomedical applications 3ed 2003







Preface to the Third Edition



In the thirteen years since the first edition of this book appeared the growth of mathematical

biology and the diversity of applications has been astonishing. Its establishment

as a distinct discipline is no longer in question. One pragmatic indication is the increasing

number of advertised positions in academia, medicine and industry around the

world; another is the burgeoning membership of societies. People working in the field

now number in the thousands. Mathematical modelling is being applied in every major

discipline in the biomedical sciences. A very different application, and surprisingly

successful, is in psychology such as modelling various human interactions, escalation

to date rape and predicting divorce.



The field has become so large that, inevitably, specialised areas have developed

which are, in effect, separate disciplines such as biofluid mechanics, theoretical ecology

and so on. It is relevant therefore to ask why I felt there was a case for a new edition of

a book called simply Mathematical Biology. It is unrealistic to think that a single book

could cover even a significant part of each subdiscipline and this new edition certainly

does not even try to do this. I feel, however, that there is still justification for a book

which can demonstrate to the uninitiated some of the exciting problems that arise in

biology and give some indication of the wide spectrum of topics that modelling can

address.



In many areas the basics are more or less unchanged but the developments during

the past thirteen years have made it impossible to give as comprehensive a picture of the

current approaches in and the state of the field as was possible in the late 1980s. Even

then important areas were not included such as stochastic modelling, biofluid mechanics

and others. Accordingly in this new edition only some of the basic modelling concepts

are discussed—such as in ecology and to a lesser extent epidemiology—but references

are provided for further reading. In other areas recent advances are discussed together

with some new applications of modelling such as in marital interaction (Volume I),

growth of cancer tumours (Volume II), temperature-dependent sex determination (Volume

I) and wolf territoriality (Volume II). There have been many new and fascinating

developments that I would have liked to include but practical space limitations made

it impossible and necessitated difficult choices. I have tried to give some idea of the

diversity of new developments but the choice is inevitably prejudiced.



As to general approach, if anything it is even more practical in that more emphasis

is given to the close connection many of the models have with experiment, clinical

data and in estimating real parameter values. In several of the chapters it is not yet

possible to relate the mathematical models to specific experiments or even biological

entities. Nevertheless such an approach has spawned numerous experiments based as

much on the modelling approach as on the actual mechanism studied. Some of the more

mathematical parts in which the biological connection was less immediate have been

excised while others that have been kept have a mathematical and technical pedagogical

aim but all within the context of their application to biomedical problems. I feel even

more strongly about the philosophy of mathematical modelling espoused in the original

preface as regards what constitutes good mathematical biology. One of the most exciting

aspects regarding the new chapters has been their genuine interdisciplinary collaborative

character. Mathematical or theoretical biology is unquestionably an interdisciplinary

science par excellence.







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