Mathematical and Statistical Estimation Approaches in Epidemiology

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.

Chapter 1: The basic reproduction number of infectious diseases: Computation and estimation using compartmental epidemic models Gerardo Chowell and Fred Brauer Chapter 2: Stochastic Epidemic Modeling Priscilla E. Greenwood and Luis F. Gordillo Chapter 3: Two critical issues in quantitative modeling of communicable diseases: Inference of unobservables and dependent happening Hiroshi Nishiura, Masayuki Kakehashi and Hisashi Inaba Chapter 4: A note on the definition of contacts, measures of mixing, and model parametrization Stephen Tennenbaum Chapter 5: The effective reproduction number as a prelude to statistical estimation of time-dependent epidemic trends Hiroshi Nishiura and Gerardo Chowell Chapter 6: Sensitivity of Model-Based Epidemiological Parameter Estimation to Model Assumptions Alun L. Lloyd Chapter 7:An ensemble trajectory method for real-time modeling and prediction of unfolding epidemics: analysis of the 2005 Marburg fever outbreak in Angola Luís M. A. Bettencourt Chapter 8: Statistical Challenges in BioSurveillance Tom Burr, Sarah Michalak and Rick Picard Chapter 9:Death Records from Historical Archives: A Valuable Source of Epidemiological Information Rodolfo Acuña-Soto Chapter 10: Sensitivity Analysis for Uncertainty Quantification in Mathematical Models Leon Arriola and James M. Hyman Chapter 11: An Inverse Problem Statistical Methodology Summary H. T. Banks, Marie Davidian, John R. Samuels, Jr. and Karyn L.Sutton Chapter 12: The epidemiological impact of rotavirus vaccination programs in the United States and Mexico Eunha Shim and Carlos Castillo-Chavez Chapter 13: Spatial and temporal dynamics of rubella in Peru, 1997-2006: Geographic patterns, age at infection and estimation of transmissibility Daniel Rios-Doria, Gerardo Chowell, Cesar Munayco-Escate, Alvaro Witthembury and Carlos Castillo-Chavez Chapter 14: TheRole of Nonlinear Relapse on Contagion Amongst Drinking Communities Ariel Cintrón-Arias, Fabio Sánchez, Xiaohong Wang, Carlos Castillo-Chavez, Dennis M. Gorman and Paul J. Gruenwald