Mathematical Models in Population Biology and EpidemiologyThis book is an introduction to the principles and practice of mathematical modeling in the biological sciences, concentrating on applications in population biology, epidemiology, and resource management. The core of the book covers models in these areas and the mathematics useful in analyzing them, including case studies representing real-life situations. The emphasis throughout is on describing the mathematical results and showing students how to apply them to biological problems while highlighting some modeling strategies. A large number and variety of examples, exercises, and projects are included. Additional ideas and information may be found on a web site associated with the book. Senior undergraduates and graduate students as well as scientists in the biological and mathematical sciences will find this book useful. Carlos Castillo-Chavez is professor of biomathematics in the departments of biometrics, statistics, and theoretical and applied mechanics at Cornell University and a member of the graduate fields of applied mathematics, ecology and evolutionary biology, and epidemiology. H is the recepient of numerous awards including two White House Awards (1992 and 1997) and QEM Giant in Space Mentoring Award (2000). Fred Brauer is a Professor Emeritus of Mathematics at the University id Wisconsin, where he taught from 1960 to 1999, and has also been an Honorary Professor of Mathematics at the University of British Columbia since 1997. |
Contents
Continuous Population Models | 3 |
Discrete Population Models | 51 |
Continuous SingleSpecies Population | 95 |
Introduction and Mathematical Preliminaries | 127 |
Continuous Models for Two Interacting Populations | 171 |
Harvesting in twospecies models | 231 |
Basic Ideas of Mathematical Epidemiology | 275 |
Models for Populations with Age Structure | 339 |
Epilogue | 371 |
A Answers to Selected Exercises | 375 |
Other editions - View all
Mathematical Models in Population Biology and Epidemiology Fred Brauer,Carlos Castillo-Chavez Limited preview - 2013 |
Mathematical Models in Population Biology and Epidemiology Fred Brauer,Carlos Castillo-Chavez Limited preview - 2011 |
Mathematical Models in Population Biology and Epidemiology Fred Brauer,Carlos Castillo-Chavez No preview available - 2010 |
Common terms and phrases
analysis approach approximately assume assumption asymptotically stable average becomes behavior biological birth called capita carrying Chapter characteristic equation close coexistence competition condition consider constant continuous corresponding curve death decreases define delay denotes depends describe determine difference equation differential equation disease distribution dynamics effect endemic epidemic equilibrium estimate example Exercises extinction fact Figure Find fixed function given gives growth rate harvesting immunity increases individuals infective initial introduced isocline limit linear logistic mathematical matrix maximum mean negative observed obtain orbit origin parameters period population population size positive possible predator prey problem Question reduces region reproductive require result roots saddle point satisfy Show simple single solution solve species tend Theorem tion unit unstable variables yield zero
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Page xiv - We have received much support and encouragement in the preparation of this book. In particular we would like to thank...