Decomposition of waves in time series of data related to Covid-19

Abstract: Here it is proposed a decomposition in components of the''waves'' which appear in the time series of data related to Covid-19 pandemic. The decomposition is based on functions of \k{appa}-statistics; in particular the \k{appa}-Weibull is used. Fitted data are those of the ''waves'' ranging from August 2020 to April 2021 in the United Kingdom, from September 2020 to May 2021 in Ireland, and from September 2020 to June 2021 in Italy. For the United Kingdom, the time series of daily infection shows a wave composed by two peaks. Among the many factors involved in the spread of infection, it seems that, in driving the onset of the second peak, the main role was played by the emergence of Alpha variant of Sars-Cov-2. Therefore, the proposed decomposition of waves in the time series is applied to study the role of Alpha variant in the spread of infection. For what concerns data from Ireland, if we decompose the analysed ''wave'' in three components, we can observed that for one of them the role of the Alpha variant was relevant for sure. In the case of Italy, the effect is less evident, because it was spread over a larger time interval.