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Bayesian Analysis of Epidemics - Zombies, Influenza, and other Diseases



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Mathematical models of epidemic dynamics offer significant insight into predicting and controlling infectious diseases. The dynamics of a disease model generally follow a susceptible, infected, and recovered (SIR) model, with some standard modifications. In this paper, we extend the work of Munz (2009) on the application of disease dynamics to the so-called "zombie apocalypse", and then apply the identical methods to influenza dynamics. Unlike Munz (2009), we include data taken from specific depictions of zombies in popular culture films and apply Markov Chain Monte Carlo (MCMC) methods on improved dynamical representations of the system. To demonstrate the usefulness of this approach, beyond the entertaining example, we apply the identical methodology to Google Trend data on influenza to establish infection and recovery rates. Finally, we discuss the use of the methods to explore hypothetical intervention policies regarding disease outbreaks.

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Most cited references 9

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A Contribution to the Mathematical Theory of Epidemics

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Estimating transmission intensity for a measles epidemic in Niamey, Niger: lessons for intervention.

The objective of this study is to estimate the effective reproductive ratio for the 2003-2004 measles epidemic in Niamey, Niger. Using the results of a retrospective and prospective study of reported cases within Niamey during the 2003-2004 epidemic, we estimate the basic reproductive ratio, effective reproductive ratio (RE) and minimal vaccination coverage necessary to avert future epidemics using a recent method allowing for estimation based on the epidemic case series. We provide these estimates for geographic areas within Niamey, thereby identifying neighbourhoods at high risk. The estimated citywide RE was 2.8, considerably lower than previous estimates, which may help explain the long duration of the epidemic. Transmission intensity varied during the course of the epidemic and within different neighbourhoods (RE range: 1.4-4.7). Our results indicate that vaccination coverage in currently susceptible children should be increased by at least 67% (vaccine efficacy 90%) to produce a citywide vaccine coverage of 90%. This research highlights the importance of local differences in vaccination coverage on the potential impact of epidemic control measures. The spatial-temporal spread of the epidemic from district to district in Niamey over 30 weeks suggests that targeted interventions within the city could have an impact.
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A Bayesian Framework for Parameter Estimation in Dynamical Models

Mathematical models in biology are powerful tools for the study and exploration of complex dynamics. Nevertheless, bringing theoretical results to an agreement with experimental observations involves acknowledging a great deal of uncertainty intrinsic to our theoretical representation of a real system. Proper handling of such uncertainties is key to the successful usage of models to predict experimental or field observations. This problem has been addressed over the years by many tools for model calibration and parameter estimation. In this article we present a general framework for uncertainty analysis and parameter estimation that is designed to handle uncertainties associated with the modeling of dynamic biological systems while remaining agnostic as to the type of model used. We apply the framework to fit an SIR-like influenza transmission model to 7 years of incidence data in three European countries: Belgium, the Netherlands and Portugal.

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16 pages, 6 figures, 2 tables. Corrected email address typo from previous version
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