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.
Download
http://s18.alxa.net/s18/srvs2/02/003...s_3ed_2003.rar
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.
Download
http://s18.alxa.net/s18/srvs2/02/003...s_3ed_2003.rar