We present several methods that have been obtained in our modeling effort for the SARS-CoV-2 epidemic. Since the early beginning of the epidemic, several parameter identification methods have been proposed to fit mathematical model to the cumulative cases data which have been made available to the public. We will focus on deterministic methods which allow to match the pattern described by the data with simple but meaningful differential equation models, as for instance the SIR model or the SIUR model which adds covert cases into the equation. We consider several methods, starting with an exponential fit of the early cumulative data of SARS-CoV2, which provides a way to compute relevant parameters at the early stages of the epidemic. In this method, the exponential function is used as a phenomenological model for the epidemic and provides a quantitative description of the qualitative behaviour of the cumulative cases curve. We also consider an extended phenomenological model, namely the Bernoulli-Verhulst model, which completely describes the behaviour of a one-wave epidemic. Finally, we will present a global method to reconstruct a consistent epidemiological model with successive waves from the data.

Quentin Griette received his PhD at the University of Montpellier in 2017 after completing his graduate studies at the École Normale Supérieure de Lyon. Between 2017 and 2018 he was awarded a JSPS postdoctoral fellowship to conduct research in Japan, between the University of Tokyo and Meiji University. Since 2018 he is an Associate Professor at the Department of Mathematics of the University of Bordeaux. His research focuses on the study of mathematical models in biology, with a particular interest in epidemiological models. Since mid-2020, he has been involved in several studies on the COVID-19 epidemic. Link: https://www.quentin.griette.fr/index.php?content=publications

Relevant publications:

Q.G. and Pierre Magal, Clarifying predictions for COVID-19 from testing data: The example of New York State. Infectious Disease Modelling 6, 2021, pp. 273-283. https://doi.org/10.1016/j.idm.2020.12.011

Q.G., Jacques Demongeot and Pierre Magal, A robust phenomenological approach to investigate COVID-19 data for France, submitted. https://www.medrxiv.org/content/10.1101/2021.02.10.21251500v1.full.pdf

Jacques Demongeot, Q.G. and Pierre Magal, SI epidemic model applied to COVID-19 data in mainland China. Royal Society Open Science 7, 2020, e-print 201878. https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.201878

Q.G., Pierre Magal and Ousmane Seydi. Unreported cases for Age Dependent COVID-19 Outbreak in Japan. Biology 9 (6), 2020, e-print 132. https://doi.org/10.3390/biology9060132