Estimation of COVID-19 dynamics in the different states of the United States using Time-Series Clustering

Rojas, I.; Rojas, F.; Valenzuela, O.

Estimation of COVID-19 dynamics and its evolution is a multidisciplinary effort, which requires the unification of heterogeneous disciplines (scientific, mathematics, epidemiological, biological/bio-chemical, virologists and health disciplines to mention the most relevant) to work together in a better understanding of this pandemic. Time series analysis is of great importance to determine both the similarity in the behavior of COVID-19 in certain countries/states and the establishment of models that can analyze and predict the transmission process of this infectious disease. In this contribution, an analysis of the different states of the United States will be carried out to measure the similarity of COVID-19 time series, using dynamic time warping distance (DTW) as a distance metric. A parametric methodology is proposed to jointly analyze infected and deceased persons. This metric allows to compare time series that have a different time length, making it very appropriate for studying the United States, since the virus did not spread simultaneously in all the states/provinces. After a measure of the similarity between the time series of the states of United States was determined, a hierarchical cluster was created, which makes it possible to analyze the behavioral relationships of the pandemic between different states and to discover interesting patterns and correlations in the underlying data of COVID-19 in the United States. With the proposed methodology, nine different clusters were obtained, showing a different behavior in the eastern zone and western zone of the United States. Finally, to make a prediction of the evolution of COVID-19 in the states, Logistic, Gompertz and SIR model was computed. With these mathematical model it is possible to have a more precise knowledge of the evolution and forecast of the pandemic.