  Addressed in this work is the performance of five popular algorithms, which
aim at assessing the dissemination dynamics of the COVID-19 disease on the
basis of the time series of new confirmed cases. The tests are based on
simulated data, generated by means of a deterministic compartmental
epidemiological model \cite{Matsinos2020a}, adapted herein to also include the
possibility of the loss of immunity by the group of the recovered (or
vaccinated) subjects. Assuming a simple temporal dependence of the effective
reproduction number (the exact details are of no relevance as far as the
conclusions of this work are concerned), time series of new cases were
generated in a time domain of nearly one year for the five top-ranking
countries in the cumulative number of infections by January 1, 2021. These
countries are (in descending order of infections): the United States of
America, India, Brazil, Russia, and the United Kingdom. The processing of each
simulated time series led to the establishment of relations between the input
(actual) and the reconstructed values of the effective reproduction number for
each country and algorithm, separately; this work argues that all five
algorithms underestimate the effective reproduction number when the latter
exceeds the critical value of $1$. The five algorithms were subsequently
applied to the real-life time series of new cases for the aforementioned five
countries, which also span a temporal interval of nearly one year; corrected
values of the effective reproduction number are obtained for these countries in
2020.
