  A great issue of discussion of an infectious disease is its basic
reproduction number R0, which provides an estimation of the contagiousness of
the disease. When R0 > 1, the disease spread will potentially lead to an
outbreak, such that of the ongoing COVID-19 pandemics. During the evolution of
an outbreak, various non-pharmaceutical interventions are employed, the impact
of which is frequently assessed by the reduction that they introduce to the
effective reproduction number Rt; reduction below 1 is an indication of
eventual dying out of the disease spread. Motivated by the fact that R0
essentially expresses the stability of the disease-free equilibrium, in this
work, Rt was examined in the view of timescale analysis. It was shown that
during the evolution of the COVID-19 outbreak in Italy, when various
interventions were in place, Rt had a clear relation with the explosive
timescale characterizing the dynamics of the outbreak. In particular, it is
shown that the existence of an explosive timescale during the progression of
the epidemics implies Rt > 1, while its absence implies Rt < 1. In addition, as
this timescale converges/diverges with the immediately slowest one, Rt
approaches to/withdraws from its threshold value 1. These results suggest that
timescale analysis can be utilized for the assessment of the impact of various
interventions, since it reflects the insight provided by the effective
reproduction number, without being hindered by the selection of the population
model, nor the parameter estimation process followed for model calibration.
