## Mathematical and Statistical Estimation Approaches in EpidemiologyGerardo Chowell, James M. Hayman, Luís M. A. Bettencourt, Carlos Castillo-Chavez 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

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 |

361 | |

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adjoint problem age-speciﬁc approach Arizona State University assumed assumption asymptotic average basic reproduction number Castillo-Chavez Chowell computed conﬁdence constant variance contact rate curve deaths deﬁned deﬁnition denotes dependent derivative deterministic difﬁcult distribution effect eigenvalue endemic epidemic models Epidemiology example exponentially distributed f(tj ﬁnal ﬁnd ﬁrst ﬁt ﬁxed function gamma distributed given GLS estimation growth rate herd immunity immunity impact incubation period infected individuals infectious diseases infectious periods inﬂuenza pandemic initial inverse problems linear Math mathematical model matrix method networks Nishiura observed obtained onset pandemic parameter estimates population probability problem drinkers random random variable regions relapse reported residual rotavirus infections rotavirus vaccination rubella SEIR serial interval signiﬁcant simulations SIR model small-world network solution spatial speciﬁc Springer Science+Business Media statistical model stochastic sufﬁciently surveillance susceptible syndrome tion total number uncertainty unvaccinated vaccine efﬁcacy values variables vector