  The long duration of the COVID-19 pandemic allowed for multiple bursts in the
infection and death rates, the so-called epidemic waves. This complex behavior
is no longer tractable by simple compartmental model and requires more
sophisticated mathematical techniques for analyzing epidemic data and
generating reliable forecasts. In this work, we propose a framework for
analyzing complex dynamical systems by dividing the data in consecutive
time-windows to be separately analyzed. We fit parameters for each time-window
through an Approximate Bayesian Computation (ABC) algorithm, and the posterior
distribution of parameters obtained for one window is used as the prior
distribution for the next window. This Bayesian learning approach is tested
with data on COVID-19 cases in multiple countries and is shown to improve ABC
performance and to produce good short-term forecasting.
