  Models with several levels of mixing (households, workplaces), as well as
various corresponding formulations for R0, have been proposed in the
literature. However, little attention has been paid to the impact of the
distribution of the population size within social structures, effect that can
help plan effective interventions. We focus on the influence on the model
outcomes of teleworking strategies, consisting in reshaping the distribution of
workplace sizes. We consider a stochastic SIR model with two levels of mixing,
accounting for a uniformly mixing general population, each individual belonging
also to a household and a workplace. The variance of the workplace size
distribution appears to be a good proxy for the impact of this distribution on
key outcomes of the epidemic, such as epidemic size and peak. In particular,
our findings suggest that strategies where the proportion of individuals
teleworking depends sublinearly on the size of the workplace outperform the
strategy with linear dependence. Besides, one drawback of the model with
multiple levels of mixing is its complexity, raising interest in a reduced
model. We propose a homogeneously mixing SIR ODE-based model, whose infection
rate is chosen as to observe the growth rate of the initial model. This reduced
model yields a generally satisfying approximation of the epidemic. These
results, robust to various changes in model structure, are very promising from
the perspective of implementing effective strategies based on social distancing
of specific contacts. Furthermore, they contribute to the effort of building
relevant approximations of individual based models at intermediate scales.
