Mathematical biology. Vol. 1: An introduction.
type: Item
instance of: scholarly article
title: Mathematical biology. Vol. 1: An introduction.
zbMATH Open document ID: 1006.92001
author: J. D. Murray
published in: Interdisciplinary Applied Mathematics
publication date: 2002-06-27T00:00:00Z
review text: 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.
reviewed by: A. Akutowicz
Mathematics Subject Classification ID: 92B05
Mathematics Subject Classification ID: 92-01
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 92C45
zbMATH DE Number: 1761227
zbMATH Keywords: population dynamics
zbMATH Keywords: chemically reacting systems
zbMATH Keywords: oscillations
zbMATH Keywords: dynamics of infectious diseases
zbMATH Keywords: Belousov-Zhabotinskij reaction system
zbMATH Keywords: marital interactions
zbMATH Keywords: HIV dynamics
zbMATH Keywords: drug therapy
MaRDI profile type: Publication
full work available at URL: b98868
OpenAlex ID: W4237997615
DOI: 10.1007/B98868
Recommended article: Q3992578
Recommended article: Q3994920
Recommended article: Q3450780
Recommended article: Q4808476
Recommended article: Dynamical models in biology
Recommended article: BIOMAT 2011. International symposium on mathematical and computational biology, Santiago, Chile, November 5--10, 2011
Recommended article: Q3138600
Recommended article: An Introduction to Mathematical Physiology and Biology
Recommended article: Piecewise deterministic processes in biological models
description: scientific article; zbMATH DE number 1761227