Mathematical Tools for Understanding Infectious Disease Dynamics ：Mathematical Tools for Understanding Infectious Disease Dynamics ( Princeton Series in Theoretical and Computational Biology )

Publication subTitle ：Mathematical Tools for Understanding Infectious Disease Dynamics

Publication series ：Princeton Series in Theoretical and Computational Biology

Author： Diekmann Odo;Heesterbeek Hans;Britton Tom

Publisher： Princeton University Press‎

Publication year： 2012

E-ISBN: 9781400845620

P-ISBN(Paperback): 9780691155395

Subject： R181 Epidemiology and the basic theory and method

Keyword：普通生物学,内科学,数理科学和化学

Language： ENG

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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 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

Chapter

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

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