Mathematical and Statistical Estimation Approaches in Epidemiology

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Gerardo Chowell, James M. Hayman, Luís M. A. Bettencourt, Carlos Castillo-Chavez
Springer Science & Business Media, Jun 6, 2009 - Mathematics - 363 pages
Mathematical and Statistical Estimation Approaches in Epidemiology compiles t- oretical 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 sci- tists 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,R . The use of this methodology 0 is illustrated, using regional data for 1918–1919 and 1968 in uenza pandemics.
 

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Contents

Computation and Estimation Using Compartmental Epidemic Models
1
Stochastic Epidemic Modeling
31
Inference of Unobservables and Dependent Happening
53
The Chain of Infection Contacts and Model Parametrization
88
The Effective Reproduction Number as a Prelude to Statistical Estimation of TimeDependent Epidemic Trends
103
Sensitivity of ModelBased Epidemiological Parameter Estimation to Model Assumptions
123
Analysis of the 2005 Marburg Fever Outbreak in Angola
142
Statistical Challenges in BioSurveillance
163
A Valuable Source of Epidemiological Information
188
Sensitivity Analysis for Uncertainty Quantification in Mathematical Models
195
An Inverse Problem Statistical Methodology Summary
249
The Epidemiological Impact of Rotavirus Vaccination Programs in the United States and Mexico
303
Geographic Patterns Age at Infection and Estimation of Transmissibility
324
The Role of Nonlinear Relapse on Contagion Amongst Drinking Communities
343
Index
361
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About the author (2009)

Gerardo Chowell is an associate professor and a Second Century Initiative Scholar (2CI) in the School of Public Health at Georgia State University in Atlanta. His research program includes the development and application of quantitative approaches for understanding the transmission dynamics and control of infectious diseases including influenza, Ebola, and dengue fever. His work has appeared in high-impact journals including The New England Journal of Medicine, PLOS Medicine, and BMC Medicine, and has been cited by major media outlets including the Washington Post and TIME magazine.

James (Mac) Hyman has developed and analyzed mathematical models for the transmission of HIV/AIDs, influenza, malaria, dengue fever, chikungunya, and infections. His current focus is to identify approaches where these models can help public health workers be more effective in mitigating the impact of emerging diseases. He was a research scientist at Los Alamos National Laboratory for over thirty years, is a past president of the Society for Industrial and Applied Mathematics (SIAM), and now holds the Phillips Distinguished Chair in Mathematics at Tulane University.

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