Mathematical and Statistical Estimation Approaches in Epidemiology compiles theoretical and practical contributions of experts in the analysis of infectious disease epidemics in a single volume. Recent collections have focused in the analyses and simulation of deterministic and stochastic models whose aim is to identify and rank epidemiological and social mechanisms responsible for disease transmission. The contributions in this volume focus on the connections between models and disease data with emphasis on the application of mathematical and statistical approaches that quantify model and data uncertainty.
The book is aimed at public health experts, applied mathematicians and scientists in the life and social sciences, particularly graduate or advanced undergraduate students, who are interested not only in building and connecting models to data but also in applying and developing methods that quantify uncertainty in the context of infectious diseases. Chowell and Brauer open this volume with an overview of the classical disease transmission models of Kermack-McKendrick including extensions that account for increased levels of epidemiological heterogeneity. Their theoretical tour is followed by the introduction of a simple methodology for the estimation of, the basic reproduction number, R0. The use of this methodology is illustrated, using regional data for 1918–1919 and 1968 influenza pandemics.
This chapter is followed by Greenwood and Gordillo’s introduction to an analogous probabilistic framework. The emphasis is now on the computation of the distribution of the final epidemic size and the quantification of stochastically sustained oscillations. Next, the differences between observable and unobservable events in infectious disease epidemiology and their relationship to rigorous contact tracing and microbiological methodology are discussed in Chapter 3 by Nishiura et al. Furthermore, concepts like “dependent happening” and their role in identifying sources of infectious disease risk or in assessing vaccine efficacy are also discussed. In Chapter 4, Tennenbaum’s engages us in a discussion of modeling perspectives and approaches through his discussion of the meaning of “contact”. He challenges the reader to come up with novel approaches that bring together “ignored” biological and mechanistic aspects of the infection process.
Chapter 5 (Nishiura and Chowell) and Chapter 7 (Bettencourt) focus on real-time assessments of the reproduction number. The exposition is spiced with references to recent epidemic outbreaks. For example, Bettencourt uses his framework to estimate disease epidemiological parameters and to assess the effects of interventions in real time using data from the 2005 outbreak of Marburg hemorrhagic fever in Angola.
In Chapter 8, Burr and colleagues review the theoretical and practical challenges associated with biosurveillance including the detection of disease outbreaks using traditional diagnosed case rates or syndromic surveillance data. In Chapter 6, Lloyd notes that parameter estimates are subject to uncertainty that arise not only from errors (noise) in the data but also from the structure of the model used in the fitting process. In other words, he argues that uncertainty must be evaluated at multiple levels to account for our ignorance or for the balance that each modeler must reach between biological detail and model complexity and objectives. Parameter estimation, Lloyd argues, must include structural sensitivity analyses. The use of historical data in epidemiological research is highlighted in Chapter 9 by Acu˜na-Soto’s contribution.
As he notes epidemiologists are reluctant to consider systematically the possibility of working with historical data albeit, as we have seen in the first Chapter, it is possible to extract valuable information from such data on influenza outbreaks. In fact, we acquired the kind of quantitative knowledge that let us quantify some of the differences between seasonal and pandemic influenza. Acu˜na-Soto’s work1, for example, on the epidemic of 1576 that killed 45% of the entire population of Mexico, highlights but a myriad of new possibilities for which the quantitative methods and approaches highlighted in this book can be put to good use.
Banks and colleagues in Chapter 11 provide a succinct overview of the statistical and computational aspects associated with inverse or parameter estimation problems for deterministic dynamical systems. Their results illustrate the impact that the marriage between statistical theory and applied mathematics is having in the study of infectious diseases while Chapter 10 (Arriola and Hyman) provides a general and thorough introduction to the field of sensitivity and uncertainty analyses, a central piece of any scientific work that is based on modeling.
The challenges and opportunities generated by studies of disease outbreak or disease dynamics in specific contexts are highlighted in the final chapters. Shim and Castillo-Chavez (Chapter 12) evaluate the potential impact that ongoing agedependent vaccination strategies (in the United States and Mexico) are likely to have in reducing the prevalence of severe rotavirus infections. Rios-Doria et al.
(Chapter 13) analyze the spatial and temporal dynamics of rubella in Peru, 1997–2006 via a wavelet time series analysis and other methods. The study is carried out in the context of changing policies that include the introduction of a vaccine and/or increases in vaccination rates. Cintron-Arias and colleagues (Chapter 15) model drinking as a “communicable” disease and, in the process, they highlight a new set of opportunities and possibilities for the applications of the mathematical and statistical approaches used in this volume. The focus here is on the evaluation of the role of relapse (ineffective treatment) on drinking dynamics but as a function of social network heterogeneity.
Contents
List Price: $189.00
The book is aimed at public health experts, applied mathematicians and scientists in the life and social sciences, particularly graduate or advanced undergraduate students, who are interested not only in building and connecting models to data but also in applying and developing methods that quantify uncertainty in the context of infectious diseases. Chowell and Brauer open this volume with an overview of the classical disease transmission models of Kermack-McKendrick including extensions that account for increased levels of epidemiological heterogeneity. Their theoretical tour is followed by the introduction of a simple methodology for the estimation of, the basic reproduction number, R0. The use of this methodology is illustrated, using regional data for 1918–1919 and 1968 influenza pandemics.
