  At the end of April 20, 2020, there were only a few new COVID-19 cases
remaining in China, whereas the rest of the world had shown increases in the
number of new cases. It is of extreme importance to develop an efficient
statistical model of COVID-19 spread, which could help in the global fight
against the virus. We propose a clustering-segmented autoregressive sigmoid
(CSAS) model to explore the space-time pattern of the log-transformed
infectious count. Four key characteristics are included in this CSAS model,
including unknown clusters, change points, stretched S-curves, and
autoregressive terms, in order to understand how this outbreak is spreading in
time and in space, to understand how the spread is affected by epidemic control
strategies, and to apply the model to updated data from an extended period of
time. We propose a nonparametric graph-based clustering method for discovering
dissimilarity of the curve time series in space, which is justified with
theoretical support to demonstrate how the model works under mild and easily
verified conditions. We propose a very strict purity score that penalizes
overestimation of clusters. Simulations show that our nonparametric graph-based
clustering method is faster and more accurate than the parametric clustering
method regardless of the size of data sets. We provide a Bayesian information
criterion (BIC) to identify multiple change points and calculate a confidence
interval for a mean response. By applying the CSAS model to the collected data,
we can explain the differences between prevention and control policies in China
and selected countries.
