RESUMO
This paper proposes a data-driven approximate Bayesian computation framework for parameter estimation and uncertainty quantification of epidemic models, which incorporates two novelties: (i) the identification of the initial conditions by using plausible dynamic states that are compatible with observational data; (ii) learning of an informative prior distribution for the model parameters via the cross-entropy method. The new methodology's effectiveness is illustrated with the aid of actual data from the COVID-19 epidemic in Rio de Janeiro city in Brazil, employing an ordinary differential equation-based model with a generalized SEIR mechanistic structure that includes time-dependent transmission rate, asymptomatics, and hospitalizations. A minimization problem with two cost terms (number of hospitalizations and deaths) is formulated, and twelve parameters are identified. The calibrated model provides a consistent description of the available data, able to extrapolate forecasts over a few weeks, making the proposed methodology very appealing for real-time epidemic modeling.
RESUMO
Several mathematical models of the human middle ear dynamics have been studied since the mid-twentieth century. Despite different methods applied, all of these models are based on deterministic approaches. Experimental data have shown that the middle ear behaves as an uncertain system due to the variability among individuals. In this context, stochastic models are useful because they can represent a population of middle ears with its intrinsic uncertainties. In this work, a nonparametric probabilistic approach is used to model the human middle ear dynamics. The lumped-element method is adopted to develop deterministic baseline models, and three different optimization processes are proposed and applied to the adjustment of the stochastic models. Results show that the stochastic models proposed can reproduce the experimental data in terms of mean and coefficient of variation. In addition, this study shows the importance of properly defining the acceptable range of each input parameter in order to obtain a reliable stochastic model.