Uncertainty quantification in mechanistic epidemic models via cross-entropy approximate Bayesian computation

Abstract

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.

Dynamic parameterization of a modified SEIRD model to analyze and forecast the dynamics of COVID-19 outbreaks in the United States

“…Fifth, we assume that five epidemiological parameters in the model (i.e., , , e , r , and d ) require a dynamic parameterization. Previous studies have represented complex COVID-19 outbreak dynamics leveraging a smaller set of dynamic parameters or only the transmission rate as a time-varying parameter [11,18,27,42,43,84]. In the development of the computational pipeline presented in this study we observed that neither constant parameters nor leveraging only as a dynamic parameter rendered a superior performance in reproducing and predicting COVID-19 outbreaks than our dynamic parameterization approach (see Supplementary Figs.…”

“…However, our approach can be straightforwardly extended by adding a preprocessing step to de-noise the epidemiological data [29,63]. Additionally, our computational pipeline could be recast in a Bayesian framework to accommodate a more robust quantification of uncertainty from the input data to model forecasting [18,35,[40][41][42][43]. With these developments, the computational pipeline could also palliate large oscillations in the daily parameter estimates between successive calibrations, and hence yield more reliable forecasts.…”

“…We think that this functional space is a practical choice that can provide sufficient smoothness to accommodate the dynamic parameterization of infectious disease models. However, future studies could investigate the performance of other alternatives within our computational pipeline, such as B-splines of different polynomial degrees and with optimally located knots [69][70][71] or logistic functions [18,42,84]. This analysis could also provide a deeper insight in the impact of noise and underreported data on the resulting dynamic parameterization.…”

“…This hybrid approach has also attracted much attention in other areas of computational biology and medicine, such as the modeling of cancer growth and therapeutic response [36][37][38][39]. To calibrate and update time-resolved parameterizations of mechanistic models of infectious disease outbreaks using incoming epidemiological data, some studies have shown promising results by leveraging Bayesian methods [18,[40][41][42][43]. However, this approach requires the estimation of unknown prior distributions for the model parameters and this may result in a significant bias in parameter identification, especially at the onset of an outbreak [18].…”

Assessing the impact of isolation policies on epidemic dynamics through swarm entropy

“…The fidelity of group simulation models has been a time-consuming challenge to address. Cunha et al ( 2 ) introduced a data-driven machine learning framework that employs the cross-entropy method to enhance the fidelity of real-time infectious disease models. Kumar and Susan ( 3 ) suggests a fuzzy time series (FTS) forecasting method based on particle swarm optimization (PSO) to enhance the accuracy of predictions.…”