The Pascal triangle is so simple and rich that it has always attracted the interest of professional and amateur mathematicians. Their coefficients satisfy a myriad of properties. Inspired by the work of Shekatkar et al., we study the divisibility patterns within the elements of the Pascal triangle, through its decomposition into Pascal's matrices, from the perspective of network science. Applying Kolmogorov-Smirnov test, we determine that the degree distribution of the resulting network follows a power-law distribution. We also study degrees, global and local clustering coefficients, stretching graph, averaged path length and the mixing assortative.
We adapt the Covasim agent-based model for predicting new COVID-19 cases by tuning the transmissibility rate with information on the impact of the most common non-pharmaceutical interventions (NPIs) obtained through machine learning models. Such impact has been estimated thanks to the information on applying pools of NPIs worldwide from the Oxford COVID-19 Government Response Tracker.
This approach permits the simulation of a whole country or a smaller region, providing information about asymptomatic, recovery, severe, and critical new cases and enabling governments and authorities to set NPIs plans to cope with the pandemic.
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