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Mathematical Tools for Understanding Infectious Disease Dynamics

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ISBN-10: 0691155399

ISBN-13: 9780691155395

Edition: 2013

Authors: Odo Diekmann, Hans Heesterbeek, Tom Britton

List price: $120.00
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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 Dynamicsfully 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…    
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Book details

List price: $120.00
Copyright year: 2013
Publisher: Oxford University Press, Incorporated
Publication date: 11/18/2012
Binding: Hardcover
Pages: 520
Size: 0.10" wide x 0.10" long x 0.10" tall
Weight: 2.552
Language: English

H�l�ne Landemore is assistant professor of political science at Yale University. She is the author of "Hume: Probability and Reasonable Choice".

Preface
A brief outline of the book
The bare bones: Basic issues in the simplest context
The epidemic in a closed population
The questions (and the underlying assumptions)
Initial growth
The final size
The epidemic in a closed population: summary
Heterogeneity: The art of averaging
Differences in infectivity
Differences in infectivity and susceptibility
The pitfall of overlooking dependence
Heterogeneity: a preliminary conclusion
Stochastic modeling: The impact of chance
The prototype stochastic epidemic model
Two special cases
Initial phase of the stochastic epidemic
Approximation of the main part of the epidemic
Approximation of the final size
The duration of the epidemic
Stochastic modeling: summary
Dynamics at the demographic time scale
Repeated outbreaks versus persistence
Fluctuations around the endemic steady state
Vaccination
Regulation of host populations
Tools for evolutionary contemplation
Markov chains: models of infection in the ICU
Time to extinction and critical community size
Beyond a single outbreak: summary
Inference, or how to deduce conclusions from data
Introduction
Maximum likelihood estimation
An example of estimation: the ICU model
The prototype stochastic epidemic model
ML-estimation of � and � in the ICU model
The challenge of reality: summary
Structured populations
The concept of state
i-states
p-states
Recapitulation, problem formulation and outlook
The basic reproduction number
The definition of R<sub>0</sub>
NGM for compartmental systems
General h-state
Conditions that simplify the computation of R<sub>0</sub>
Sub-models for the kernel
Sensitivity analysis of R<sub>0</sub>
Extended example: two diseases
Pair formation models
Invasion under periodic environmental conditions
Targeted control
Summary
Other indicators of severity
The probability of a major outbreak
The intrinsic growth rate
A brief look at final size and endemic level
Simplifications under separable mixing
Age structure
Demography
Contacts
The next-generation operator
Interval decomposition
The endemic steady state
Vaccination
Spatial spread
Posing the problem
Warming up: the linear diffusion equation
Verbal reflections suggesting robustness
Linear structured population models
The nonlinear situation
Summary: the speed of propagation
Addendum on local finiteness
Macroparasites
Introduction
Counting parasite load
The calculation of R<sub>0</sub> for life cycles
A 'pathological' model
What is contact?
Introduction
Contact duration
Consistency conditions
Effects of subdivision
Stochastic final size and multi-level mixing
Network models (an idiosyncratic view)
A primer on pair approximation
Case studies on inference
Estimators of R<sub>0</sub> derived from mechanistic models
Introduction
Final size and age-structured data
Estimating R<sub>0</sub> from a transmission experiment
Estimators based on the intrinsic growth rate
Data-driven modeling of hospital infections
Introduction
The longitudinal surveillance data
The Markov chain bookkeeping framework
The forward process
The backward process
Looking both ways
A brief guide to computer intensive statistics
Inference using simple epidemic models
Inference using 'complicated' epidemic models
Bayesian statistics
Markov chain Monte Carlo methodology
Large simulation studies
Elaborations
Elaborations for Part I
Elaborations for Chapter 1
Elaborations for Chapter 2
Elaborations for Chapter 3
Elaborations for Chapter 4
Elaborations for Chapter 5
Elaborations for Part II
Elaborations for Chapter 7
Elaborations for Chapter 8
Elaborations for Chapter 9
Elaborations for Chapter 10
Elaborations for Chapter 11
Elaborations for Chapter 12
Elaborations for Part III
Elaborations for Chapter 13
Elaborations for Chapter 15
Bibliography
Index