Abstract
We develop a site-bond percolation model, called PERCOVID, in order to describe the time evolution of all epidemics propagating through respiratory tract or by skin contacts in human populations. This model is based on a network of social relationships representing interconnected households experiencing governmental non-pharmaceutical interventions. As a very first testing ground, we apply our model to the understanding of the dynamics of the COVID-19 pandemic in France from December 2019 up to December 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 social interactions by comparing two typical scenarios with low or high strengths of social relationships as compared to France during the first wave in March 2020. We investigate finally the role played by the α and δ 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 and August 2021 would not result in a new major epidemic wave in France.
Highlights
We develop a site-bond percolation model, called PERCOVID, in order to describe the time evolution of all epidemics propagating through respiratory tract or by skin contacts in human populations
The modelisation of epidemics propagating through respiratory tract or by skin contacts in human populations relies on two observations: they propagate through the formation of clusters of increasing size and this propagation is mainly governed by the density and the intensity of the social relationships in the population under study
We describe in this study the general properties of the PERCOVID percolation model, detail its construction and show how the virus propagation displays a sharp transition between a percolation and non-percolation regime depending on the density and intensity of social relationships
Summary
We develop a site-bond percolation model, called PERCOVID, in order to describe the time evolution of all epidemics propagating through respiratory tract or by skin contacts in human populations. Note that the conditions to reach the herd immunity do not depend only on the epidemiological parameters like the infectiousness of the virus or the contamination duration of an infected person, and on the social behavior of the population through the value of the density and intensity of their social relationships.
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