  Within the context that Greece promises a success story in the fight against
the disease, this paper proposes a novel method to study the evolution of the
Greek COVID-19 infection-curve in relation to the anti-COVID-19 policies
applied to control the pandemic. Based on the ongoing spreading of COVID-19 and
the insufficient data for applying classic time-series approaches, the analysis
builds on the visibility graph algorithm to study the Greek COVID-19
infection-curve as a complex network. By using the modularity optimization
algorithm, the generated visibility graph is divided into communities defining
periods of different connectivity in the time-series body. These periods reveal
a sequence of different typologies in the evolution of the disease, starting
with a power pattern, where a second order polynomial (U-shaped) pattern
intermediates, being followed by a couple of exponential patterns, and ending
up with a current logarithmic pattern revealing that the evolution of the Greek
COVID-19 infection-curve tends into saturation. The network analysis also
illustrates stability of hubs and instability of medium and low-degree nodes,
implying a low probability to meet maximum (infection) values at the future and
high uncertainty in the variability of other values below the average. The
overall approach contributes to the scientific research by proposing a novel
method for the structural decomposition of a time-series into periods, which
allows removing from the series the disconnected past-data facilitating better
forecasting, and provides insights of good policy and decision-making practices
and management that may help other countries improve their performance in the
war against COVID-19.
