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.
Individual perception of vaccine safety is an important factor in determining a persons adherence to a vaccination program and its consequences for disease control. This perception, or belief, about the safety of a given vaccine is not a static parameter but a variable subject to environmental influence. To complicate matters, perception of risk (or safety) does not correspond to actual risk. In this paper we propose a way to include the dynamics of such beliefs into a realistic epidemiological model, yielding a more complete depiction of the mechanisms underlying the unraveling of vaccination campaigns. The methodology proposed is based on Bayesian inference and can be extended to model more complex belief systems associated with decision models. We found the method is able to produce behaviors which approximate what has been observed in real vaccine and disease scare situations. The framework presented comprises a set of useful tools for an adequate quantitative representation of a common yet complex public-health issue. These tools include representation of beliefs as Bayesian probabilities, usage of logarithmic pooling to combine probability distributions representing opinions, and usage of natural conjugate priors to efficiently compute the Bayesian posterior. This approach allowed a comprehensive treatment of the uncertainty regarding vaccination behavior in a realistic epidemiological model.
This study describes the main features of pandemic influenza A (H1N1) in Brazil during 2009. Brazil is a large country that extends roughly from latitudes 5ºN to 34ºS. Brazil has tropical and sub-tropical climates, a heterogeneous population distribution, and intense urbanization in the southern portions of the country and along its Atlantic coast. Our analysis points to a wide variation in infection rates throughout the country, and includes both latitudinal effects and strong variations in detection rates. Two states (out of a total of 23) were responsible for 73% of all cases reported. Real time reproduction numbers demonstrate that influenza transmission was sustained in the country, beginning in May of 2009. Finally, this study discusses the challenges in understanding the infection dynamics of influenza and the adequacy of Brazils influenza monitoring system.
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