  We study the reported data from the COVID-19 pandemic outbreak in January -
May 2020 in 119 countries. We observe that the time series of active cases in
individual countries (the difference of the total number of confirmed
infections and the sum of the total number of reported deaths and recovered
cases) display a strong agreement with polynomial growth and at a later
epidemic stage also with a combined polynomial growth with exponential decay.
Our results are also formulated in terms of compartment type mathematical
models of epidemics. Within these models the universal scaling characterizing
the observed regime in an advanced epidemic stage can be interpreted as an
algebraic decay of the relative reproduction number $R_0$ as $T_M/t$, where
$T_M$ is a constant and $t$ is the duration of the epidemic outbreak. We show
how our findings can be applied to improve predictions of the reported pandemic
data and estimate some epidemic parameters. Note that although the model shows
a good agreement with the reported data we do not make any claims about the
real size of the pandemics as the relation of the observed reported data to the
total number of infected in the population is still unknown.
