Background and Objective: The COVID19 pandemic associates a continuous diffusion at low intensity, with a majority of patients with poor clinical signs, and rapid accelerations with the combination of super spreading patients and situations, with high rates of severe cases. The nature and intensity of social relationships play a central role to predict its evolution. To better take into account the role of these relationships, we built a model based on percolation theory, and showed that it was a good predictor of the incidence of hospitalization. In this work, we compare our model, called PERCOVID, to the SEIR (Suspected, Exposed, Infected, Recovered) model considered as the reference for modeling epidemics. Methods: Time study was divided in five periods which played a major role in the propagation of the pandemic in France: initial underground propagation (December 2019 / January 2020), first wave and first lockdown (February / March 2020), first summer after lockdown (June / August 2020), spread of alpha variant (March / May 2021), decline of vaccine efficiency (October / November 2021). For each period, we shall compare the results of the PERCOVID and SEIR models for the same epidemiological and sociological parameters, emphasizing the role of local spread of the epidemic as compared to long-range contamination. Results: In the periods of underground propagation and acceleration of the virus or its variants, SEIR type predictions largely overestimate the incidence rate as compared to predictions from PERCOVID. Both models perform similarly in the period of epidemic slowdowns, particularly when the mobility of the population is important. Conclusions: PERCOVID is a powerful tool in order to disentangle the intrinsic properties of the virus, like its infectiousness, from the nature of social relationships in the population under study and from the influence of any regulation issued by national authorities.