Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downloaded at the web site of the Centre for Disease Modeling (www.cdm.yorku.ca ).
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris Editors Mathematical Biosciences Subseries: P.K. Maini, Oxford
1945
Fred Brauer · Pauline van den Driessche Jianhong Wu (Eds.)
Mathematical Epidemiology With Contributions by: L.J.S. Allen · C.T. Bauch · C. Castillo-Chavez · D.J.D. Earn Z. Feng · M.A. Lewis · J. Li · M. Martcheva · M. Nu˜no J. Watmough · M.J. Wonham · P. Yan
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Editors Fred Brauer
Jianhong Wu
Department of Mathematics University of British Columbia Vancouver, B.C. V6T 1Z2, Canada
[email protected]
Center for Disease Modeling Department of Mathematics and Statistics York University Toronto, Ontario M3J 1P3, Canada
[email protected]
Pauline van den Driessche Department of Mathematics and Statistics University of Victoria PO BOX 3060 STN CSC Victoria, B.C. V8W 3R4, Canada
[email protected]
ISBN: 978-3-540-78910-9 DOI: 10.1007/978-3-540-78911-6
e-ISBN: 978-3-540-78911-6
Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2008923889 Mathematics Subject Classification (2000): 92D30, 92D25, 34D05, 60J80, 60G05 c 2008 Springer-Verlag Berlin Heidelberg ° This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg The artwork on the cover page was designed by Ping Yan Printed on acid-free paper 987654321 springer.com
Preface
Mathematical epidemiology has a long history, going