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
Author(s): Odo Diekmann; Hans Heesterbeek; Tom Britton
Series: Princeton Series in Theoretical and Computational Biology
Publisher: Princeton University Press
Year: 2013
Language: English
Pages: xiv+502
Cover
Title
Copyright
Contents
Preface
A brief outline of the book
I: The bare bones: Basic issues in the simplest context
1 The epidemic in a closed population
1.1 The questions (and the underlying assumptions)
1.2 Initial growth
1.3 The final size
1.4 The epidemic in a closed population: summary
2 Heterogeneity: The art of averaging
2.1 Differences in infectivity
2.2 Differences in infectivity and susceptibility
2.3 The pitfall of overlooking dependence
2.4 Heterogeneity: a preliminary conclusion
3 Stochastic modeling: The impact of chance
3.1 The prototype stochastic epidemic model
3.2 Two special cases
3.3 Initial phase of the stochastic epidemic
3.4 Approximation of the main part of the epidemic
3.5 Approximation of the final size
3.6 The duration of the epidemic
3.7 Stochastic modeling: summary
4 Dynamics a t the demographic time scale
4.1 Repeated outbreaks versus persistence
4.2 Fluctuations around the endemic steady state
4.3 Vaccination
4.4 Regulation of host populations
4.5 Tools for evolutionary contemplation
4.6 Markov chains: models of infection in the ICU
4.7 Time to extinction and critical community size
4.8 Beyond a single outbreak: summary
5 Inference, or how to deduce conclusions from data
5.1 Introduction
5.2 Maximum likelihood estimation
5.3 An example of estimation: the ICU model
5.4 The prototype stochastic epidemic model
5.5 ML-estimation of and in the ICU model
5.6 The challenge of reality: summary
II: Structured populations
6 The concept of state
6.1 i-states
6.2 p-states
6.3 Recapitulation, problem formulation and outlook
7 The basic reproduction number
7.1 The definition of R[sub(0)]
7.2 NGM for compartmental systems
7.3 General h-state
7.4 Conditions that simplify the computation of R[sub(0)]
7.5 Sub-models for the kernel
7.6 Sensitivity analysis of R[sub(0)]
7.7 Extended example: two diseases
7.8 Pair formation models
7.9 Invasion under periodic environmental conditions
7.10 Targeted control
7.11 Summary
8 Other indicators of severity
8.1 The probability of a major outbreak
8.2 The intrinsic growth rate
8.3 A brief look at final size and endemic level
8.4 Simplifications under separable mixing
9 Age structure
9.1 Demography
9.2 Contacts
9.3 The next-generation operator
9.4 Interval decomposition
9.5 The endemic steady state
9.6 Vaccination
10 Spatial spread
10.1 Posing the problem
10.2 Warming up: the linear diffusion equation
10.3 Verbal reffections suggesting robustness
10.4 Linear structured population models
10.5 The nonlinear situation
10.6 Summary: the speed of propagation
10.7 Addendum on local finiteness
11 Macroparasites
11.1 Introduction
11.2 Counting parasite load
11.3 The calculation of R[sub(0)] for life cycles
11.4 A 'pathological' model
12 What is contact?
12.1 Introduction
12.2 Contact duration
12.3 Consistency conditions
12.4 Effects of subdivision
12.5 Stochastic final size and multi-level mixing
12.6 Network models (an idiosyncratic view)
12.7 A primer on pair approximation
III: Case studies on inference
13 Estimators of R[sub(0)] derived from mechanistic models
13.1 Introduction
13.2 Final size and age-structured data
13.3 Estimating R[sub(0)] from a transmission experiment
13.4 Estimators based on the intrinsic growth rate
14 Data-driven modeling of hospital infections
14.1 Introduction
14.2 The longitudinal surveillance data
14.3 The Markov chain bookkeeping framework
14.4 The forward process
14.5 The backward process
14.6 Looking both ways
15 A brief guide to computer intensive statistics
15.1 Inference using simple epidemic models
15.2 Inference using 'complicated' epidemic models
15.3 Bayesian statistics
15.4 Markov chain Monte Carlo methodology
15.5 Large simulation studies
IV: Elaborations
16 Elaborations for Part I
16.1 Elaborations for Chapter 1
16.2 Elaborations for Chapter 2
16.3 Elaborations for Chapter 3
16.4 Elaborations for Chapter 4
16.5 Elaborations for Chapter 5
17 Elaborations for Part II
17.1 Elaborations for Chapter 7
17.2 Elaborations for Chapter 8
17.3 Elaborations for Chapter 9
17.4 Elaborations for Chapter 10
17.5 Elaborations for Chapter 11
17.6 Elaborations for Chapter 12
18 Elaborations for Part III
18.1 Elaborations for Chapter 13
18.2 Elaborations for Chapter 15
Bibliography
Index
