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Maia Martcheva

An Introduction to Mathematical Epidemiology

Texts in Applied Mathematics Volume 61

Editors-in-chief: Stuart Antman, College Park, MD, USA Leslie Greengard, New York, NY, USA Philip Holmes, Princeton, NJ, USA

Series Editors: James Keener, Salt Lake City UT, USA Robert Kohn, New York NY, USA Paul Newton, Los Angeles CA, USA Charles Peskin, New York NY, USA Robert Pego, Pittsburgh PA, USA Lenya Ryzhik, Stanford CA, USA Amit Singer, Princeton NJ, USA Angela Stevens, M¨unster, Germany Andrew Stuart, Coventry, UK Thomas Witelski, Durham NC, USA

More information about this series at http://www.springer.com/series/1214

Maia Martcheva

An Introduction to Mathematical Epidemiology

123

Maia Martcheva Department of Mathematics University of Florida Gainesville, FL

ISSN 0939-2475 Texts in Applied Mathematics ISBN 978-1-4899-7611-6 DOI 10.1007/978-1-4899-7612-3

ISSN 2196-9949 (electronic) ISBN 978-1-4899-7612-3 (eBook)

Library of Congress Control Number: 2015947259 Mathematics Subject Classification (2010): 92D30, 34D20, 35F50 Springer New York Heidelberg Dordrecht London © Springer Science+Business Media New York 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Science+Business Media LLC New York is part of Springer Science+Business Media (www. springer.com)

Preface

This book is an introductory text to the methods and tools that are nowadays widely used and accepted in the mathematical epidemiology literature. It is intended to start from a beginner level and accelerate to research level. It targets upper undergraduate mathematics students, and mathematics, physics, and engineering graduate students. The book will also be suitable for mathematics researchers who wish to build a background and advance to research level in mathematical epidemiology. The book is expected to be useful to mathematical epidemiologists as a reference text. Chapter 1 discusses some historical aspects of modeling infectious diseases. It also