Catalogue


Mathematical tools for understanding infectious diseases dynamics [electronic resource] /
Odo Diekmann, Hans Heesterbeek, and Tom Britton.
imprint
Princeton : Princeton University Press, c2013.
description
xiv, 502 p. ; 26 cm.
ISBN
9780691155395 (hardback)
format(s)
Book
More Details
author
imprint
Princeton : Princeton University Press, c2013.
isbn
9780691155395 (hardback)
restrictions
Licensed for access by U. of T. users.
catalogue key
8843333
 
Includes bibliographical references (p. [491]-496) and index.
A Look Inside
About the Author
Author Affiliation
Odo Diekmann is professor of applied analysis at Utrecht University. Hans Heesterbeek is professor of theoretical epidemiology at Utrecht University. Tom Britton is professor of mathematical statistics at Stockholm University.
Excerpts
Flap Copy
"This landmark volume describes for readers how one should view the theoretical side of mathematical epidemiology as a whole. A particularly important need is for a book that integrates deterministic and stochastic epidemiological models, and this is the first one that does this. I know of no better overview of the subject. It belongs on the shelf of everyone working in mathematical epidemiology."-- Fred Brauer, University of British Columbia
Flap Copy
"This landmark volume describes for readers how one should view the theoretical side of mathematical epidemiology as a whole. A particularly important need is for a book that integrates deterministic and stochastic epidemiological models, and this is the first one that does this. I know of no better overview of the subject. It belongs on the shelf of everyone working in mathematical epidemiology."--Fred Brauer, University of British Columbia
Summaries
Main Description
Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual and population levels. This book gives readers the necessary skills to correctly formulate and analyze mathematical models in infectious disease epidemiology, and is the first treatment of the subject to integrate deterministic and stochastic models and methods. Mathematical Tools for Understanding Infectious Disease Dynamics fully explains how to translate biological assumptions into mathematics to construct useful and consistent models, and how to use the biological interpretation and mathematical reasoning to analyze these models. It shows how to relate models to data through statistical inference, and how to gain important insights into infectious disease dynamics by translating mathematical results back to biology. This comprehensive and accessible book also features numerous detailed exercises throughout; full elaborations to all exercises are provided. Covers the latest research in mathematical modeling of infectious disease epidemiology Integrates deterministic and stochastic approaches Teaches skills in model construction, analysis, inference, and interpretation Features numerous exercises and their detailed elaborations Motivated by real-world applications throughout
Library of Congress Summary
"Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual and population levels. This book gives readers the necessary skills to correctly formulate and analyze mathematical models in infectious disease epidemiology, and is the first treatment of the subject to integrate deterministic and stochastic models and methods. Mathematical Tools for Understanding Infectious Disease Dynamics fully explains how to translate biological assumptions into mathematics to construct useful and consistent models, and how to use the biological interpretation and mathematical reasoning to analyze these models. It shows how to relate models to data through statistical inference, and how to gain important insights into infectious disease dynamics by translating mathematical results back to biology. This comprehensive and accessible book also features numerous detailed exercises throughout; full elaborations to all exercises are provided. Covers the latest research in mathematical modeling of infectious disease epidemiology Integrates deterministic and stochastic approaches Teaches skills in model construction, analysis, inference, and interpretation Features numerous exercises and their detailed elaborations Motivated by real-world applications throughout "--
Bowker Data Service Summary
Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual & population levels. This book gives readers the necessary skills to correctly forumate & analyze mathematical models in infectious disease epidemiology, & is the first treatment of the subject to integrate deterministic & stochastic models & methods.
