Mathematical Tools for Understanding Infectious Disease Dynamics:

Overview

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 ...

See more details below
Other sellers (Hardcover)
  • All (3) from $63.37   
  • New (2) from $63.37   
  • Used (1) from $65.98   
Mathematical Tools for Understanding Infectious Disease Dynamics

Available on NOOK devices and apps  
  • NOOK Devices
  • Samsung Galaxy Tab 4 NOOK 7.0
  • Samsung Galaxy Tab 4 NOOK 10.1
  • NOOK HD Tablet
  • NOOK HD+ Tablet
  • NOOK eReaders
  • NOOK Color
  • NOOK Tablet
  • Tablet/Phone
  • NOOK for Windows 8 Tablet
  • NOOK for iOS
  • NOOK for Android
  • NOOK Kids for iPad
  • PC/Mac
  • NOOK for Windows 8
  • NOOK for PC
  • NOOK for Mac

Want a NOOK? Explore Now

NOOK Book (eBook - Course Book)
$51.49
BN.com price
(Save 42%)$90.00 List Price

Overview

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
Read More Show Less

Editorial Reviews

From the Publisher
"A much needed book. Mathematical Tools for Understanding Infectious Disease Dynamics is a welcome addition to the current literature and will hopefully help to unify the many different views in the field."—Laura Matrajt, SIAM Review

"The overtly pedagogical features of this text make it an outstanding choice for someone trying to learn the basic tools of the trade. The mathematician who makes a serious study of this text will be in an excellent position to work fruitfully with biologists or epidemiologists on either theoretical or data-driven problems of disease transmission."—Carl A. Toews, Mathematical Reviews

Read More Show Less

Product Details

Meet the Author

Odo Diekmann is professor of mathematical analysis at Utrecht University. Hans Heesterbeek is professor of theoretical epidemiology at Utrecht University. Tom Britton is professor of mathematical statistics at Stockholm University.

Read More Show Less

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

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)