During the course of a day an individual typically mixes with different groups
of individuals. Epidemic models incorporating population structure with
individuals being able to infect different groups of individuals have received
extensive attention in the literature. However, almost exclusively the models
assume that individuals are able to simultaneously infect members of all groups,
whereas in reality individuals will typically only be able to infect members of
any group they currently reside in. In the current work we develop a model
where individuals move between a community and their household during the
course of the day, only infecting within their current group. By defining a novel
branching process approximation with an explicit expression for the probability
generating function of the offspring distribution, we are able to derive the
probability of a major epidemic outbreak.