A tentative tracking of the SARS-Cov2 pandemic in France, based on a corrected SIR model including vaccination effects

¹ Université de Paris, INSERM, Laboratory for Vascular Translational Science (LVTS), F-75018 Paris, France
² Member of the Editorial Committee of the Ecole Polytechnique alumni review, 12 rue de Poitiers, 75007 Paris, France
³ Université de Versailles Saint-Quentin, 45 avenue des Etats-Unis, 78035 Versailles cedex, France

^* corresponding author: varret_francois@yahoo.fr

Published online: 28 April 2022

Abstract

We developed successive extensions of the SIR model in order to track the dynamics of the SARS-Cov2 disease. The analysis of health system available data is published in a chronicle accessible on the net: https://corona-circule.github.io/lettres/. This chronicle was initiated on late march 2020 and up to now contains 50 issues. A constant concern was the reliability of the data: for instance, we very soon evidenced that the number of confirmed cases, because of the asymptomatic carriers and the erratic testing policy, was hugely underestimated. By the end of 2020 we made a basic change in the model which consisted in accounting for a constant contagiousness time (SIR-tcc) instead of the probabilistic evolution of the end of the infection assumed so far. Recently we completed this SIR-tcc model for the vaccination effects in order to properly track the evolution of the group immunity threshold. Calculations were performed using the Excel facility (Microsoft), allowing a manual fitting of the model parameters. The results have dealt with a large number of countries, but we focus here on the data regarding France. Further pieces of information are also presented, in order to help elucidating some the factors responsible for the complex history of the pandemic dynamics. (submitted dec 14^th 2021)