Predicted effects of summer holidays and seasonality on the SARS-Cov-2 epidemic in France

The SARS-CoV-2 epidemic in France has had a large death toll. It has not affected all regions similarly, since the death rate can vary several folds between regions where the epidemic has remained at a low level and regions where it got an early burst. The epidemic has been slowed down by a lockdown that lasted for almost eight weeks, and individuals can now move between metropolitan French regions without restriction. In this report we investigate the effect on the epidemic of summer holidays, during which millions of individuals will move between French regions. Additionally, we evaluate the effect of strong or weak seasonality and of several values for the reproduction number on the epidemic, in particular on the timing, the height and the spread of a second wave. To do so, we extend a SEIR model to simulate the effect of summer migrations between regions on the number and distribution of new infections. We find that the model predicts little effect of summer migrations on the epidemic. However, all the reproduction numbers above 1.0 and the seasonality parameters we tried result in a second epidemic wave, with a peak date that can vary between October 2020 and April 2021. If the sanitary measures currently in place manage to keep the reproduction number below 1.0, the second wave will be avoided. If they keep the reproduction number at a low value, for instance at 1.1 as in one of our simulations, the second wave is flattened and could be similar to the first wave.