Mathematical Tools for Understanding
Infectious Disease Dynamics
PRINCETON SERIES
IN THEORETICAL AND COMPUTATIONAL BIOLOGY
Series Editor, Simon A. Levin
Mathematical Tools for Understanding Infectious Disease Dynamics,
by Odo Diekmann, Hans Heesterbeek, and Tom Britton
The Calculus of Selfishness,
by Karl Sigmund
The Geographic Spread of Infectious Diseases: Models and Applications,
by Lisa Sattenspiel with contributions from Alun Lloyd
Theories of Population Variation in Genes and Genomes,
by Freddy Bugge Christiansen
Analysis of Evolutionary Processes,
by Fabio Dercole and Sergio Rinaldi
Mathematics in Population Biology,
by Horst R. Thieme
Individual-based Modeling and Ecology,
by Volker Grimm and Steven F. Railsback
Mathematical Tools for Understanding
Infectious Disease Dynamics
Odo Diekmann, Hans Heesterbeek, and
Tom Britton
PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD
c 2013 by Princeton University Press
Copyright Published by Princeton University Press
41 William Street, Princeton, New Jersey 08540
In the United Kingdom: Princeton University Press
6 Oxford Street, Woodstock, Oxfordshire, OX20 1TW
All Rights Reserved
Library of Congress Cataloging-in-Publication Data
Diekmann, O.
Mathematical tools for understanding infectious disease dynamics / Odo Diekmann,
Hans Heesterbeek, and Tom Britton.
p. cm. – (Princeton series in theoretical and computational biology)
Includes bibliographical references and index.
ISBN 978-0-691-15539-5 (hardback)
1. Epidemiology–Mathematical models–Congresses. 2. Epidemiology–Mathematical
models. 3. Communicable diseases–Mathematical models. I. Heesterbeek, Hans, 1960II. Britton, Tom. III. Title.
RA652.2.M3D54 2013
614.4–dc23
2012012058
British Library Cataloging-in-Publication Data is available
This book has been composed in LATEX
The publisher would like to acknowledge the authors of this volume for providing the
camera-ready copy from which this book was printed.
Printed on acid-free paper. ∞
press.princeton.edu
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
I simply wish that, in a matter which so closely concerns the well-being of
the human race, no decision shall be made without all knowledge which a
little analysis and calculation can provide.
Daniel Bernoulli, 1760, on smallpox inoculation
As a matter of fact all epidemiology, concerned as it is with variation of
disease from time to time or from place to place, must be considered
mathematically (. . .) and the mathematical method of treatment is really
nothing but the application of careful reasoning to the problems at hand.
Sir Ronald Ross, 1911, The Prevention of Malaria
We shall end by establishing a new science. But first let you and me unlock
the door and then anybody can go in who likes.
Sir Ronald Ross in a letter to A.G. McKendrick, 1911
This page intentionally left blank