The Role of Mathematical Models in Explaining Recurrent Outbreaks of Infectious Childhood Diseases
Infectious childhood diseases such as measles are characterized by recurrent outbreaks. Mathematicians have long used models in an effort to better understand and predict these recurrent outbreak patterns. This paper summarizes and comments upon those eff
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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 back to the smallpox model of Daniel Bernoulli in 1760. Much of the basic theory was developed between 1900 and 1935, and there has been steady progress since that time. More recently, models to evaluate the effect of control measures have been used to assist in the formulation of policy decisions, notably for the foot and mouth disease outbreak in Great Britain in 2001. The SARS (Severe Acute Respiratory Syndrome) epidemic of 2002–2003 aroused great interest in the use of mathematical models to predict the course of an infectious disease and to compare the effects of different control strategies. This revived interest has been reinforced by the current threat of an influenza pandemic. Mathematical epidemiology differs from most sciences as it does not lend itself to experimental validation of models. Experiments are usually impossible and would probably be unethical. This gives great importance to mathematical models as a possible tool
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