What the COVID-19 pandemic teaches us about modelling epidemics: Percolation versus SEIR

From the study of four typical periods of the SARS-CoV-2 virus propagation in France in 2019, 2020 and 2021, we investigate the role played by the local spread of the epidemic as compared to a long-range propagation. While the local spread of the epidemic is driven by the social relationships in the population under consideration, the long-range propagation does not involve any close connection - either geographical or sociological - between individuals. This comparison is done using the PERCOVID model based on percolation theory as compared to the SEIR model based on the global evolution of the number of persons in various compartments. This study is a first step in using PERCOVID as a new tool in public health for the early detection of respiratory track epidemics in countries with very different social behaviors.