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During the course of an epidemic, one of the most challenging tasks forauthorities is to decide what kind of restrictive measures to introduce andwhen these should be enforced. In order to take informed decisions in a fullyrational manner, the onset of a critical regime, characterized by anexponential growth of the contagion, must be identified as quickly as possible.Providing rigorous quantitative tools to detect such an onset represents animportant contribution from the scientific community to proactively support thepolitical decision makers. In this paper, leveraging the quickest detectiontheory, we propose a mathematical model of the COVID-19 pandemic evolution anddevelop decision tools to rapidly detect the passage from a controlled regimeto a critical one. A new sequential test -- referred to as MAST (mean-agnosticsequential test) -- is presented, and demonstrated on publicly availableCOVID-19 infection data from different countries. Then, the performance of MASTis investigated for the second pandemic wave, showing an effective trade-offbetween average decision delay $\Delta$ and risk $R$, where $R$ is inverselyproportional to the time required to declare the need to take unnecessaryrestrictive measures. Ideally, the decision mechanism should react as quick aspossible for a given level of risk. We find that all the countries share thesame behaviour in terms of quickest detection, specifically the risk scalesexponentially with the delay, $R \sim \exp{(-\omega \Delta)}$, where $\omega$depends on the specific nation. For a reasonably small risk level, say, onepossibility in ten thousand (i.e., unmotivated implementation ofcountermeasures every 27 years, on the average), the proposed algorithm detectsthe onset of the critical regime with delay between a few days to three weeks,much earlier than when the exponential growth becomes evident.

Decision Support for the Quickest Detection of Critical COVID-19 Phases