Mathematical Models in Population Biology and Epidemiology

1. Front Matter

   Pages i-xxiii

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2. Simple Single Species Models

   1. Front Matter

      Pages 1-1

      PDF

   2. Continuous Population Models

      • Fred Brauer, Carlos Castillo-Chávez

      Pages 3-49

   3. Discrete Population Models

      • Fred Brauer, Carlos Castillo-Chávez

      Pages 51-94

   4. Continuous Single-Species Population Models with Delays

      • Fred Brauer, Carlos Castillo-Chávez

      Pages 95-124

3. Models for Interacting Species

   1. Front Matter

      Pages 125-125

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   2. Introduction and Mathematical Preliminaries

      • Fred Brauer, Carlos Castillo-Chávez

      Pages 127-170

   3. Continuous Models for Two Interacting Populations

      • Fred Brauer, Carlos Castillo-Chávez

      Pages 171-229

   4. Harvesting in two-species models

      • Fred Brauer, Carlos Castillo-Chávez

      Pages 231-272

4. Structured Populations Models

   1. Front Matter

      Pages 273-273

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   2. Basic Ideas of Mathematical Epidemiology

      • Fred Brauer, Carlos Castillo-Chávez

      Pages 275-337

   3. Models for Populations with Age Structure

      • Fred Brauer, Carlos Castillo-Chávez

      Pages 339-370

5. Epilogue

   1. Epilogue

      • Fred Brauer, Carlos Castillo-Chávez

      Pages 371-372

6. Back Matter

   Pages 373-417

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As the world population exceeds the six billion mark, questions of population explosion, of how many people the earth can support and under which conditions, become pressing. Some of the questions and challenges raised can be addressed through the use of mathemathical models, but not all. The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions such as these. Part I focusses on single-species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models - the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity - the subject of Part III. This book, which includes both examples and exercises, will be useful to practitioners, graduate students, and scientists working in the field.

• Biome
• Ecology
• Epidemiology
• biology
• evolution
• evolutionary biology
• population structure
• statistics

From the reviews:

ZENTRALBLATT MATH

"The work provides an easily accessible, but concise introduction to the subject. Both graduate students and professionals will find the book an understandable, absorbing, and penetrating treatment of a beautiful theory."

UK NONLINEAR NEWS

"This book is aimed at biological-science students but it deserves a wider audience. The range of examples included makes it a good read for mathematically-literate non-biologists. Science and engineering students could also read this book and it could be a good text for a biomathematics course…The authors’ approach of not getting stuck in theory makes this book easier to read…A strength of the book is the large number of biologically-motivated problem sets. These and the references to the original biological papers would be valuable resources for an instructor. The book was written as a textbook but anyone who is curious about mathematical biology would benefit from reading it. There is enough theory to prevent the book from being trivial and the emphasis on applications carries the reader into unexpected territory."

MATHEMATICAL REVIEWS

"…on close examination the presentation has a number of distinguishing features. First, the authors carefully discuss the underling assumptions of each model and, where appropriate, illustrate their points with real data. Second, the authors extend the discussion of discrete time maps to include systems of difference equations. Third, the authors provide very convincing arguments for the inclusion of time delays in models for population growth. Finally, the chapter on the effects of harvesting on the growth of populations would be an excellent addition to an undergraduate course in mathematical economics. This textbook is user friendly and at times captivating. At first look students may be slightly intimidated since the text contains a lot of equations. However they will soon be delighted to see that number of equation is because the authors show all of the steps in the derivations. Moreover the authors increase the relevance of this text by carefully discussing the underlying assumptions of each model and by placing the model in its proper historical context…A textbook on biomathematics must overcome two major hurdles: (1) convince biologists that the mathematics is useful in a way that is accessible to them; and (2) convince mathematicians that the topic is not trivial and hence worthy of their time. This text gets a ‘two thumbs up’."

ECOLOGY

"The organization within each subsection is incredibly thorough, gradually adding mathematical twists to each previous equation or model. Biological examples are provided if and when they relate to a given equation and the examples are highly idealized…this books format is also reasonable for a survey of applied mathematics because the format facilitates comparison across fields of biology…There is some very useful information within this book."

"It is a useful book which gives a good introduction to the modelling of biology and some other similar fields. ... This book gives and discusses many continuous and discrete models from population dynamics, epidemiology, and resource management. A large number and variety of examples, exercises are included. The book is warmly recommended to undergraduate and graduate students as well as to scientists in mathematical or biological sciences." (József Terjéki, Acta Scientiarum Mathematicarum, Vol. 69, 2003)

"There are some jewels in this text ... . This book is intended for the student who has had a year of calculus, some background in elementary differential equations, and a little matrix theory. ... There is some very useful information within this book. The book includes problems, ‘projects, an in-book appendix, and a future on-line appendix. Answers are provided for some but not all problems, to encourage students to become involved and not just be spectators." (Janet Foley, Ecology, Vol. 83 (1), 2002)

"The role of mathematics in ecology and epidemiology has had a long history ... The current volume focuses on this interface between mathematics and biology. ... The book is written in the theorem proof style that mathematicians will feel comfortable with. ... The succinct and clear section on mathematical epidemiology is one of the highlights of the book. ... There are extensive problems throughout the text; these are all essentially mathematical exercises. ... the book does present advanced mathematical ideas quite clearly." (Alan Hastings, The Quarterly Review of Biology, Vol. 77 (3), 2002)

"This book is aimed at biological-science students but it deserves a wider audience. The range of examples included makes it a good read for mathematically-literate non-biologists. ... A strength of the book is the large number of biologically-motivated problem sets. These and the references to the original biological papers would be valuable resources for an instructor. The book was written as a textbook but anyone who is curious about mathematical biology would benefit from reading it." (Geoffrey Aldis, UK Nonlinear News, August, 2001)

• Department of Mathematics, University of British Columbia, Vancouver, Canada

  Fred Brauer

• Dept. of Theoretical and Applied Mechanics, Mathematical and Theoretical Biology Institute, USA

  Carlos Castillo-Chávez

• Biometrics Department, Cornell University, Ithaca, USA

  Carlos Castillo-Chávez