1-C Nonlinear Covid-19 Epidemic Model and Application to the Epidemic Prediction in France

We have shown in a previous paper that the standard time-invariant SIR model was not effective to predict the 2019-20 coronavirus pandemic propagation. We have proposed a new model predicting z the logarithm of the number of detected-contaminated people. It follows a linear dynamical system z9= b-a z. We show here that we can improve this prediction using a non linear model z9 = b-a z^r where r is an exponent that we have also to estimate from data. Some countries have an epidemic with a bell shaped form that we call unimodal epidemic. With this new model, we fit observed data of different countries having an unimodal epidemic with a surprising quality. We discuss also the prediction quality obtained with these models at the epidemic start in France. Finally, we evaluate the containment impact on the Covid French mortality in hospitals.