Mathematical modelling and projecting the second wave of COVID-19 pandemic in Europe.

A second wave of the COVID-19 pandemic has spurred in most of the European countries since the summer of 2020, and currently it remains uncertain when and how this can be fully controlled.1 In this study, we aim to nowcast and forecast the possible development of the second COVID-19 wave in representative European countries including Spain, France and the Netherlands by mathematical modelling. We adopted a SPMILHRD model based on the modification of the classic epidemic compartmental model SEIR (online supplemental methods; figure 1). How rapid an epidemic can spread largely depends on the reproductive number R. R must be below 1 to stop an outbreak. The transmission dynamics of COVID-19 can vary tremendously depending on the effectiveness of control measures. To better understand the epidemic spread, we thus estimated the time-varying reproduction number Rt based on real-word reported data (figure 2A). By incorporating R t in the SPMILHRD model, we recapitulated the COVID-19 epidemics in three representative European countries including Spain, France and the Netherlands (figure 2B). After the outbreaks at the end of February, control measures including lockdown and social distancing were implemented in these countries,2 resulting in gradual reduction of R t until below 1 during April and May and the control of local epidemics. However, we observed the time-varying reproduction number has continuously exceeded 1 since 22 June in Spain, 26 June in France and 09 July …