Covid-19 Epidemic Prediction in France: the Multimodal Case.

In two previous papers we have proposed models to estimate the Covid-19 epidemic when the number of daily positive cases has a bell shaped form that we call a mode. We have observed that each Covid variant produces this type of epidemic shape at a different moment, resulting in a multimodal epidemic shape. We will show in this document that each mode can still be estimated with models described in the two previous papers provides we replace the cumulated number of positive cases y by the cumulated number of positive cases reduced by a parameter P to be estimated. Therefore denoting z the logarithm of y -P, z follows approximately the differential equation [z] = b -azr where a, b, r have also to be estimated from the observed data. We will show the obtained predictions on the four French modes April, November 2020, May and September 2021. The comparison between the prediction obtained before the containment decisions made by the French government and the observed data afterwards suggests the inefficiency of the epidemic lockdowns.