Change Point Modeling of Covid-19 Data in the United States

Abstract

To simultaneously model the change point and the possibly nonlinear relationship in the Covid-19 data of the US, a continuous second-order free knot spline model was proposed. Using the least squares method, the change point of the daily new cases against the total confirmed cases up to the previous day was estimated to be 04 April 2020. Before the point, the daily new cases were proportional to the total cases with a ratio of 0.287, suggesting that each patient had 28.7% chance to infect another person every day. After the point, however, such ratio was no longer maintained and the daily new cases were decreasing slowly. At the individual state level, it was found that most states had change points. Before its change point for each state, the daily new cases were still proportional to the total cases. And all the ratios were about the same except for New York State in which the ratio was much higher (probably due to its high population density and heavy usage of public transportation). But after the points, different states had different patterns. One interesting observation was that the change point of one state was about 3 weeks lagged behind the state declaration of emergency. This might suggest that there was a lag period, which could help identify possible causes for the second wave. In the end, consistency and asymptotic normality of the estimates were briefly discussed where the criterion functions are continuous but not differentiable (irregular).