Within the complex framework of anti-COVID-19 health management, where the criteria of diagnostic testing, the availability of public-health resources and services, and the applied anti-COVID-19 policies vary between countries, the reliability and accuracy in the modeling of temporal spread can prove to be effective in the worldwide fight against the disease. This paper applies an exploratory time-series analysis to the evolution of the disease in Greece, which currently suggests a success story of COVID-19 management. The proposed method builds on a recent conceptualization of detecting connective communities in a time-series and develops a novel spline regression model where the knot vector is determined by the community detection in the complex network. Overall, the study contributes to the COVID-19 research by proposing a free of disconnected past-data and reliable framework of forecasting, which can facilitate decision-making and management of the available health resources.

The scale-free (SF) property is a major concept in complex networks, and it is based on the definition that an SF network has a degree distribution that follows a power-law (PL) pattern. This paper highlights that not all networks with a PL degree distribution arise through a Barabási−Albert (BA) preferential attachment growth process, a fact that, although evident from the literature, is often overlooked by many researchers. For this purpose, it is demonstrated, with simulations, that established measures of network topology do not suffice to distinguish between BA networks and other (random-like and latticelike) SF networks with the same degree distribution. Additionally, it is examined whether an existing self-similarity metric proposed for the definition of the SF property is also capable of distinguishing different SF topologies with the same degree distribution. To contribute to this discrimination, this paper introduces a spectral metric, which is shown to be more capable of distinguishing between different SF topologies with the same degree distribution, in comparison with the existing metrics.network science | Barabási−Albert networks | preferential attachment | pattern recognition | power-law degree distribution

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Within the context of Greece promising a success story in the fight against the disease, this paper proposes a novel method for studying 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 spread 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 towards saturation. In terms of Gaussian modeling, this successive compression of the COVID-19 infection curve into five parts implies that the pandemic in Greece is about to reach the second (decline) half of the bell-shaped distribution. The network analysis also illustrates stability of hubs and instability of medium and low-degree nodes, implying a low probability of meeting maximum (infection) values in 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.

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