Mathematical biology. Vol. 1: An introduction. 3rd ed.

*(English)*Zbl 1006.92001
Interdisciplinary Applied Mathematics 17. New York, NY: Springer (ISBN 978-0-387-22437-4/ebook; 978-0-387-95223-9/hbk). xiii, 551 p. (2002).

This book is the first volume of a pair which can be considered as a tour in mathematical biology. The first edition from 1989, in a single volume, has been reviewed in Zbl 0682.92001. The main biological themes are population dynamics, chemically reacting systems (involving oscillations), cellular and biomedical aspects. The mathematical tools are ordinary differential equations, discrete models and partial differential equations, but they are not restricted to a specific type of biological models; one may use both for a given application adapting to the degree of acuity in the modelling. Moreover, the biological distinctions have to be modulated when for instance in chapter ten one studies the dynamics of infectious diseases (where a population dynamics component is present but it acts at the cellular level). So, methods and models are integrated. The author adds that he favours modelling techniques which will be efficient for understanding the phenomena occuring but also for predicting events; this implies that the interface between mathematical results and experimental implementations should be kept in mind.

One finds also topics which are related to systems science like stability and feedback (note that this latter concept is seen as a term which can be varied in an ODE model of enzyme production and it has a biological interpretation, but the more interesting question would be to ask why biology needs feedback loops and how they get generated). On the way one finds classical equations of the mathematical fauna (predator-prey systems of the Volterra type, Fitz-Nagumo model in neural communication, Belousov-Zhabotinskij reaction system) and exotic topics arising from the above-mentioned frame: temperature-dependent sex determination among crocodiles, discrete modelling of marital interactions, HIV dynamics and drug therapy. A chapter deals with fractals. The bibliography contains almost six hundred entries and there is an extensive index at the end.

One finds also topics which are related to systems science like stability and feedback (note that this latter concept is seen as a term which can be varied in an ODE model of enzyme production and it has a biological interpretation, but the more interesting question would be to ask why biology needs feedback loops and how they get generated). On the way one finds classical equations of the mathematical fauna (predator-prey systems of the Volterra type, Fitz-Nagumo model in neural communication, Belousov-Zhabotinskij reaction system) and exotic topics arising from the above-mentioned frame: temperature-dependent sex determination among crocodiles, discrete modelling of marital interactions, HIV dynamics and drug therapy. A chapter deals with fractals. The bibliography contains almost six hundred entries and there is an extensive index at the end.

Reviewer: A.Akutowicz (Berlin)

##### MSC:

92B05 | General biology and biomathematics |

92-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology |

92D25 | Population dynamics (general) |

92D30 | Epidemiology |

92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |