Stages of COVID-19 pandemic and paths to herd immunity by vaccination: dynamical model comparing Austria, Luxembourg and Sweden

Kemp, F.; Proverbio, D.; Aalto, A.; Mombaerts, L.; Fouquier d Herouel, A.; Husch, A.; Ley, C.; Goncalves, J.; Skupin, A.; Magni, S.

Background. Worldwide more than 72 million people have been infected and 1.6 million died withSARS-CoV-2 by 15th December 2020. Non-pharmaceutical interventions which decrease social interaction have been implemented to reduce the spread of SARS-CoV-2 and to mitigate stress on healthcare systems and prevent deaths. The pandemic has been tackled with disparate strategies by distinct countries resulting in different epidemic dynamics. However, with vaccines now becoming available, the current urgent open question is how the interplay between vaccination strategies and social interaction will shape the pandemic in the next months. Methods. To address this question, we developed an extended Susceptible-Exposed-Infectious-Removed (SEIR) model including social interaction, undetected cases and the progression of patients trough hospitals, intensive care units (ICUs) and death. We calibrated our model to data of Luxembourg, Austria and Sweden, until 15th December 2020. We incorporated the effect of vaccination to investigate under which conditions herd immunity would be achievable in 2021. Results. The model reveals that Sweden has the highest fraction of undetected cases, Luxembourg displays the highest fraction of infected population, and all three countries are far from herd immunity as of December 2020. The model quantifies the level of social interactions, and allows to assess the level which would keep Reff(t) below 1. In December 2020, this level is around 1/3 of what it was before the pandemic for all the three countries. The model allows to estimate the vaccination rate needed for herd immunity and shows that 2700 vaccinations/day are needed in Luxembourg to reach it by mid of April and 45,000 for Austria and Sweden. The model estimates that vaccinating the whole population of a country within 1 year could lead to herd immunity by July in Luxembourg and by August in Austria and Sweden. Conclusion. The model allows to shed light on the dynamics of the epidemics in different waves and countries. Our results emphasize that vaccination will help considerably but not immediately and therefore social measures will remain important for several months before they can be fully alleviated.