Misspecified modeling of subsequent waves during COVID-19 outbreak: A change-point growth model

In the analysis of cumulative counts of SARS-CoV-2 infections, such as deaths or cases, common parametric models based on log-logistic growth curves adapt well to describe a single wave at a time. Unfortunately, in Italy, as well as all over the globe, from February 2020 to March 2021 more than one wave has been observed. In this paper, we propose a method to fit more than one wave in the same model. In particular, we discuss an approach based on a change-point model in a pseudo-likelihood framework that takes into account some model misspecification issues, such as those concerning the assumption of Poisson marginals and those relating to overdispersion and autocorrelation. An application to data collected in Italy is discussed.