  We study a multilayer SIR model with two levels of mixing, namely a global
level which is uniformly mixing, and a local level with two layers
distinguishing household and workplace contacts, respectively. We establish the
large population convergence of the corresponding stochastic process. For this
purpose, we use an individual-based model whose state space explicitly takes
into account the duration of infectious periods. This allows to deal with the
natural correlation of the epidemic states of individuals whose household and
workplace share a common infected. In a general setting where a non-exponential
distribution of infectious periods may be considered, convergence to the unique
deterministic solution of a measurevalued equation is obtained. In the
particular case of exponentially distributed infectious periods, we show that
it is possible to further reduce the obtained deterministic limit, leading to a
closed, finite dimensional dynamical system capturing the epidemic dynamics.
This model reduction subsequently is studied from a numerical point of view. We
illustrate that the dynamical system derived from the large population
approximation is a pertinent model reduction when compared to simulations of
the stochastic process or to an alternative edgebased compartmental model, both
in terms of accuracy and computational cost.
