We develop a site-bond percolation model, called PERCOVID, in order to describe the time evolution of COVID epidemics and more generally all epidemics propagating through respiratory tract in human populations. This model is based on a network of social relationships representing interconnected households experiencing governmental non-pharmaceutical interventions. The model successfully accounts for the COVID-19 epidemiological data in metropolitan France from December 2019 up to July 2021. Our model shows the impact of lockdowns and curfews, as well as the influence of the progressive vaccination campaign in order to keep COVID-19 pandemic under the percolation threshold. We illustrate the role played by the social interactions by comparing a typical scenario for the epidemic evolution in France, Germany and Italy during the first wave from January to May 2020. We investigate finally the role played by the alpha and delta variants in the evolution of the epidemic in France till autumn 2021, paying particular attention to the essential role played by the vaccination. Our model predicts that the rise of the epidemic observed in July 2021 will not result in a fourth major epidemic wave in France.
PERCOVID: A Model to Describe COVID Percolation on a Network of Social Relationships