This chapter is followed by Greenwood and Gordillo’s introduction to an analogous probabilistic framework. The emphasis is now on the computation of the distribution of the final epidemic size and the quantification of stochastically sustained oscillations. Next, the differences between observable and unobservable events in infectious disease epidemiology and their relationship to rigorous contact tracing and microbiological methodology are discussed in Chapter 3 by Nishiura et al. Furthermore, concepts like “dependent happening” and their role in identifying sources of infectious disease risk or in assessing vaccine efficacy are also discussed. In Chapter 4, Tennenbaum’s engages us in a discussion of modeling perspectives and approaches through his discussion of the meaning of “contact”. He challenges the reader to come up with novel approaches that bring together “ignored” biological and mechanistic aspects of the infection process.
Chapter 5 (Nishiura and Chowell) and Chapter 7 (Bettencourt) focus on real-time assessments of the reproduction number. The exposition is spiced with references to recent epidemic outbreaks. For example, Bettencourt uses his framework to estimate disease epidemiological parameters and to assess the effects of interventions in real time using data from the 2005 outbreak of Marburg hemorrhagic fever in Angola.
In Chapter 8, Burr and colleagues review the theoretical and practical challenges associated with biosurveillance including the detection of disease outbreaks using traditional diagnosed case rates or syndromic surveillance data. In Chapter 6, Lloyd notes that parameter estimates are subject to uncertainty that arise not only from errors (noise) in the data but also from the structure of the model used in the fitting process. In other words, he argues that uncertainty must be evaluated at multiple levels to account for our ignorance or for the balance that each modeler must reach between biological detail and model complexity and objectives. Parameter estimation, Lloyd argues, must include structural sensitivity analyses. The use of historical data in epidemiological research is highlighted in Chapter 9 by Acu˜na-Soto’s contribution.
As he notes epidemiologists are reluctant to consider systematically the possibility of working with historical data albeit, as we have seen in the first Chapter, it is possible to extract valuable information from such data on influenza outbreaks. In fact, we acquired the kind of quantitative knowledge that let us quantify some of the differences between seasonal and pandemic influenza. Acu˜na-Soto’s work1, for example, on the epidemic of 1576 that killed 45% of the entire population of Mexico, highlights but a myriad of new possibilities for which the quantitative methods and approaches highlighted in this book can be put to good use.
Banks and colleagues in Chapter 11 provide a succinct overview of the statistical and computational aspects associated with inverse or parameter estimation problems for deterministic dynamical systems. Their results illustrate the impact that the marriage between statistical theory and applied mathematics is having in the study of infectious diseases while Chapter 10 (Arriola and Hyman) provides a general and thorough introduction to the field of sensitivity and uncertainty analyses, a central piece of any scientific work that is based on modeling.
The challenges and opportunities generated by studies of disease outbreak or disease dynamics in specific contexts are highlighted in the final chapters. Shim and Castillo-Chavez (Chapter 12) evaluate the potential impact that ongoing agedependent vaccination strategies (in the United States and Mexico) are likely to have in reducing the prevalence of severe rotavirus infections. Rios-Doria et al.
(Chapter 13) analyze the spatial and temporal dynamics of rubella in Peru, 1997–2006 via a wavelet time series analysis and other methods. The study is carried out in the context of changing policies that include the introduction of a vaccine and/or increases in vaccination rates. Cintron-Arias and colleagues (Chapter 15) model drinking as a “communicable” disease and, in the process, they highlight a new set of opportunities and possibilities for the applications of the mathematical and statistical approaches used in this volume. The focus here is on the evaluation of the role of relapse (ineffective treatment) on drinking dynamics but as a function of social network heterogeneity.
Contents
- The Basic Reproduction Number of Infectious Diseases: Computation and Estimation Using Compartmental Epidemic Models
- Stochastic Epidemic Modeling
- Two Critical Issues in Quantitative Modeling of Communicable Diseases: Inference of Unobservables and Dependent Happening
- The Chain of Infection, Contacts, and Model Parametrization
- The Effective Reproduction Number as a Prelude to Statistical Estimation of Time-Dependent Epidemic Trends
- Sensitivity of Model-Based Epidemiological Parameter Estimation to Model Assumptions
- An Ensemble Trajectory Method for Real-Time Modeling and Prediction of Unfolding Epidemics: Analysis of the 2005 Marburg Fever Outbreak in Angola
- Statistical Challenges in BioSurveillance
- Death Records from Historical Archives: A Valuable Source of Epidemiological Information
- Sensitivity Analysis for Uncertainty Quantification in Mathematical Models
- An Inverse Problem Statistical Methodology Summary
- The Epidemiological Impact of Rotavirus Vaccination Programs in the United States and Mexico
- Spatial and Temporal Dynamics of Rubella in Peru, 1997–2006: Geographic Patterns, Age at Infection and Estimation of Transmissibility
- The Role of Nonlinear Relapse on Contagion Amongst Drinking Communities
- Index
Product Details
- Authors: Gerardo Chowell, James M. Hayman, Luís M. A. Bettencourt and Carlos Castillo-Chavez
- Hardcover: 384 pages
- Publisher: Springer; 1 edition (June 25, 2009)
- Language: English
- ISBN-10: 9048123127
- ISBN-13: 978-9048123124
- Product Dimensions: 9.5 x 6.3 x 1.2 inches
List Price: $189.00