Monitoring the post-containment COVID-19 crisis in Guadeloupe: Early-warning signals of destabilisation through bootstrapped probability density functions

We propose a method to detect early-warning information in relation with subtle changes occurring in the trend of evolution in data time series of the COVID-19 epidemic spread (e.g. daily new cases). The method is simple and easy to implement on laptop computers. It is designed to be able to provide reliable results even with very small amounts of data (i.e. {approx} 10 - 20). The results are given as compact graphics easy to interpret. The data are separated into two subsets: the old data used as control points to statistically define a "trend" and the recent data that are tested to evaluate their conformity with this trend. The trend is characterised by bootstrapping in order to obtain probability density functions of the expected misfit of each data point. The probability densities are used to compute distance matrices where data clusters and outliers are easily visually recognised. In addition to be able to detect very subtle changes in trend, the method is also able to detect outliers. A simulated case is analysed where R0 is slowly augmented (i.e. from 1.5 to 2.0 in 20 days) to pass from a stable damped control of the epidemic spread to an exponentially diverging situation. The method is able to give an early warning signal as soon as the very beginning of the R0 variation. Application to the data of Guadeloupe shows that a small destabilising event occurred in the data near April 30, 2020. This may be due to an increase of R0 0.7 around April 13-15, 2020.