Omicron, the latest SARS-CoV-2 Variant of Concern (VOC), first appeared in Africa in November 2021. At present, the question of whether a new VOC will out-compete the currently predominant variant is important for governments seeking to determine if current surveillance strategies and responses are appropriate and reasonable. Based on both virus genomes and daily-confirmed cases, we compare the additive differences in growth rates and reproductive numbers (R_0) between VOCs and their predominant variants through a Bayesian framework and phylo-dynamics analysis. Faced with different variants, we evaluate the effects of current policies and vaccinations against VOCs and predominant variants. The model also predicts the date on which a VOC may become dominant based on simulation and real data in the early stage. The results suggest that the overall additive difference in growth rates of B.1.617.2 and predominant variants was 0.44 (95% confidence interval, 95% CI: −0.38, 1.25) in February 2021, and that the VOC had a relatively high R_0. The additive difference in the growth rate of BA.1 in the United Kingdom was 6.82 times the difference between Delta and Alpha, and the model successfully predicted the dominating process of Alpha, Delta and Omicron. Current vaccination strategies remain similarly effective against Delta compared to the previous variants. Our model proposes a reliable Bayesian framework to predict the spread trends of VOCs based on early-stage data, and evaluates the effects of public health policies, which may help us better prepare for the upcoming Omicron variant, which is now spreading at an unprecedented speed.

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An order 3 magic hexagon resembles the shape of a 19-cell honeycomb, arranged in a 3 4 5 4 3 manner. The requirement is to fill the numbers 1-19 in the grids so that each row (15 in total) adds up to 38. Previously invented methods aimed at solving this problem and proving its uniqueness were either not rigorous enough or too intricate. So by analyzing its properties, I wanted to find a combinatorial solution to its construction, prove its uniqueness, and investigate whether its mathematical principles can be used in real-world applications. The difficulty depends on the viewpoint, so the first step was to label each grid in a convenient way. I chose to look at the magic hexagon as a network composed of a center and rings. Then the connections and restrictions of each number set could be found by formula derivation. In a similar fashion, symmetrical properties were also found. The next step was to analyze possible distributions of odd and even numbers. Out of the 9 configurations, only 1 proved to be usable. The final step was construction. With all the properties known, the few impossibilities were easily eliminated, and only one solution remained, thus proving its uniqueness. The procedures used on the order 3 magic hexagon may be extended to those of higher orders, providing more ease in their construction. The unique properties of magic hexagons may be used in some fields of application, such as in password systems, large-scale roof structure, composite material, national security systems and many other fields.