Uncertainty Quantification in Epidemiological Models for COVID-19 Pandemic

The main goal of this paper is to develop the forward and inverse modeling of the Coronavirus (COVID-19) pandemic using novel computational methodologies in order to accurately estimate and predict the pandemic. This leads to governmental decisions support in implementing effective protective measures and prevention of new outbreaks. To this end, we use the logistic equation and the SIR system of ordinary differential equations to model the spread of the COVID-19 pandemic. For the inverse modeling, we propose Bayesian inversion techniques, which are robust and reliable approaches, in order to estimate the unknown parameters of the epidemiological models. We use an adaptive Markov-chain Monte-Carlo (MCMC) algorithm for the estimation of a posteriori probability distribution and confidence intervals for the unknown model parameters as well as for the reproduction number. Furthermore, we present a fatality analysis for COVID-19 in Austria, which is also of importance for governmental protective decision making. We perform our analyses on the publicly available data for Austria to estimate the main epidemiological model parameters and to study the effectiveness of the protective measures by the Austrian government. The estimated parameters and the analysis of fatalities provide useful information for decision makers and makes it possible to perform more realistic forecasts of future outbreaks.