Table Of ContentSattenspielfinal-feb27 February 27, 2009
The Geographic Spread of
Infectious Diseases
Sattenspielfinal-feb27 February 27, 2009
PRINCETONSERIESINTHEORETICALANDCOMPUTATIONAL
BIOLOGY
Series Editor, Simon A. Levin
The Geographic Spread of Infectious Diseases: Models and Applica-
tions, by Lisa Sattenspiel with contributions from Alun Lloyd
Theories of Population Variation in Genes and Genomes, by Freddy
Bugge Christiansen
AnalysisofEvolutionaryProcesses,byFabioDercoleandSergioRinaldi
Mathematics in Population Biology, by Horst R. Thieme
Individual-based Modeling and Ecology, by Volker Grimm and Steven
F. Railsback
Sattenspielfinal-feb27 February 27, 2009
The Geographic Spread of
Infectious Diseases
Models and Applications
Lisa Sattenspiel
with contributions from Alun Lloyd
PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD
Sattenspielfinal-feb27 February 27, 2009
Copyright (cid:13)c 2009 by Princeton University Press
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
Sattenspiel, Lisa.
Thegeographicspreadofinfectiousdiseases: modelsandapplications
/ Lisa Sattenspiel with contributions from Alun Lloyd.
p. cm. (Princeton series in theoretical and computational biology)
Includes bibliographical references and index.
ISBN 978-0-691-12132-1 (hardcover : alk. paper) 1. Communicable
diseases–Epidemiology–Mathematical models. I. Lloyd, Alun, 1970- II.
Title. III. Series.
[DNLM: 1. Communicable Diseases–epidemiology. 2. Communicable
Diseases transmission. 3. Disease Outbreaks–statistics & numerical
data. 4. Epidemiologic Methods. 5. Models, Theoretical. WA 110
S253g 2009]
RA643.S39 2009
614.401’5118–dc22 2008038171
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
Sattenspielfinal-feb27 February 27, 2009
Dedicated to Steven, Matthew, Elisabeth, and Stephanie who make
my life a constant joy and to Franki and Ed (in spirit) who
ultimately made this all possible. Love always — Lisa
Sattenspielfinal-feb27 February 27, 2009
The formidable task of developing models for endemic disease
maybecomparedtobuildingahouseinahurry. Practicalwork-
ers insist on building a complete house, and are not too worried
thatitmayneedreplacinglater. Theoreticiansinsistonbuilding
reliablefoundationsandarenottooworriedifthehouseisnever
finished. Both points of view have their merits, and ideally we
need to combine these.
— Mollison and Kuulasmaa, Spatial Epidemic Models
Sattenspielfinal-feb27 February 27, 2009
Contents
Preface ix
Chapter 1. Introduction 1
1.1 Mathematical Models and the Geographic Spread of Epidemics 5
1.2 Structure of this Book 11
Chapter 2. The Art of Epidemic Modeling: Concepts and Basic Structures 12
2.1 Essential Biological and Epidemiological Concepts 12
2.2 The Cornerstone of Many Epidemic Models — the SIR Model 16
2.3 Demography and Epidemic Models 23
2.4 More Complex Models 25
2.5 The Basic Reproductive Number Revisited 53
Chapter 3. Modeling the Geographic Spread of Influenza Epidemics 58
3.1 A Brief Overview of the Biology of Influenza 58
3.2 Population-based Influenza Models 61
3.3 Individual-based Influenza Models 77
3.4 So What Kind of Model Should One Use to Study Influenza
Transmission? 84
Chapter 4. Modeling Geographic Spread I: Population-based Approaches 86
4.1 Spatial Structure and Disease Transmission: Basic Themes 86
4.2 Spatial Modeling Frameworks 89
4.3 Metapopulation Models 90
4.4 Spatially Continuous Models 102
Chapter 5. Spatial Heterogeneity and Endemicity: The Case of Measles 117
5.1 The Persistence and Long-term Cycling of Measles 122
5.2 SpatialHeterogeneity,Synchrony,andtheSpatialSpreadofMeasles 125
Chapter 6. Modeling Geographic Spread II: Individual-based Approaches 134
6.1 Historical Underpinnings of the Use of Networks in Epidemiology 137
6.2 The Nature of Networks 140
6.3 The Language of Network Analysis 142
6.4 Major Classes of Networks 150
6.5 The Influence of Networks on the Dynamics of Epidemic Spread 159
6.6 Theoretical Analysis of Network Models 162
Sattenspielfinal-feb27 February 27, 2009
viii CONTENTS
6.7 The Basic Reproductive Number in Network Models 168
6.8 Infection Control on Networks 171
6.9 Why Aren’t There More Applications of Network Models for
Spatial Spread? 173
Chapter 7. Spatial Models and the Control of Foot-and-Mouth Disease 176
7.1 Modeling the Geographic Spread of FMD 180
7.2 The Official Response to the Epidemic and Its Aftermath 185
Chapter 8. Maps, Projections, and GIS: Geographers’ Approaches 191
8.1 Mapping Methods 191
8.2 Identifying Patterns of Disease Diffusion 195
8.3 Epidemic Projections 204
8.4 Detection of Disease Clustering 208
8.5 New and Potential Directions 211
Chapter 9. Revisiting SARS and Looking to the Future 215
9.1 DidMathematicalModelingHelptoStopthe2003SARSEpidemic? 215
9.2 Modeling the Geographic Spread of Past, Present, and Future
Infectious Disease Epidemics: Lessons and Advice 223
Bibliography 237
Index 279
Sattenspielfinal-feb27 February 27, 2009
Preface
Inearly2002,withthehelpofAlunLloyd,StevenTanner,BenBolker,
and Tony Sun, I took on the task of creating a state-of-the-art review
ofmodelsforthegeographicspreadofhumaninfectiousdiseases, with
particularattentiontothosemodelsthatwereusedforpracticalstud-
iesinvolvinglargeepidemiologicaldatasets. Whatwasoriginallycon-
ceived of as a substantive review paper (50 pages or so) turned into
a 250-page report. That report formed the nucleus for the present
book, which has been updated and reorganized to reflect a recent
astronomical rise in interest in modeling the geographic spread of in-
fectious diseases. Credit for the core of chapters 2, 4, and 6 must
go to Alun Lloyd; I mostly provided abundant critiques and revisions
to supplement his clear exposition of the technical details related to
modeling geographic spread. The majority of the rest of the book is
primarily my work, although many of my ideas have been influenced
by my numerous discussions with Alun about spatial modeling and
its applications.
The goal of this book is to introduce how mathematical and com-
puter models are used to study the geographic spread of infectious
diseases. It is not intended to be a textbook from which one can
learn all the relevant mathematical techniques and theory. Rather,
it is designed to introduce the reader to the large body of work in
this area, to stimulate discussion of the models and applications, and
hopefully to generate enough interest in the field to draw new re-
searchers to the area and help those already working in mathematical
epidemiology to recognize new and interesting problems. The book is
not intended to provide an in-depth analysis and review of all models
that have been developed to study the geographic spread of infectious
diseases. Rather, the focus is on those models that have been used
in applications to actual epidemics, which means, of necessity, that
many high-quality, but theoretically oriented studies are intentionally
omitted from discussion.
The primary audience is readers who have background in ecology,
epidemiology,humanbiology,andrelatednatural,physical,andsocial
sciences, and who have sufficient mathematical background to tackle
