  National stay-at-home orders, or lockdowns, were imposed in several countries
to drastically reduce the social interactions mainly responsible for the
transmission of the SARS-CoV-2 virus. Despite being essential to slow down the
COVID-19 pandemic, these containment measures are associated with an economic
burden. In this work, we propose a network approach to model the implementation
of a partial lockdown, breaking the society into disconnected components, or
partitions. Our model is composed by two main ingredients: a multiplex network
representing human contacts within different contexts, formed by a Household
layer, a Work layer, and a third Social layer including generic social
interactions, and a Susceptible-Infected-Recovered process that mimics the
epidemic spreading. We compare different partition strategies, with a twofold
aim: reducing the epidemic outbreak and minimizing the economic cost associated
to the partial lockdown. We also show that the inclusion of unconstrained
social interactions dramatically increases the epidemic spreading, while
different kinds of restrictions on social interactions help in keeping the
benefices of the network partition.
