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Mathematical Tools for Understanding Infectious Disease Dynamics
Odo Diekmann, Hans Heesterbeek & Tom Britton

Book Description | Reviews
Preface [in PDF format]

TABLE OF CONTENTS:

Preface xi
A brief outline of the book xii

I The bare bones: Basic issues in the simplest context 1

  • 1 The epidemic in a closed population 3
    • 1.1 The questions (and the underlying assumptions) 3
    • 1.2 Initial growth 4
    • 1.3 The final size 14
    • 1.4 The epidemic in a closed population: summary 28
  • 2 Heterogeneity: The art of averaging 33
    • 2.1 Differences in infectivity 33
    • 2.2 Differences in infectivity and susceptibility 39
    • 2.3 The pitfall of overlooking dependence 41
    • 2.4 Heterogeneity: a preliminary conclusion 43
  • 3 Stochastic modeling: The impact of chance 45
    • 3.1 The prototype stochastic epidemic model 46
    • 3.2 Two special cases 48
    • 3.3 Initial phase of the stochastic epidemic 51
    • 3.4 Approximation of the main part of the epidemic 58
    • 3.5 Approximation of the final size 60
    • 3.6 The duration of the epidemic 69
    • 3.7 Stochastic modeling: summary 71
  • 4 Dynamics at the demographic time scale 73
    • 4.1 Repeated outbreaks versus persistence 73
    • 4.2 Fluctuations around the endemic steady state 75
    • 4.3 Vaccination 84
    • 4.4 Regulation of host populations 87
    • 4.5 Tools for evolutionary contemplation 91
    • 4.6 Markov chains: models of infection in the ICU 101
    • 4.7 Time to extinction and critical community size 107
    • 4.8 Beyond a single outbreak: summary 124
  • 5 Inference, or how to deduce conclusions from data 127
    • 5.1 Introduction 127
    • 5.2 Maximum likelihood estimation 127
    • 5.3 An example of estimation: the ICU model 130
    • 5.4 The prototype stochastic epidemic model 134
    • 5.5 ML-estimation of α and β in the ICU model 146
    • 5.6 The challenge of reality: summary 148

II Structured populations 151

  • 6 The concept of state 153
    • 6.1 i-states 153
    • 6.2 p-states 157
    • 6.3 Recapitulation, problem formulation and outlook 159
  • 7 The basic reproduction number 161
    • 7.1 The definition of R0 161
    • 7.2 NGM for compartmental systems 166
    • 7.3 General h-state 173
    • 7.4 Conditions that simplify the computation of R0 175
    • 7.5 Sub-models for the kernel 179
    • 7.6 Sensitivity analysis of R0 181
    • 7.7 Extended example: two diseases 183
    • 7.8 Pair formation models 189
    • 7.9 Invasion under periodic environmental conditions 192
    • 7.10 Targeted control 199
    • 7.11 Summary 203
  • 8 Other indicators of severity 205
    • 8.1 The probability of a major outbreak 205
    • 8.2 The intrinsic growth rate 212
    • 8.3 A brief look at final size and endemic level 219
    • 8.4 Simplifications under separable mixing 221
  • 9 Age structure 227
    • 9.1 Demography 227
    • 9.2 Contacts 228
    • 9.3 The next-generation operator 229
    • 9.4 Interval decomposition 232
    • 9.5 The endemic steady state 233
    • 9.6 Vaccination 234
  • 10 Spatial spread 239
    • 10.1 Posing the problem 239
    • 10.2 Warming up: the linear diffusion equation 240
    • 10.3 Verbal reflections suggesting robustness 242
    • 10.4 Linear structured population models 244
    • 10.5 The nonlinear situation 246
    • 10.6 Summary: the speed of propagation 248
    • 10.7 Addendum on local finiteness 249
  • 11 Macroparasites 251
    • 11.1 Introduction 251
    • 11.2 Counting parasite load 253
    • 11.3 The calculation of R0 for life cycles 260
    • 11.4 A 'pathological' model 261
  • 12 What is contact? 265
    • 12.1 Introduction 265
    • 12.2 Contact duration 265
    • 12.3 Consistency conditions 272
    • 12.4 Effects of subdivision 274
    • 12.5 Stochastic final size and multi-level mixing 278
    • 12.6 Network models (an idiosyncratic view) 286
    • 12.7 A primer on pair approximation 302

III Case studies on inference 307

  • 13 Estimators of R0 derived from mechanistic models 309
    • 13.1 Introduction 309
    • 13.2 Final size and age-structured data 311
    • 13.3 Estimating R0 from a transmission experiment 319
    • 13.4 Estimators based on the intrinsic growth rate 320
  • 14 Data-driven modeling of hospital infections 325
    • 14.1 Introduction 325
    • 14.2 The longitudinal surveillance data 326
    • 14.3 The Markov chain bookkeeping framework 327
    • 14.4 The forward process 329
    • 14.5 The backward process 333
    • 14.6 Looking both ways 334
  • 15 A brief guide to computer intensive statistics 337
    • 15.1 Inference using simple epidemic models 337
    • 15.2 Inference using 'complicated' epidemic models 338
    • 15.3 Bayesian statistics 339
    • 15.4 Markov chain Monte Carlo methodology 341
    • 15.5 Large simulation studies 344

IV Elaborations 347

  • 16 Elaborations for Part I 349
    • 16.1 Elaborations for Chapter 1 349
    • 16.2 Elaborations for Chapter 2 368
    • 16.3 Elaborations for Chapter 3 375
    • 16.4 Elaborations for Chapter 4 380
    • 16.5 Elaborations for Chapter 5 402
  • 17 Elaborations for Part II 407
    • 17.1 Elaborations for Chapter 7 407
    • 17.2 Elaborations for Chapter 8 432
    • 17.3 Elaborations for Chapter 9 445
    • 17.4 Elaborations for Chapter 10 451
    • 17.5 Elaborations for Chapter 11 455
    • 17.6 Elaborations for Chapter 12 465
  • 18 Elaborations for Part III 483
    • 18.1 Elaborations for Chapter 13 483
    • 18.2 Elaborations for Chapter 15 488

Bibliography 491
Index 497

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File created: 4/17/2014

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