Historically, infectious diseases have greatly impacted human health, necessitating a robust understanding of their trends, processes, and transmission. This study focuses on the COVID-19 pandemic, employing mathematical, statistical, and machine-learning methods to examine its time-series data. We quantify data irregularity using approximate entropy, revealing higher volatility in the U.S., Italy, and India compared to China. We employ the Dynamic Time Warping algorithm to assess regional similarity, finding a strong correlation between the U.S. and Italy. The Seasonal Trend Decomposition using the LOESS algorithm illuminates strong trend degrees in all observed regions, but China's prevention measures show marked effectiveness. These tools, whilst already valuable, still present opportunities for development in both theory and practice.