The Topological Properties of COVID-19 Global Activity Time Series Forecasting

Abstract

Topological data analysis (TDA) is a combination of statistical, computational and topological methods that would allow one to find shape-like structures in data. The mathematical concepts of time series and topological data analysis are seldomly used in conjunction. The goal of this paper is to introduce readers to the combination of time series forecasting with topological data analysis as a technique to solve real world problems. The COVID-19 pandemic is a relevant topic that is known worldwide and will be the test subject used in this experiment. A time series forecast was produced to determine future trends of Coronavirus cases in the top 10 most affected countries. This forecast can inform health officials and improve regulations for the future in an effort to circumvent the effects of COVID-19. Performing topological data analysis on this forecast generated the unique topological structure of the time series dataset. This paper concluded that a majority of the screened countries will continue to see a rise in deaths for the next 6 months. Additionally, the topological structure derived from the forecast model consisted of a loop and immeasurable points. By writing this paper, the author encourages others to find innovative solutions to modern problems using this combination of mathematics.