Table of Contents
Prefacep. xi
A brief outline of the bookp. xii
The bare bones: Basic issues in the simplest contextp. 1
The epidemic in a closed populationp. 3
The questions (and the underlying assumptions)p. 3
Initial growthp. 4
The final sizep. 14
The epidemic in a closed population: summaryp. 28
Heterogeneity: The art of averagingp. 33
Differences in infectivityp. 33
Differences in infectivity and susceptibilityp. 39
The pitfall of overlooking dependencep. 41
Heterogeneity: a preliminary conclusionp. 43
Stochastic modeling: The impact of chancep. 45
The prototype stochastic epidemic modelp. 46
Two special casesp. 48
Initial phase of the stochastic epidemicp. 51
Approximation of the main part of the epidemicp. 58
Approximation of the final sizep. 60
The duration of the epidemicp. 69
Stochastic modeling: summaryp. 71
Dynamics at the demographic time scalep. 73
Repeated outbreaks versus persistencep. 73
Fluctuations around the endemic steady statep. 75
Vaccinationp. 84
Regulation of host populationsp. 87
Tools for evolutionary contemplationp. 91
Markov chains: models of infection in the ICUp. 101
Time to extinction and critical community sizep. 107
Beyond a single outbreak: summaryp. 124
Inference, or how to deduce conclusions from datap. 127
Introductionp. 127
Maximum likelihood estimationp. 127
An example of estimation: the ICU modelp. 130
The prototype stochastic epidemic modelp. 134
ML-estimation of ¿ and ß in the ICU modelp. 146
The challenge of reality: summaryp. 148
Structured populationsp. 151
The concept of statep. 153
i-statesp. 153
p-statesp. 157
Recapitulation, problem formulation and outlookp. 159
The basic reproduction numberp. 161
The definition of R0p. 161
NGM for compartmental systemsp. 166
General h-statep. 173
Conditions that simplify the computation of R0p. 175
Sub-models for the kernelp. 179
Sensitivity analysis of R0p. 181
Extended example: two diseasesp. 183
Pair formation modelsp. 189
Invasion under periodic environmental conditionsp. 192
Targeted controlp. 199
Summaryp. 203
Other indicators of severityp. 205
The probability of a major outbreakp. 205
The intrinsic growth ratep. 212
A brief look at final size and endemic levelp. 219
Simplifications under separable mixingp. 221
Age structurep. 227
Demographyp. 227
Contactsp. 228
The next-generation operatorp. 229
Interval decompositionp. 232
The endemic steady statep. 233
Vaccinationp. 234
Spatial spreadp. 239
Posing the problemp. 239
Warming up: the linear diffusion equationp. 240
Verbal reflections suggesting robustnessp. 242
Linear structured population modelsp. 244
The nonlinear situationp. 246
Summary: the speed of propagationp. 248
Addendum on local finitenessp. 249
Macroparasitesp. 251
Introductionp. 251
Counting parasite loadp. 253
The calculation of R0 for life cyclesp. 260
A 'pathological' modelp. 261
What is contact?p. 265
Introductionp. 265
Contact durationp. 265
Consistency conditionsp. 272
Effects of subdivisionp. 274
Stochastic final size and multi-level mixingp. 278
Network models (an idiosyncratic view)p. 286
A primer on pair approximationp. 302
Case studies on inferencep. 307
Estimators of R0 derived from mechanistic modelsp. 309
Introductionp. 309
Final size and age-structured datap. 311
Estimating R0 from a transmission experimentp. 319
Estimators based on the intrinsic growth ratep. 320
Data-driven modeling of hospital infectionsp. 325
Introductionp. 325
The longitudinal surveillance datap. 326
The Markov chain bookkeeping frameworkp. 327
The forward processp. 329
The backward processp. 333
Looking both waysp. 334
A brief guide to computer intensive statisticsp. 337
Inference using simple epidemic modelsp. 337
Inference using 'complicated' epidemic modelsp. 338
Bayesian statisticsp. 339
Markov chain Monte Carlo methodologyp. 341
Large simulation studiesp. 344
Elaborationsp. 347
Elaborations for Part Ip. 349
Elaborations for Chapter 1p. 349
Elaborations for Chapter 2p. 368
Elaborations for Chapter 3p. 375
Elaborations for Chapter 4p. 380
Elaborations for Chapter 5p. 402
Elaborations for Part IIp. 407
Elaborations for Chapter 7p. 407
Elaborations for Chapter 8p. 432
Elaborations for Chapter 9p. 445
Elaborations for Chapter 10p. 451
Elaborations for Chapter 11p. 455
Elaborations for Chapter 12p. 465
Elaborations for Part IIIp. 483
Elaborations for Chapter 13p. 483
Elaborations for Chapter 15p. 488
Bibliographyp. 491
Indexp. 497
Table of Contents provided by Ingram. All Rights Reserved.

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