عنوان

Quantitative methods for investigating infectious disease outbreaks /

3030219232

3030219240

3030219259

9783030219239

9783030219246

9783030219253

3030219224

9783030219222

Quantitative methods for investigating infectious disease outbreaks /

[Book]

Ping Yan, Gerardo Chowell.

Cham :

Springer,

[2019]

1 online resource (xiii, 354 pages) :

illustrations (some color)

Texts in applied mathematics,

volume 70

0939-2475 ;

Intro; Preface; Contents; 1 Introduction; 1.1 The Motivation; 1.2 Structure of the Book with Brief Summary; 2 Shapes of Hazard Functions and Lifetime Distributions; 2.1 Definitions and the Scale Parameter; 2.1.1 The Hazard Function, the Distribution Functions, and Some Commonly Used Summary Measures; 2.1.2 The Scale Parameter; 2.2 The Shapes of Hazard Functions; 2.2.1 The Constant Hazard Function and the Exponential Distribution; 2.2.2 Monotonic Hazard Functions Without Upper Limit; 2.2.3 Hazard Functions that Converge to a Positive Constant as x→∞; The Gamma Distribution

2.3.2 Some Highly Skewed, Heavy Tailed DistributionsThe Pareto Distributions; 2.4 The Laplace Transform for Life Distributions; 2.4.1 Laplace Transform of the Sum of Two Independent Random Variables; 2.4.2 Moment Generating Property; 2.4.3 As a Probability Comparing X Against an Exponentially Distributed Lifetime Y; 2.4.4 Laplace Transform as a Survival Function; 2.5 Comparing Two Lifetimes X1 and X2; 2.5.1 Comparing Magnitudes; Stochastic and Hazard Rate Ordering of Lifetimes; 2.5.2 Comparing Variabilities; A General Description of Variability Is Based on ``Majorization''

3.2 Random Count Distributions as Generated by Stochastic Disease Transmission Models3.2.1 Mixture of Poisson Distributions and Processes; The Negative Binomial Distribution as a Mixed-Poisson Distribution; Other Mixed-Poisson Distributions; 3.2.2 Highly Skewed Data: Proneness, Contagion, or Spells?; 3.3 General Formulation of a Counting Process; 3.3.1 Review of Some of the Counting Processes that Have Been Mentioned Earlier; The Time-Homogeneous Poisson Process Given by Definition 11; Counting Processes with the Negative Binomial Distribution as the Marginal Distribution for Count Numbers

The Inverse-Gaussian Distribution: Non-monotone and Converge to a Positive Constant as x→∞2.2.4 Two Empirical Distributions for Disease Progression Characterized by Non-monotone Hazard Functions; The Log-Normal Distribution as a Model for the Incubation Period; The Log-Logistic Distribution; 2.2.5 Parametric Lifetime Distributions with More than Two Parameters; 2.3 The Residual Life Distribution and the Tail Property; 2.3.1 The Residual Life Distribution as Uniquely Determined by the Hazard Function; The Shape of Hazard Functions and the Tail Property

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This book provides a systematic treatment of the mathematical underpinnings of work in the theory of outbreak dynamics and their control, covering balanced perspectives between theory and practice including new material on contemporary topics in the field of infectious disease modelling. Specifically, it presents a unified mathematical framework linked to the distribution theory of non-negative random variables; the many examples used in the text, are introduced and discussed in light of theoretical perspectives. The book is organized into 9 chapters: The first motivates the presentation of the material on subsequent chapters; Chapter 2-3 provides a review of basic concepts of probability and statistical models for the distributions of continuous lifetime data and the distributions of random counts and counting processes, which are linked to phenomenological models. Chapters 4 focuses on dynamic behaviors of a disease outbreak during the initial phase while Chapters 5-6 broadly cover compartment models to investigate the consequences of epidemics as the outbreak moves beyond the initial phase. Chapter 7 provides a transition between mostly theoretical topics in earlier chapters and Chapters 8 and 9 where the focus is on the data generating processes and statistical issues of fitting models to data as well as specific mathematical epidemic modeling applications, respectively. This book is aimed at a wide audience ranging from graduate students to established scientists from quantitatively-oriented fields of epidemiology, mathematics and statistics. The numerous examples and illustrations make understanding of the mathematics of disease transmission and control accessible. Furthermore, the examples and exercises, make the book suitable for motivated students in applied mathematics, either through a lecture course, or through self-study. This text could be used in graduate schools or special summer schools covering research problems in mathematical biology.

Springer Nature

com.springer.onix.9783030219239

Quantitative methods for investigating infectious disease outbreaks.

9783030219222

Epidemiology-- Statistical methods.

Epidemiology-- Statistical methods.

MAT003000

PBW

PBW

Yan, Ping, (Of Public Health Agency of Canada)

Chowell, Gerardo

20200823092248.0

pn

[Book]

Y